pyangle-0.90/0000755000175000001440000000000010135235533012653 5ustar akusers00000000000000pyangle-0.90/pyangle/0000755000175000001440000000000010135235533014312 5ustar akusers00000000000000pyangle-0.90/pyangle/__init__.py0000644000175000001440000001251510135233704016425 0ustar akusers00000000000000import pyangle.internals as internals class tTriangulationParameters(internals.tTriangulationParameters): def _constituents(self): return [ ("Points", self.Points), ("PointAttributes", self.PointAttributes), ("PointMarkers", self.PointMarkers), ("Triangles", self.Triangles), ("TriangleAttributes", self.TriangleAttributes), ("TriangleAreas", self.TriangleAreas), ("Neighbors", self.Neighbors), ("Segments", self.Segments), ("SegmentMarkers", self.SegmentMarkers), ("Holes", self.Holes), ("Regions", self.Regions), ("Edges", self.Edges), ("EdgeMarkers", self.EdgeMarkers), ("Normals", self.Normals)] def __getstate__(self): def dumpArray(array): try: return [ [array.getSub(i,j) for j in range(array.unit())] for i in range(array.size())] except RuntimeError: # not allocated return None return self.NumberOfPointAttributes, \ self.NumberOfTriangleAttributes, \ [(name, dumpArray(arr)) for name, arr in self._constituents()] def __setstate__(self, (p_attr_count, t_attr_count, state)): self.NumberOfPointAttributes = p_attr_count self.NumberOfTriangleAttributes = t_attr_count for name, array in state: matching_constituents = filter( lambda (constit_name, constit_array): name == constit_name, self._constituents()) if len(matching_constituents) != 1: raise RuntimeError, "Unknown constituent during unpickling" dest_name, dest_array = matching_constituents[0] if array is None: dest_array.deallocate() else: if dest_array.size() != len(array): dest_array.setSize(len(array)) for i,tup in zip(range(len(array)), array): for j,v in zip(range(len(tup)), tup): dest_array.setSub(i, j, v) def triangulate(input_p, verbose = False, refinement_func = None): opts = "pzqj" if verbose: opts += "VV" else: opts += "Q" if refinement_func is not None: opts += "u" output_p = tTriangulationParameters() internals.triangulate(opts, input_p, output_p, tTriangulationParameters(), refinement_func) return output_p def refine(input_p, verbose = False, refinement_func = None): opts = "razj" if input_p.Segments.size() != 0: opts += "p" if verbose: opts += "VV" else: opts += "Q" if refinement_func is not None: opts += "u" output_p = tTriangulationParameters() internals.triangulate(opts, input_p, output_p, tTriangulationParameters(), refinement_func) return output_p def setPoints(input_p, points, point_markers = None): pointcount = len(points) input_p.Points.setSize(pointcount) for i, pt in zip(range(pointcount),points): input_p.Points.setSub(i, 0, pt[0]) input_p.Points.setSub(i, 1, pt[1]) if point_markers is not None: assert len(point_markers) == pointcount for i, mark in zip(range(pointcount), point_markers): input_p.PointMarkers.set(i, mark) def setSegments(input_p, segments, segment_markers = None): input_p.Segments.setSize(len(segments)) for i, seg in zip(range(len(segments)), segments): input_p.Segments.setSub(i, 0, seg[0]) input_p.Segments.setSub(i, 1, seg[1]) if segment_markers is not None: assert len(segment_markers) == len(segments) for i, mark in zip(range(len(segment_markers)), segment_markers): input_p.SegmentMarkers.set(i, mark) def setHoles(input_p, hole_starts): holecount = len(hole_starts) input_p.Holes.setSize(len(hole_starts)) for i in range(0, holecount): input_p.Holes.setSub(i, 0, hole_starts[i][0]) input_p.Holes.setSub(i, 1, hole_starts[i][1]) def dumpParameters(par): def dumpArray(name, array): subs = array.unit() print "array %s: %d elements, %d values per element" % (name, array.size(), subs) if array.size() == 0 or array.unit() == 0: return try: array.get(0) except RuntimeError: print " not allocated" return for i in range(array.size()): print " %d:" % i, for j in range(subs): print array.getSub(i,j), print for name, arr in par._constituents(): dumpArray(name, arr) def writeGnuplotMesh(gnuplot_file, out_p): gp_file = file(gnuplot_file, "w") pts = out_p.Points tris = out_p.Triangles for tri in range(out_p.Triangles.size()): for pt in range(0, 3): gp_file.write("%f %f 0\n" % ( pts.getSub(tris.getSub(tri, pt), 0), pts.getSub(tris.getSub(tri, pt), 1))) gp_file.write("%f %f 0\n\n" % ( pts.getSub(tris.getSub(tri, 0), 0), pts.getSub(tris.getSub(tri, 0), 1))) pyangle-0.90/src/0000755000175000001440000000000010135235533013442 5ustar akusers00000000000000pyangle-0.90/src/pyangle.cpp0000644000175000001440000002746610135233704015622 0ustar akusers00000000000000#include "triangle.h" #include #include #include #include using namespace boost::python; using namespace std; class tSizeChangeNotifier; class tSizeChangeNotificationReceiver { public: virtual ~tSizeChangeNotificationReceiver() { } virtual void notifySizeChange(tSizeChangeNotifier *master, unsigned size) = 0; }; class tSizeChangeNotifier { typedef vector tNotificationReceiverList; tNotificationReceiverList NotificationReceivers; public: virtual ~tSizeChangeNotifier() { } virtual unsigned size() const = 0; virtual void setSize(unsigned size) { tNotificationReceiverList::iterator first = NotificationReceivers.begin(), last = NotificationReceivers.end(); while (first != last) (*first++)->notifySizeChange(this, size); } void registerForNotification(tSizeChangeNotificationReceiver *rec) { NotificationReceivers.push_back(rec); } void unregisterForNotification(tSizeChangeNotificationReceiver *rec) { tNotificationReceiverList::iterator first = NotificationReceivers.begin(), last = NotificationReceivers.end(); while (first != last) { if (rec == *first) { NotificationReceivers.erase(first); return; } first++; } } }; class tVertex : public boost::noncopyable { public: REAL *Data; public: tVertex(REAL *data) : Data(data) { } REAL x() { return Data[ 0 ]; } REAL y() { return Data[ 1 ]; } }; template class tForeignArray : public tSizeChangeNotifier, public tSizeChangeNotificationReceiver, public boost::noncopyable { ElementT *&Contents; int &NumberOf; unsigned Unit; tSizeChangeNotifier *SlaveTo; string Name; public: tForeignArray(const string &name, ElementT *&cts, int &number_of, unsigned unit = 1, tSizeChangeNotifier *slave_to = NULL) : Contents(cts), NumberOf(number_of), Unit(unit), SlaveTo(slave_to), Name(name) { Contents = NULL; if (SlaveTo) { SlaveTo->registerForNotification(this); setSizeInternal(SlaveTo->size()); } else setSize(0); } ~tForeignArray() { if (SlaveTo) SlaveTo->unregisterForNotification(this); if (Contents) free(Contents); Contents = NULL; if (!SlaveTo) NumberOf = 0; } unsigned size() const { return NumberOf; } unsigned unit() const { return Unit; } void deallocate() { if (Contents != NULL) free(Contents); Contents = NULL; } void setSize(unsigned size) { if (SlaveTo) throw runtime_error("sizes of slave arrays cannot be changed"); else setSizeInternal(size); } void setup() { if (!SlaveTo) throw runtime_error("cannot setup non-slave array"); else setSizeInternal(NumberOf); } void notifySizeChange(tSizeChangeNotifier *master, unsigned size) { setSizeInternal(size); } void setSizeInternal(unsigned size) { if (!SlaveTo) NumberOf = size; if (Contents != NULL) free(Contents); if (size == 0 || Unit == 0) Contents = NULL; else { Contents = (ElementT *) malloc(sizeof(ElementT) * Unit * size); if (Contents == NULL) throw bad_alloc(); } tSizeChangeNotifier::setSize(size); } void setUnit(unsigned unit) { if (unit != Unit) { Unit = unit; setSizeInternal(NumberOf); } } void set(unsigned index, ElementT value) { if (index >= NumberOf * Unit) throw runtime_error("index out of bounds"); if (Contents == NULL) throw runtime_error("Array unallocated"); Contents[ index ] = value; } void setSub(unsigned index, unsigned sub_index, ElementT value) { set(index * Unit + sub_index, value); } ElementT get(unsigned index) { if (index >= NumberOf * Unit) throw runtime_error("index out of bounds"); if (Contents == NULL) throw runtime_error("Array unallocated"); return Contents[ index ]; } ElementT getSub(unsigned index, unsigned sub_index) { return get(index * Unit + sub_index); } tForeignArray &operator=(tForeignArray const &src) { if (SlaveTo) assert(src.size() == SlaveTo->size()); else setSize(src.size()); setUnit(src.Unit); if (src.Contents) memcpy(Contents, src.Contents, sizeof(ElementT) * Unit * src.size()); else { free(Contents); Contents = NULL; } return *this; } }; struct tTriangulationParameters : public triangulateio, public boost::noncopyable { public: tForeignArray Points; // in/out tForeignArray PointAttributes; // in/out tForeignArray PointMarkers; // in/out tForeignArray Triangles; // in/out tForeignArray TriangleAttributes; // in/out tForeignArray TriangleAreas; // in only tForeignArray Neighbors; // out only tForeignArray Segments; // in/out tForeignArray SegmentMarkers; // in/out tForeignArray Holes; // in only tForeignArray Regions; // in only tForeignArray Edges; // out only tForeignArray EdgeMarkers; // out only tForeignArray Normals; // out only public: tTriangulationParameters() : Points("Points", pointlist, numberofpoints, 2), PointAttributes("PointAttributes", pointattributelist, numberofpoints, 0, &Points), PointMarkers("PointMarkers", pointmarkerlist, numberofpoints, 1, &Points), Triangles("Triangles", trianglelist, numberoftriangles, 3), TriangleAttributes("TriangleAttributes", triangleattributelist, numberoftriangles, 0, &Triangles), TriangleAreas("TriangleAreas", trianglearealist, numberoftriangles, 1, &Triangles), Neighbors("Neighbors", neighborlist, numberoftriangles, 3, &Triangles), Segments("Segments", segmentlist, numberofsegments, 2), SegmentMarkers("SegmentMarkers", segmentmarkerlist, numberofsegments, 1, &Segments), Holes("Holes", holelist, numberofholes, 2), Regions("Regions", regionlist, numberofregions, 4), Edges("Edges", edgelist, numberofedges, 2), EdgeMarkers("EdgeMarkers", edgemarkerlist, numberofedges, 1, &Edges), Normals("Normals", normlist, numberofedges, 2, &Edges) { numberofpointattributes = 0; numberofcorners = 3; numberoftriangleattributes = 0; } unsigned numberOfPointAttributes() const { return numberofpointattributes; } unsigned numberOfTriangleAttributes() const { return numberoftriangleattributes; } void setNumberOfPointAttributes(unsigned attrs) { PointAttributes.setUnit(attrs); numberofpointattributes = attrs; } void setNumberOfTriangleAttributes(unsigned attrs) { TriangleAttributes.setUnit(attrs); numberoftriangleattributes = attrs; } tTriangulationParameters &operator=(const tTriangulationParameters &src) { numberofpointattributes = src.numberofpointattributes ; numberofcorners = src.numberofcorners; numberoftriangleattributes = src.numberoftriangleattributes; Points = src.Points; PointAttributes = src.PointAttributes; PointMarkers = src.PointMarkers; Triangles = src.Triangles; TriangleAttributes = src.TriangleAttributes; TriangleAreas = src.TriangleAreas; Neighbors = src.Neighbors; Segments = src.Segments; SegmentMarkers = src.SegmentMarkers; Holes = src.Holes; Regions = src.Regions; Edges = src.Edges; EdgeMarkers = src.EdgeMarkers; Normals = src.Normals; return *this; } }; tTriangulationParameters *copyTriangulationParameters(const tTriangulationParameters &src) { auto_ptr copy(new tTriangulationParameters); *copy = src; return copy.release(); } object RefinementFunction; int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area) { // return 1 if triangle is too large, 0 otherwise try { tVertex org(triorg); tVertex dest(tridest); tVertex apex(triapex); return extract(RefinementFunction( boost::ref(org), boost::ref(dest), boost::ref(apex), area)); } catch (exception &ex) { cerr << "*** Oops. Your Python refinement function raised an exception." << endl << "*** " << ex.what() << endl << "*** Sorry, we can't continue." << endl; abort(); } catch (...) { cerr << "*** Oops. Your Python refinement function raised an exception." << endl << "*** Sorry, we can't continue." << endl; abort(); } } void triangulateWrapper(char *options, tTriangulationParameters &in, tTriangulationParameters &out, tTriangulationParameters &voronoi, object refinement_func) { RefinementFunction = refinement_func; triangulate(options, &in, &out, &voronoi); RefinementFunction = object(); // i.e. None out.holelist = NULL; out.numberofholes = 0; out.regionlist = NULL; out.numberofregions = 0; } BOOST_PYTHON_MODULE(internals) { def("triangulate", triangulateWrapper); class_ ("tTriangulationParameters", init<>()) .def_readonly("Points", &tTriangulationParameters::Points) .def_readonly("PointAttributes", &tTriangulationParameters::PointAttributes) .def_readonly("PointMarkers", &tTriangulationParameters::PointMarkers) .def_readonly("Triangles", &tTriangulationParameters::Triangles) .def_readonly("TriangleAttributes", &tTriangulationParameters::TriangleAttributes) .def_readonly("TriangleAreas", &tTriangulationParameters::TriangleAreas) .def_readonly("Neighbors", &tTriangulationParameters::Neighbors) .def_readonly("Segments", &tTriangulationParameters::Segments) .def_readonly("SegmentMarkers", &tTriangulationParameters::SegmentMarkers) .def_readonly("Holes", &tTriangulationParameters::Holes) .def_readonly("Regions", &tTriangulationParameters::Regions) .def_readonly("Edges", &tTriangulationParameters::Edges) .def_readonly("EdgeMarkers", &tTriangulationParameters::EdgeMarkers) .def_readonly("Normals", &tTriangulationParameters::Normals) .add_property("NumberOfPointAttributes", &tTriangulationParameters::numberOfPointAttributes, &tTriangulationParameters::setNumberOfPointAttributes) .add_property("NumberOfTriangleAttributes", &tTriangulationParameters::numberOfTriangleAttributes, &tTriangulationParameters::setNumberOfTriangleAttributes) .def("copy", ©TriangulationParameters, return_value_policy()) .enable_pickling(true) ; class_, boost::noncopyable> ("tRealArray", no_init) .def("size", &tForeignArray::size) .def("setSize", &tForeignArray::setSize) .def("setup", &tForeignArray::setup) .def("unit", &tForeignArray::unit) .def("set", &tForeignArray::set) .def("setSub", &tForeignArray::setSub) .def("get", &tForeignArray::get) .def("getSub", &tForeignArray::getSub) .def("deallocate", &tForeignArray::deallocate) ; class_, boost::noncopyable> ("tIntArray", no_init) .def("size", &tForeignArray::size) .def("setSize", &tForeignArray::setSize) .def("setup", &tForeignArray::setup) .def("unit", &tForeignArray::unit) .def("set", &tForeignArray::set) .def("setSub", &tForeignArray::setSub) .def("get", &tForeignArray::get) .def("getSub", &tForeignArray::getSub) .def("deallocate", &tForeignArray::deallocate) ; class_, tVertex, boost::noncopyable>("tVertex", no_init) .def("x", &tVertex::x) .def("y", &tVertex::y) ; } pyangle-0.90/src/triangle.c0000644000175000001440000236454710135233704015436 0ustar akusers00000000000000/*****************************************************************************/ /* */ /* 888888888 ,o, / 888 */ /* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ /* 888 888 888 88b 888 888 888 888 888 d888 88b */ /* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ /* 888 888 888 C888 888 888 888 / 888 q888 */ /* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ /* "8oo8D */ /* */ /* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ /* (triangle.c) */ /* */ /* Version 1.4 */ /* November 1, 2002 */ /* */ /* Copyright 1993, 1995, 1997, 1998, 2002 */ /* Jonathan Richard Shewchuk */ /* 2360 Woolsey #H */ /* Berkeley, California 94705-1927 */ /* jrs@cs.berkeley.edu */ /* */ /* This program may be freely redistributed under the condition that the */ /* copyright notices (including this entire header and the copyright */ /* notice printed when the `-h' switch is selected) are not removed, and */ /* no compensation is received. Private, research, and institutional */ /* use is free. You may distribute modified versions of this code UNDER */ /* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ /* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ /* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ /* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ /* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ /* WITH THE AUTHOR. (If you are not directly supplying this code to a */ /* customer, and you are instead telling them how they can obtain it for */ /* free, then you are not required to make any arrangement with me.) */ /* */ /* Hypertext instructions for Triangle are available on the Web at */ /* */ /* http://www.cs.cmu.edu/~quake/triangle.html */ /* */ /* Some of the references listed below are marked with an asterisk. [*] */ /* These references are available for downloading from the Web page */ /* */ /* http://www.cs.cmu.edu/~quake/triangle.research.html */ /* */ /* Three papers discussing aspects of Triangle are available. A short */ /* overview appears in "Triangle: Engineering a 2D Quality Mesh */ /* Generator and Delaunay Triangulator," in Applied Computational */ /* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */ /* Manocha, editors, Lecture Notes in Computer Science volume 1148, */ /* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */ /* Workshop on Applied Computational Geometry). [*] */ /* */ /* The algorithms are discussed in the greatest detail in "Delaunay */ /* Refinement Algorithms for Triangular Mesh Generation," Computational */ /* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */ /* */ /* More detail about the data structures may be found in my dissertation: */ /* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */ /* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */ /* Pittsburgh, Pennsylvania, 18 May 1997. [*] */ /* */ /* Triangle was created as part of the Archimedes project in the School of */ /* Computer Science at Carnegie Mellon University. Archimedes is a */ /* system for compiling parallel finite element solvers. For further */ /* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */ /* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */ /* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */ /* Media on Parallel Computers," Computer Methods in Applied Mechanics */ /* and Engineering 152(1-2):85-102, 22 January 1998. */ /* */ /* Triangle's Delaunay refinement algorithm for quality mesh generation is */ /* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */ /* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */ /* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */ /* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */ /* Annual Symposium on Computational Geometry (San Diego, California), */ /* pages 274-280, Association for Computing Machinery, May 1993. */ /* */ /* The Delaunay refinement algorithm has been modified so that it */ /* consistently meshes domains with small input angles, as described in */ /* my lengthy journal article listed above, or in abbreviated form in */ /* Jonathan Richard Shewchuk, "Mesh Generation for Domains with Small */ /* Angles," Proceedings of the Sixteenth Annual Symposium on */ /* Computational Geometry (Hong Kong), pages 1-10, Association for */ /* Computing Machinery, June 2000. [*] */ /* */ /* My implementation of the divide-and-conquer and incremental Delaunay */ /* triangulation algorithms follows closely the presentation of Guibas */ /* and Stolfi, even though I use a triangle-based data structure instead */ /* of their quad-edge data structure. (In fact, I originally implemented */ /* Triangle using the quad-edge data structure, but the switch to a */ /* triangle-based data structure sped Triangle by a factor of two.) The */ /* mesh manipulation primitives and the two aforementioned Delaunay */ /* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ /* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ /* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ /* 4(2):74-123, April 1985. */ /* */ /* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */ /* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */ /* Delaunay Triangulation," International Journal of Computer and */ /* Information Science 9(3):219-242, 1980. Triangle's improvement of the */ /* divide-and-conquer algorithm by alternating between vertical and */ /* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */ /* Conquer Algorithm for Constructing Delaunay Triangulations," */ /* Algorithmica 2(2):137-151, 1987. */ /* */ /* The incremental insertion algorithm was first proposed by C. L. Lawson, */ /* "Software for C1 Surface Interpolation," in Mathematical Software III, */ /* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */ /* For point location, I use the algorithm of Ernst P. Mucke, Isaac */ /* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */ /* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */ /* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */ /* ACM, May 1996. [*] If I were to randomize the order of vertex */ /* insertion (I currently don't bother), their result combined with the */ /* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */ /* Random Sampling in Computational Geometry II," Discrete & */ /* Computational Geometry 4(1):387-421, 1989, would yield an expected */ /* O(n^{4/3}) bound on running time. */ /* */ /* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */ /* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */ /* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */ /* boundary of the triangulation are maintained in a splay tree for the */ /* purpose of point location. Splay trees are described by Daniel */ /* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */ /* Trees," Journal of the ACM 32(3):652-686, July 1985. */ /* */ /* The algorithms for exact computation of the signs of determinants are */ /* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */ /* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */ /* Computational Geometry 18(3):305-363, October 1997. (Also available */ /* as Technical Report CMU-CS-96-140, School of Computer Science, */ /* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */ /* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */ /* Adaptive Floating-Point Geometric Predicates," Proceedings of the */ /* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */ /* Many of the ideas for my exact arithmetic routines originate with */ /* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */ /* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */ /* Computer Society Press, 1991. [*] Many of the ideas for the correct */ /* evaluation of the signs of determinants are taken from Steven Fortune */ /* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */ /* tional Geometry," Proceedings of the Ninth Annual Symposium on */ /* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */ /* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */ /* lations," International Journal of Computational Geometry & Applica- */ /* tions 5(1-2):193-213, March-June 1995. */ /* */ /* For definitions of and results involving Delaunay triangulations, */ /* constrained and conforming versions thereof, and other aspects of */ /* triangular mesh generation, see the excellent survey by Marshall Bern */ /* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */ /* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */ /* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */ /* */ /* The time for incrementally adding PSLG (planar straight line graph) */ /* segments to create a constrained Delaunay triangulation is probably */ /* O(t^2) per segment in the worst case and O(t) per segment in the */ /* common case, where t is the number of triangles that intersect the */ /* segment before it is inserted. This doesn't count point location, */ /* which can be much more expensive. I could improve this to O(d log d) */ /* time, but d is usually quite small, so it's not worth the bother. */ /* (This note does not apply to conforming Delaunay triangulations, for */ /* which a different method is used to insert segments.) */ /* */ /* The time for adding segments to a conforming Delaunay triangulation is */ /* not clear, but does not depend upon t alone. In some cases, very */ /* small features (like a vertex lying next to a segment) can cause a */ /* single segment to be split an arbitrary number of times. Of course, */ /* floating-point precision is a practical barrier to how much this can */ /* happen. */ /* */ /* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */ /* in the worst case and O(d) in the common case, where d is the degree */ /* of the vertex being deleted. I could improve this to O(d log d) time, */ /* but d is usually quite small, so it's not worth the bother. */ /* */ /* Ruppert's Delaunay refinement algorithm typically generates triangles */ /* at a linear rate (constant time per triangle) after the initial */ /* triangulation is formed. There may be pathological cases where */ /* quadratic time is required, but these never arise in practice. */ /* */ /* The geometric predicates (circumcenter calculations, segment */ /* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */ /* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh.html . */ /* */ /* If you make any improvements to this code, please please please let me */ /* know, so that I may obtain the improvements. Even if you don't change */ /* the code, I'd still love to hear what it's being used for. */ /* */ /* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ /* whatsoever. This code is provided "as-is". Use at your own risk. */ /* */ /*****************************************************************************/ /* For single precision (which will save some memory and reduce paging), */ /* define the symbol SINGLE by using the -DSINGLE compiler switch or by */ /* writing "#define SINGLE" below. */ /* */ /* For double precision (which will allow you to refine meshes to a smaller */ /* edge length), leave SINGLE undefined. */ /* */ /* Double precision uses more memory, but improves the resolution of the */ /* meshes you can generate with Triangle. It also reduces the likelihood */ /* of a floating exception due to overflow. Finally, it is much faster */ /* than single precision on 64-bit architectures like the DEC Alpha. I */ /* recommend double precision unless you want to generate a mesh for which */ /* you do not have enough memory. */ /* #define SINGLE */ #if 0 #ifdef SINGLE #define REAL float #else /* not SINGLE */ #define REAL double #endif /* not SINGLE */ #endif /* If yours is not a Unix system, define the NO_TIMER compiler switch to */ /* remove the Unix-specific timing code. */ /* #define NO_TIMER */ /* To insert lots of self-checks for internal errors, define the SELF_CHECK */ /* symbol. This will slow down the program significantly. It is best to */ /* define the symbol using the -DSELF_CHECK compiler switch, but you could */ /* write "#define SELF_CHECK" below. If you are modifying this code, I */ /* recommend you turn self-checks on until your work is debugged. */ /* #define SELF_CHECK */ /* To compile Triangle as a callable object library (triangle.o), define the */ /* TRILIBRARY symbol. Read the file triangle.h for details on how to call */ /* the procedure triangulate() that results. */ /* #define TRILIBRARY */ /* It is possible to generate a smaller version of Triangle using one or */ /* both of the following symbols. Define the REDUCED symbol to eliminate */ /* all features that are primarily of research interest; specifically, the */ /* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */ /* all meshing algorithms above and beyond constrained Delaunay */ /* triangulation; specifically, the -r, -q, -a, -S, and -s switches. */ /* These reductions are most likely to be useful when generating an object */ /* library (triangle.o) by defining the TRILIBRARY symbol. */ /* #define REDUCED */ /* #define CDT_ONLY */ /* On some machines, my exact arithmetic routines might be defeated by the */ /* use of internal extended precision floating-point registers. The best */ /* way to solve this problem is to set the floating-point registers to use */ /* single or double precision internally. On 80x86 processors, this may */ /* be accomplished by setting the CPU86 symbol for the Microsoft C */ /* compiler, or the LINUX symbol for the gcc compiler running on Linux. */ /* */ /* An inferior solution is to declare certain values as `volatile', thus */ /* forcing them to be stored to memory and rounded off. Unfortunately, */ /* this solution might slow Triangle down quite a bit. To use volatile */ /* values, write "#define INEXACT volatile" below. Normally, however, */ /* INEXACT should be defined to be nothing. ("#define INEXACT".) */ /* */ /* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */ /* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */ /* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */ /* available as Section 6.6 of my dissertation). */ /* #define CPU86 */ /* #define LINUX */ #define INEXACT /* Nothing */ /* #define INEXACT volatile */ /* Maximum number of characters in a file name (including the null). */ #define FILENAMESIZE 512 /* Maximum number of characters in a line read from a file (including the */ /* null). */ #define INPUTLINESIZE 512 /* For efficiency, a variety of data structures are allocated in bulk. The */ /* following constants determine how many of each structure is allocated */ /* at once. */ #define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */ #define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */ #define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */ #define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */ /* Number of encroached subsegments allocated at once. */ #define BADSUBSEGPERBLOCK 252 /* Number of skinny triangles allocated at once. */ #define BADTRIPERBLOCK 4092 /* Number of flipped triangles allocated at once. */ #define FLIPSTACKERPERBLOCK 252 /* Number of splay tree nodes allocated at once. */ #define SPLAYNODEPERBLOCK 508 /* The vertex types. A DEADVERTEX has been deleted entirely. An */ /* UNDEADVERTEX is not part of the mesh, but is written to the output */ /* .node file and affects the node indexing in the other output files. */ #define INPUTVERTEX 0 #define SEGMENTVERTEX 1 #define FREEVERTEX 2 #define DEADVERTEX -32768 #define UNDEADVERTEX -32767 /* The next line is used to outsmart some very stupid compilers. If your */ /* compiler is smarter, feel free to replace the "int" with "void". */ /* Not that it matters. */ #define VOID void /* Two constants for algorithms based on random sampling. Both constants */ /* have been chosen empirically to optimize their respective algorithms. */ /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */ /* how large a random sample of triangles to inspect. */ #define SAMPLEFACTOR 11 /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */ /* of boundary edges should be maintained in the splay tree for point */ /* location on the front. */ #define SAMPLERATE 10 /* A number that speaks for itself, every kissable digit. */ #define PI 3.141592653589793238462643383279502884197169399375105820974944592308 /* Another fave. */ #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732 /* And here's one for those of you who are intimidated by math. */ #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333 #include #include #include #include #ifndef NO_TIMER #include #endif /* not NO_TIMER */ #ifdef CPU86 #include #endif /* CPU86 */ #ifdef LINUX #include #endif /* LINUX */ #ifdef TRILIBRARY #include "triangle.h" #endif /* TRILIBRARY */ /* A few forward declarations. */ #ifndef TRILIBRARY char *readline(); char *findfield(); #endif /* not TRILIBRARY */ /* Labels that signify whether a record consists primarily of pointers or of */ /* floating-point words. Used to make decisions about data alignment. */ enum wordtype {POINTER, FLOATINGPOINT}; /* Labels that signify the result of point location. The result of a */ /* search indicates that the point falls in the interior of a triangle, on */ /* an edge, on a vertex, or outside the mesh. */ enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE}; /* Labels that signify the result of vertex insertion. The result indicates */ /* that the vertex was inserted with complete success, was inserted but */ /* encroaches upon a subsegment, was not inserted because it lies on a */ /* segment, or was not inserted because another vertex occupies the same */ /* location. */ enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX, DUPLICATEVERTEX}; /* Labels that signify the result of direction finding. The result */ /* indicates that a segment connecting the two query points falls within */ /* the direction triangle, along the left edge of the direction triangle, */ /* or along the right edge of the direction triangle. */ enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR}; /*****************************************************************************/ /* */ /* The basic mesh data structures */ /* */ /* There are three: vertices, triangles, and subsegments (abbreviated */ /* `subseg'). These three data structures, linked by pointers, comprise */ /* the mesh. A vertex simply represents a mesh vertex and its properties. */ /* A triangle is a triangle. A subsegment is a special data structure used */ /* to represent an impenetrable edge of the mesh (perhaps on the outer */ /* boundary, on the boundary of a hole, or part of an internal boundary */ /* separating two triangulated regions). Subsegments represent boundaries, */ /* defined by the user, that triangles may not lie across. */ /* */ /* A triangle consists of a list of three vertices, a list of three */ /* adjoining triangles, a list of three adjoining subsegments (when */ /* segments exist), an arbitrary number of optional user-defined */ /* floating-point attributes, and an optional area constraint. The latter */ /* is an upper bound on the permissible area of each triangle in a region, */ /* used for mesh refinement. */ /* */ /* For a triangle on a boundary of the mesh, some or all of the neighboring */ /* triangles may not be present. For a triangle in the interior of the */ /* mesh, often no neighboring subsegments are present. Such absent */ /* triangles and subsegments are never represented by NULL pointers; they */ /* are represented by two special records: `dummytri', the triangle that */ /* fills "outer space", and `dummysub', the omnipresent subsegment. */ /* `dummytri' and `dummysub' are used for several reasons; for instance, */ /* they can be dereferenced and their contents examined without violating */ /* protected memory. */ /* */ /* However, it is important to understand that a triangle includes other */ /* information as well. The pointers to adjoining vertices, triangles, and */ /* subsegments are ordered in a way that indicates their geometric relation */ /* to each other. Furthermore, each of these pointers contains orientation */ /* information. Each pointer to an adjoining triangle indicates which face */ /* of that triangle is contacted. Similarly, each pointer to an adjoining */ /* subsegment indicates which side of that subsegment is contacted, and how */ /* the subsegment is oriented relative to the triangle. */ /* */ /* The data structure representing a subsegment may be thought to be */ /* abutting the edge of one or two triangle data structures: either */ /* sandwiched between two triangles, or resting against one triangle on an */ /* exterior boundary or hole boundary. */ /* */ /* A subsegment consists of a list of two vertices, a list of two */ /* adjoining subsegments, and a list of two adjoining triangles. One of */ /* the two adjoining triangles may not be present (though there should */ /* always be one), and neighboring subsegments might not be present. */ /* Subsegments also store a user-defined integer "boundary marker". */ /* Typically, this integer is used to indicate what boundary conditions are */ /* to be applied at that location in a finite element simulation. */ /* */ /* Like triangles, subsegments maintain information about the relative */ /* orientation of neighboring objects. */ /* */ /* Vertices are relatively simple. A vertex is a list of floating-point */ /* numbers, starting with the x, and y coordinates, followed by an */ /* arbitrary number of optional user-defined floating-point attributes, */ /* followed by an integer boundary marker. During the segment insertion */ /* phase, there is also a pointer from each vertex to a triangle that may */ /* contain it. Each pointer is not always correct, but when one is, it */ /* speeds up segment insertion. These pointers are assigned values once */ /* at the beginning of the segment insertion phase, and are not used or */ /* updated except during this phase. Edge flipping during segment */ /* insertion will render some of them incorrect. Hence, don't rely upon */ /* them for anything. */ /* */ /* Other than the exception mentioned above, vertices have no information */ /* about what triangles, subfacets, or subsegments they are linked to. */ /* */ /*****************************************************************************/ /*****************************************************************************/ /* */ /* Handles */ /* */ /* The oriented triangle (`otri') and oriented subsegment (`osub') data */ /* structures defined below do not themselves store any part of the mesh. */ /* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */ /* */ /* Oriented triangles and oriented subsegments will usually be referred to */ /* as "handles." A handle is essentially a pointer into the mesh; it */ /* allows you to "hold" one particular part of the mesh. Handles are used */ /* to specify the regions in which one is traversing and modifying the mesh.*/ /* A single `triangle' may be held by many handles, or none at all. (The */ /* latter case is not a memory leak, because the triangle is still */ /* connected to other triangles in the mesh.) */ /* */ /* An `otri' is a handle that holds a triangle. It holds a specific edge */ /* of the triangle. An `osub' is a handle that holds a subsegment. It */ /* holds either the left or right side of the subsegment. */ /* */ /* Navigation about the mesh is accomplished through a set of mesh */ /* manipulation primitives, further below. Many of these primitives take */ /* a handle and produce a new handle that holds the mesh near the first */ /* handle. Other primitives take two handles and glue the corresponding */ /* parts of the mesh together. The orientation of the handles is */ /* important. For instance, when two triangles are glued together by the */ /* bond() primitive, they are glued at the edges on which the handles lie. */ /* */ /* Because vertices have no information about which triangles they are */ /* attached to, I commonly represent a vertex by use of a handle whose */ /* origin is the vertex. A single handle can simultaneously represent a */ /* triangle, an edge, and a vertex. */ /* */ /*****************************************************************************/ /* The triangle data structure. Each triangle contains three pointers to */ /* adjoining triangles, plus three pointers to vertices, plus three */ /* pointers to subsegments (declared below; these pointers are usually */ /* `dummysub'). It may or may not also contain user-defined attributes */ /* and/or a floating-point "area constraint." It may also contain extra */ /* pointers for nodes, when the user asks for high-order elements. */ /* Because the size and structure of a `triangle' is not decided until */ /* runtime, I haven't simply declared the type `triangle' as a struct. */ typedef REAL **triangle; /* Really: typedef triangle *triangle */ /* An oriented triangle: includes a pointer to a triangle and orientation. */ /* The orientation denotes an edge of the triangle. Hence, there are */ /* three possible orientations. By convention, each edge always points */ /* counterclockwise about the corresponding triangle. */ struct otri { triangle *tri; int orient; /* Ranges from 0 to 2. */ }; /* The subsegment data structure. Each subsegment contains two pointers to */ /* adjoining subsegments, plus two pointers to vertices, plus two pointers */ /* to adjoining triangles, plus one boundary marker. */ typedef REAL **subseg; /* Really: typedef subseg *subseg */ /* An oriented subsegment: includes a pointer to a subsegment and an */ /* orientation. The orientation denotes a side of the edge. Hence, there */ /* are two possible orientations. By convention, the edge is always */ /* directed so that the "side" denoted is the right side of the edge. */ struct osub { subseg *ss; int ssorient; /* Ranges from 0 to 1. */ }; /* The vertex data structure. Each vertex is actually an array of REALs. */ /* The number of REALs is unknown until runtime. An integer boundary */ /* marker, and sometimes a pointer to a triangle, is appended after the */ /* REALs. */ /* typedef REAL *vertex; */ /* moved to header file. */ /* A queue used to store encroached subsegments. Each subsegment's vertices */ /* are stored so that we can check whether a subsegment is still the same. */ struct badsubseg { subseg encsubseg; /* An encroached subsegment. */ vertex subsegorg, subsegdest; /* Its two vertices. */ }; /* A queue used to store bad triangles. The key is the square of the cosine */ /* of the smallest angle of the triangle. Each triangle's vertices are */ /* stored so that one can check whether a triangle is still the same. */ struct badtriang { triangle poortri; /* A skinny or too-large triangle. */ REAL key; /* cos^2 of smallest (apical) angle. */ vertex triangorg, triangdest, triangapex; /* Its three vertices. */ struct badtriang *nexttriang; /* Pointer to next bad triangle. */ }; /* A stack of triangles flipped during the most recent vertex insertion. */ /* The stack is used to undo the vertex insertion if the vertex encroaches */ /* upon a subsegment. */ struct flipstacker { triangle flippedtri; /* A recently flipped triangle. */ struct flipstacker *prevflip; /* Previous flip in the stack. */ }; /* A node in a heap used to store events for the sweepline Delaunay */ /* algorithm. Nodes do not point directly to their parents or children in */ /* the heap. Instead, each node knows its position in the heap, and can */ /* look up its parent and children in a separate array. The `eventptr' */ /* points either to a `vertex' or to a triangle (in encoded format, so */ /* that an orientation is included). In the latter case, the origin of */ /* the oriented triangle is the apex of a "circle event" of the sweepline */ /* algorithm. To distinguish site events from circle events, all circle */ /* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */ struct event { REAL xkey, ykey; /* Coordinates of the event. */ VOID *eventptr; /* Can be a vertex or the location of a circle event. */ int heapposition; /* Marks this event's position in the heap. */ }; /* A node in the splay tree. Each node holds an oriented ghost triangle */ /* that represents a boundary edge of the growing triangulation. When a */ /* circle event covers two boundary edges with a triangle, so that they */ /* are no longer boundary edges, those edges are not immediately deleted */ /* from the tree; rather, they are lazily deleted when they are next */ /* encountered. (Since only a random sample of boundary edges are kept */ /* in the tree, lazy deletion is faster.) `keydest' is used to verify */ /* that a triangle is still the same as when it entered the splay tree; if */ /* it has been rotated (due to a circle event), it no longer represents a */ /* boundary edge and should be deleted. */ struct splaynode { struct otri keyedge; /* Lprev of an edge on the front. */ vertex keydest; /* Used to verify that splay node is still live. */ struct splaynode *lchild, *rchild; /* Children in splay tree. */ }; /* A type used to allocate memory. firstblock is the first block of items. */ /* nowblock is the block from which items are currently being allocated. */ /* nextitem points to the next slab of free memory for an item. */ /* deaditemstack is the head of a linked list (stack) of deallocated items */ /* that can be recycled. unallocateditems is the number of items that */ /* remain to be allocated from nowblock. */ /* */ /* Traversal is the process of walking through the entire list of items, and */ /* is separate from allocation. Note that a traversal will visit items on */ /* the "deaditemstack" stack as well as live items. pathblock points to */ /* the block currently being traversed. pathitem points to the next item */ /* to be traversed. pathitemsleft is the number of items that remain to */ /* be traversed in pathblock. */ /* */ /* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */ /* what sort of word the record is primarily made up of. alignbytes */ /* determines how new records should be aligned in memory. itembytes and */ /* itemwords are the length of a record in bytes (after rounding up) and */ /* words. itemsperblock is the number of items allocated at once in a */ /* single block. items is the number of currently allocated items. */ /* maxitems is the maximum number of items that have been allocated at */ /* once; it is the current number of items plus the number of records kept */ /* on deaditemstack. */ struct memorypool { VOID **firstblock, **nowblock; VOID *nextitem; VOID *deaditemstack; VOID **pathblock; VOID *pathitem; enum wordtype itemwordtype; int alignbytes; int itembytes, itemwords; int itemsperblock; long items, maxitems; int unallocateditems; int pathitemsleft; }; /* Global constants. */ REAL splitter; /* Used to split REAL factors for exact multiplication. */ REAL epsilon; /* Floating-point machine epsilon. */ REAL resulterrbound; REAL ccwerrboundA, ccwerrboundB, ccwerrboundC; REAL iccerrboundA, iccerrboundB, iccerrboundC; REAL o3derrboundA, o3derrboundB, o3derrboundC; /* Random number seed is not constant, but I've made it global anyway. */ unsigned long randomseed; /* Current random number seed. */ /* Mesh data structure. Triangle operates on only one mesh, but the mesh */ /* structure is used (instead of global variables) to allow reentrancy. */ struct mesh { /* Variables used to allocate memory for triangles, subsegments, vertices, */ /* viri (triangles being eaten), encroached segments, bad (skinny or too */ /* large) triangles, and splay tree nodes. */ struct memorypool triangles; struct memorypool subsegs; struct memorypool vertices; struct memorypool viri; struct memorypool badsubsegs; struct memorypool badtriangles; struct memorypool flipstackers; struct memorypool splaynodes; /* Variables that maintain the bad triangle queues. The queues are */ /* ordered from 63 (highest priority) to 0 (lowest priority). */ struct badtriang *queuefront[64]; struct badtriang *queuetail[64]; int nextnonemptyq[64]; int firstnonemptyq; /* Variable that maintains the stack of recently flipped triangles. */ struct flipstacker *lastflip; /* Other variables. */ REAL xmin, xmax, ymin, ymax; /* x and y bounds. */ REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ int invertices; /* Number of input vertices. */ int inelements; /* Number of input triangles. */ int insegments; /* Number of input segments. */ int holes; /* Number of input holes. */ int regions; /* Number of input regions. */ int undeads; /* Number of input vertices that don't appear in the mesh. */ long edges; /* Number of output edges. */ int mesh_dim; /* Dimension (ought to be 2). */ int nextras; /* Number of attributes per vertex. */ int eextras; /* Number of attributes per triangle. */ long hullsize; /* Number of edges in convex hull. */ int steinerleft; /* Number of Steiner points not yet used. */ int vertexmarkindex; /* Index to find boundary marker of a vertex. */ int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */ int highorderindex; /* Index to find extra nodes for high-order elements. */ int elemattribindex; /* Index to find attributes of a triangle. */ int areaboundindex; /* Index to find area bound of a triangle. */ int checksegments; /* Are there segments in the triangulation yet? */ int checkquality; /* Has quality triangulation begun yet? */ int readnodefile; /* Has a .node file been read? */ long samples; /* Number of random samples for point location. */ long incirclecount; /* Number of incircle tests performed. */ long counterclockcount; /* Number of counterclockwise tests performed. */ long orient3dcount; /* Number of 3D orientation tests performed. */ long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ long circumcentercount; /* Number of circumcenter calculations performed. */ long circletopcount; /* Number of circle top calculations performed. */ /* Triangular bounding box vertices. */ vertex infvertex1, infvertex2, infvertex3; /* Pointer to the `triangle' that occupies all of "outer space." */ triangle *dummytri; triangle *dummytribase; /* Keep base address so we can free() it later. */ /* Pointer to the omnipresent subsegment. Referenced by any triangle or */ /* subsegment that isn't really connected to a subsegment at that */ /* location. */ subseg *dummysub; subseg *dummysubbase; /* Keep base address so we can free() it later. */ /* Pointer to a recently visited triangle. Improves point location if */ /* proximate vertices are inserted sequentially. */ struct otri recenttri; }; /* End of `struct mesh'. */ /* Data structure for command line switches and file names. This structure */ /* is used (instead of global variables) to allow reentrancy. */ struct behavior { /* Switches for the triangulator. */ /* poly: -p switch. refine: -r switch. */ /* quality: -q switch. */ /* minangle: minimum angle bound, specified after -q switch. */ /* goodangle: cosine squared of minangle. */ /* vararea: -a switch without number. */ /* fixedarea: -a switch with number. */ /* maxarea: maximum area bound, specified after -a switch. */ /* usertest: -u switch. */ /* regionattrib: -A switch. convex: -c switch. */ /* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */ /* firstnumber: inverse of -z switch. All items are numbered starting */ /* from `firstnumber'. */ /* edgesout: -e switch. voronoi: -v switch. */ /* neighbors: -n switch. geomview: -g switch. */ /* nobound: -B switch. nopolywritten: -P switch. */ /* nonodewritten: -N switch. noelewritten: -E switch. */ /* noiterationnum: -I switch. noholes: -O switch. */ /* noexact: -X switch. */ /* order: element order, specified after -o switch. */ /* nobisect: count of how often -Y switch is selected. */ /* steiner: maximum number of Steiner points, specified after -S switch. */ /* incremental: -i switch. sweepline: -F switch. */ /* dwyer: inverse of -l switch. */ /* splitseg: -s switch. */ /* nolenses: -L switch. docheck: -C switch. */ /* quiet: -Q switch. verbose: count of how often -V switch is selected. */ /* usesegments: -p, -r, -q, or -c switch; determines whether segments are */ /* used at all. */ /* */ /* Read the instructions to find out the meaning of these switches. */ int poly, refine, quality, vararea, fixedarea, usertest; int regionattrib, convex, weighted, jettison; int firstnumber; int edgesout, voronoi, neighbors, geomview; int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; int noholes, noexact, nolenses; int incremental, sweepline, dwyer; int splitseg; int docheck; int quiet, verbose; int usesegments; int order; int nobisect; int steiner; REAL minangle, goodangle; REAL maxarea; /* Variables for file names. */ #ifndef TRILIBRARY char innodefilename[FILENAMESIZE]; char inelefilename[FILENAMESIZE]; char inpolyfilename[FILENAMESIZE]; char areafilename[FILENAMESIZE]; char outnodefilename[FILENAMESIZE]; char outelefilename[FILENAMESIZE]; char outpolyfilename[FILENAMESIZE]; char edgefilename[FILENAMESIZE]; char vnodefilename[FILENAMESIZE]; char vedgefilename[FILENAMESIZE]; char neighborfilename[FILENAMESIZE]; char offfilename[FILENAMESIZE]; #endif /* not TRILIBRARY */ }; /* End of `struct behavior'. */ /*****************************************************************************/ /* */ /* Mesh manipulation primitives. Each triangle contains three pointers to */ /* other triangles, with orientations. Each pointer points not to the */ /* first byte of a triangle, but to one of the first three bytes of a */ /* triangle. It is necessary to extract both the triangle itself and the */ /* orientation. To save memory, I keep both pieces of information in one */ /* pointer. To make this possible, I assume that all triangles are aligned */ /* to four-byte boundaries. The decode() routine below decodes a pointer, */ /* extracting an orientation (in the range 0 to 2) and a pointer to the */ /* beginning of a triangle. The encode() routine compresses a pointer to a */ /* triangle and an orientation into a single pointer. My assumptions that */ /* triangles are four-byte-aligned and that the `unsigned long' type is */ /* long enough to hold a pointer are two of the few kludges in this program.*/ /* */ /* Subsegments are manipulated similarly. A pointer to a subsegment */ /* carries both an address and an orientation in the range 0 to 1. */ /* */ /* The other primitives take an oriented triangle or oriented subsegment, */ /* and return an oriented triangle or oriented subsegment or vertex; or */ /* they change the connections in the data structure. */ /* */ /* Below, triangles and subsegments are denoted by their vertices. The */ /* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */ /* c. These vertices occur in counterclockwise order about the triangle. */ /* The handle abc may simultaneously denote vertex a, edge ab, and triangle */ /* abc. */ /* */ /* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */ /* b. If ab is thought to be directed upward (with b directly above a), */ /* then the handle ab is thought to grasp the right side of ab, and may */ /* simultaneously denote vertex a and edge ab. */ /* */ /* An asterisk (*) denotes a vertex whose identity is unknown. */ /* */ /* Given this notation, a partial list of mesh manipulation primitives */ /* follows. */ /* */ /* */ /* For triangles: */ /* */ /* sym: Find the abutting triangle; same edge. */ /* sym(abc) -> ba* */ /* */ /* lnext: Find the next edge (counterclockwise) of a triangle. */ /* lnext(abc) -> bca */ /* */ /* lprev: Find the previous edge (clockwise) of a triangle. */ /* lprev(abc) -> cab */ /* */ /* onext: Find the next edge counterclockwise with the same origin. */ /* onext(abc) -> ac* */ /* */ /* oprev: Find the next edge clockwise with the same origin. */ /* oprev(abc) -> a*b */ /* */ /* dnext: Find the next edge counterclockwise with the same destination. */ /* dnext(abc) -> *ba */ /* */ /* dprev: Find the next edge clockwise with the same destination. */ /* dprev(abc) -> cb* */ /* */ /* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */ /* rnext(abc) -> *a* */ /* */ /* rprev: Find the previous edge (clockwise) of the adjacent triangle. */ /* rprev(abc) -> b** */ /* */ /* org: Origin dest: Destination apex: Apex */ /* org(abc) -> a dest(abc) -> b apex(abc) -> c */ /* */ /* bond: Bond two triangles together at the resepective handles. */ /* bond(abc, bad) */ /* */ /* */ /* For subsegments: */ /* */ /* ssym: Reverse the orientation of a subsegment. */ /* ssym(ab) -> ba */ /* */ /* spivot: Find adjoining subsegment with the same origin. */ /* spivot(ab) -> a* */ /* */ /* snext: Find next subsegment in sequence. */ /* snext(ab) -> b* */ /* */ /* sorg: Origin sdest: Destination */ /* sorg(ab) -> a sdest(ab) -> b */ /* */ /* sbond: Bond two subsegments together at the respective origins. */ /* sbond(ab, ac) */ /* */ /* */ /* For interacting tetrahedra and subfacets: */ /* */ /* tspivot: Find a subsegment abutting a triangle. */ /* tspivot(abc) -> ba */ /* */ /* stpivot: Find a triangle abutting a subsegment. */ /* stpivot(ab) -> ba* */ /* */ /* tsbond: Bond a triangle to a subsegment. */ /* tsbond(abc, ba) */ /* */ /*****************************************************************************/ /********* Mesh manipulation primitives begin here *********/ /** **/ /** **/ /* Fast lookup arrays to speed some of the mesh manipulation primitives. */ int plus1mod3[3] = {1, 2, 0}; int minus1mod3[3] = {2, 0, 1}; /********* Primitives for triangles *********/ /* */ /* */ /* decode() converts a pointer to an oriented triangle. The orientation is */ /* extracted from the two least significant bits of the pointer. */ #define decode(ptr, otri) \ (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \ (otri).tri = (triangle *) \ ((unsigned long) (ptr) ^ (unsigned long) (otri).orient) /* encode() compresses an oriented triangle into a single pointer. It */ /* relies on the assumption that all triangles are aligned to four-byte */ /* boundaries, so the two least significant bits of (otri).tri are zero. */ #define encode(otri) \ (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient) /* The following handle manipulation primitives are all described by Guibas */ /* and Stolfi. However, Guibas and Stolfi use an edge-based data */ /* structure, whereas I use a triangle-based data structure. */ /* sym() finds the abutting triangle, on the same edge. Note that the edge */ /* direction is necessarily reversed, because the handle specified by an */ /* oriented triangle is directed counterclockwise around the triangle. */ #define sym(otri1, otri2) \ ptr = (otri1).tri[(otri1).orient]; \ decode(ptr, otri2); #define symself(otri) \ ptr = (otri).tri[(otri).orient]; \ decode(ptr, otri); /* lnext() finds the next edge (counterclockwise) of a triangle. */ #define lnext(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = plus1mod3[(otri1).orient] #define lnextself(otri) \ (otri).orient = plus1mod3[(otri).orient] /* lprev() finds the previous edge (clockwise) of a triangle. */ #define lprev(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = minus1mod3[(otri1).orient] #define lprevself(otri) \ (otri).orient = minus1mod3[(otri).orient] /* onext() spins counterclockwise around a vertex; that is, it finds the */ /* next edge with the same origin in the counterclockwise direction. This */ /* edge is part of a different triangle. */ #define onext(otri1, otri2) \ lprev(otri1, otri2); \ symself(otri2); #define onextself(otri) \ lprevself(otri); \ symself(otri); /* oprev() spins clockwise around a vertex; that is, it finds the next edge */ /* with the same origin in the clockwise direction. This edge is part of */ /* a different triangle. */ #define oprev(otri1, otri2) \ sym(otri1, otri2); \ lnextself(otri2); #define oprevself(otri) \ symself(otri); \ lnextself(otri); /* dnext() spins counterclockwise around a vertex; that is, it finds the */ /* next edge with the same destination in the counterclockwise direction. */ /* This edge is part of a different triangle. */ #define dnext(otri1, otri2) \ sym(otri1, otri2); \ lprevself(otri2); #define dnextself(otri) \ symself(otri); \ lprevself(otri); /* dprev() spins clockwise around a vertex; that is, it finds the next edge */ /* with the same destination in the clockwise direction. This edge is */ /* part of a different triangle. */ #define dprev(otri1, otri2) \ lnext(otri1, otri2); \ symself(otri2); #define dprevself(otri) \ lnextself(otri); \ symself(otri); /* rnext() moves one edge counterclockwise about the adjacent triangle. */ /* (It's best understood by reading Guibas and Stolfi. It involves */ /* changing triangles twice.) */ #define rnext(otri1, otri2) \ sym(otri1, otri2); \ lnextself(otri2); \ symself(otri2); #define rnextself(otri) \ symself(otri); \ lnextself(otri); \ symself(otri); /* rprev() moves one edge clockwise about the adjacent triangle. */ /* (It's best understood by reading Guibas and Stolfi. It involves */ /* changing triangles twice.) */ #define rprev(otri1, otri2) \ sym(otri1, otri2); \ lprevself(otri2); \ symself(otri2); #define rprevself(otri) \ symself(otri); \ lprevself(otri); \ symself(otri); /* These primitives determine or set the origin, destination, or apex of a */ /* triangle. */ #define org(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3] #define dest(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3] #define apex(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[(otri).orient + 3] #define setorg(otri, vertexptr) \ (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr #define setdest(otri, vertexptr) \ (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr #define setapex(otri, vertexptr) \ (otri).tri[(otri).orient + 3] = (triangle) vertexptr /* Bond two triangles together. */ #define bond(otri1, otri2) \ (otri1).tri[(otri1).orient] = encode(otri2); \ (otri2).tri[(otri2).orient] = encode(otri1) /* Dissolve a bond (from one side). Note that the other triangle will still */ /* think it's connected to this triangle. Usually, however, the other */ /* triangle is being deleted entirely, or bonded to another triangle, so */ /* it doesn't matter. */ #define dissolve(otri) \ (otri).tri[(otri).orient] = (triangle) m->dummytri /* Copy an oriented triangle. */ #define otricopy(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = (otri1).orient /* Test for equality of oriented triangles. */ #define otriequal(otri1, otri2) \ (((otri1).tri == (otri2).tri) && \ ((otri1).orient == (otri2).orient)) /* Primitives to infect or cure a triangle with the virus. These rely on */ /* the assumption that all subsegments are aligned to four-byte boundaries.*/ #define infect(otri) \ (otri).tri[6] = (triangle) \ ((unsigned long) (otri).tri[6] | (unsigned long) 2l) #define uninfect(otri) \ (otri).tri[6] = (triangle) \ ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l) /* Test a triangle for viral infection. */ #define infected(otri) \ (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l) /* Check or set a triangle's attributes. */ #define elemattribute(otri, attnum) \ ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] #define setelemattribute(otri, attnum, value) \ ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value /* Check or set a triangle's maximum area bound. */ #define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex] #define setareabound(otri, value) \ ((REAL *) (otri).tri)[m->areaboundindex] = value /* Check or set a triangle's deallocation. Its second pointer is set to */ /* NULL to indicate that it is not allocated. (Its first pointer is used */ /* for the stack of dead items.) Its fourth pointer (its first vertex) */ /* is set to NULL in case a `badtriang' structure points to it. */ #define deadtri(tria) ((tria)[1] == (triangle) NULL) #define killtri(tria) \ (tria)[1] = (triangle) NULL; \ (tria)[3] = (triangle) NULL /********* Primitives for subsegments *********/ /* */ /* */ /* sdecode() converts a pointer to an oriented subsegment. The orientation */ /* is extracted from the least significant bit of the pointer. The two */ /* least significant bits (one for orientation, one for viral infection) */ /* are masked out to produce the real pointer. */ #define sdecode(sptr, osub) \ (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \ (osub).ss = (subseg *) \ ((unsigned long) (sptr) & ~ (unsigned long) 3l) /* sencode() compresses an oriented subsegment into a single pointer. It */ /* relies on the assumption that all subsegments are aligned to two-byte */ /* boundaries, so the least significant bit of (osub).ss is zero. */ #define sencode(osub) \ (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient) /* ssym() toggles the orientation of a subsegment. */ #define ssym(osub1, osub2) \ (osub2).ss = (osub1).ss; \ (osub2).ssorient = 1 - (osub1).ssorient #define ssymself(osub) \ (osub).ssorient = 1 - (osub).ssorient /* spivot() finds the other subsegment (from the same segment) that shares */ /* the same origin. */ #define spivot(osub1, osub2) \ sptr = (osub1).ss[(osub1).ssorient]; \ sdecode(sptr, osub2) #define spivotself(osub) \ sptr = (osub).ss[(osub).ssorient]; \ sdecode(sptr, osub) /* snext() finds the next subsegment (from the same segment) in sequence; */ /* one whose origin is the input subsegment's destination. */ #define snext(osub1, osub2) \ sptr = (osub1).ss[1 - (osub1).ssorient]; \ sdecode(sptr, osub2) #define snextself(osub) \ sptr = (osub).ss[1 - (osub).ssorient]; \ sdecode(sptr, osub) /* These primitives determine or set the origin or destination of a */ /* subsegment. */ #define sorg(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[2 + (osub).ssorient] #define sdest(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[3 - (osub).ssorient] #define setsorg(osub, vertexptr) \ (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr #define setsdest(osub, vertexptr) \ (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr /* These primitives read or set a boundary marker. Boundary markers are */ /* used to hold user-defined tags for setting boundary conditions in */ /* finite element solvers. */ #define mark(osub) (* (int *) ((osub).ss + 6)) #define setmark(osub, value) \ * (int *) ((osub).ss + 6) = value /* Bond two subsegments together. */ #define sbond(osub1, osub2) \ (osub1).ss[(osub1).ssorient] = sencode(osub2); \ (osub2).ss[(osub2).ssorient] = sencode(osub1) /* Dissolve a subsegment bond (from one side). Note that the other */ /* subsegment will still think it's connected to this subsegment. */ #define sdissolve(osub) \ (osub).ss[(osub).ssorient] = (subseg) m->dummysub /* Copy a subsegment. */ #define subsegcopy(osub1, osub2) \ (osub2).ss = (osub1).ss; \ (osub2).ssorient = (osub1).ssorient /* Test for equality of subsegments. */ #define subsegequal(osub1, osub2) \ (((osub1).ss == (osub2).ss) && \ ((osub1).ssorient == (osub2).ssorient)) /* Check or set a subsegment's deallocation. Its second pointer is set to */ /* NULL to indicate that it is not allocated. (Its first pointer is used */ /* for the stack of dead items.) Its third pointer (its first vertex) */ /* is set to NULL in case a `badsubseg' structure points to it. */ #define deadsubseg(sub) ((sub)[1] == (subseg) NULL) #define killsubseg(sub) \ (sub)[1] = (subseg) NULL; \ (sub)[2] = (subseg) NULL /********* Primitives for interacting triangles and subsegments *********/ /* */ /* */ /* tspivot() finds a subsegment abutting a triangle. */ #define tspivot(otri, osub) \ sptr = (subseg) (otri).tri[6 + (otri).orient]; \ sdecode(sptr, osub) /* stpivot() finds a triangle abutting a subsegment. It requires that the */ /* variable `ptr' of type `triangle' be defined. */ #define stpivot(osub, otri) \ ptr = (triangle) (osub).ss[4 + (osub).ssorient]; \ decode(ptr, otri) /* Bond a triangle to a subsegment. */ #define tsbond(otri, osub) \ (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \ (osub).ss[4 + (osub).ssorient] = (subseg) encode(otri) /* Dissolve a bond (from the triangle side). */ #define tsdissolve(otri) \ (otri).tri[6 + (otri).orient] = (triangle) m->dummysub /* Dissolve a bond (from the subsegment side). */ #define stdissolve(osub) \ (osub).ss[4 + (osub).ssorient] = (subseg) m->dummytri /********* Primitives for vertices *********/ /* */ /* */ #define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex] #define setvertexmark(vx, value) \ ((int *) (vx))[m->vertexmarkindex] = value #define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1] #define setvertextype(vx, value) \ ((int *) (vx))[m->vertexmarkindex + 1] = value #define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex] #define setvertex2tri(vx, value) \ ((triangle *) (vx))[m->vertex2triindex] = value /** **/ /** **/ /********* Mesh manipulation primitives end here *********/ /********* User-defined triangle evaluation routine begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* triunsuitable() Determine if a triangle is unsuitable, and thus must */ /* be further refined. */ /* */ /* You may write your own procedure that decides whether or not a selected */ /* triangle is too big (and needs to be refined). There are two ways to do */ /* this. */ /* */ /* (1) Modify the procedure `triunsuitable' below, then recompile */ /* Triangle. */ /* */ /* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */ /* to this file, or by using the appropriate compiler switch). This way, */ /* you can compile triangle.c separately from your test. Write your own */ /* `triunsuitable' procedure in a separate C file (using the same prototype */ /* as below). Compile it and link the object code with triangle.o. */ /* */ /* This procedure returns 1 if the triangle is too large and should be */ /* refined; 0 otherwise. */ /* */ /*****************************************************************************/ #ifdef EXTERNAL_TEST #ifdef ANSI_DECLARATORS extern int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area); #else /* not ANSI_DECLARATORS */ extern int triunsuitable(); #endif /* not ANSI_DECLARATORS */ #else /* not EXTERNAL_TEST */ #ifdef ANSI_DECLARATORS int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area) #else /* not ANSI_DECLARATORS */ int triunsuitable(triorg, tridest, triapex, area) vertex triorg; /* The triangle's origin vertex. */ vertex tridest; /* The triangle's destination vertex. */ vertex triapex; /* The triangle's apex vertex. */ REAL area; /* The area of the triangle. */ #endif /* not ANSI_DECLARATORS */ { REAL dxoa, dxda, dxod; REAL dyoa, dyda, dyod; REAL oalen, dalen, odlen; REAL maxlen; dxoa = triorg[0] - triapex[0]; dyoa = triorg[1] - triapex[1]; dxda = tridest[0] - triapex[0]; dyda = tridest[1] - triapex[1]; dxod = triorg[0] - tridest[0]; dyod = triorg[1] - tridest[1]; /* Find the squares of the lengths of the triangle's three edges. */ oalen = dxoa * dxoa + dyoa * dyoa; dalen = dxda * dxda + dyda * dyda; odlen = dxod * dxod + dyod * dyod; /* Find the square of the length of the longest edge. */ maxlen = (dalen > oalen) ? dalen : oalen; maxlen = (odlen > maxlen) ? odlen : maxlen; if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) { return 1; } else { return 0; } } #endif /* not EXTERNAL_TEST */ /** **/ /** **/ /********* User-defined triangle evaluation routine ends here *********/ /********* Memory allocation wrappers begin here *********/ /** **/ /** **/ #ifdef ANSI_DECLARATORS VOID *trimalloc(int size) #else /* not ANSI_DECLARATORS */ VOID *trimalloc(size) int size; #endif /* not ANSI_DECLARATORS */ { VOID *memptr; memptr = malloc(size); if (memptr == (VOID *) NULL) { printf("Error: Out of memory.\n"); exit(1); } return(memptr); } #ifdef ANSI_DECLARATORS void trifree(VOID *memptr) #else /* not ANSI_DECLARATORS */ void trifree(memptr) VOID *memptr; #endif /* not ANSI_DECLARATORS */ { free(memptr); } /** **/ /** **/ /********* Memory allocation wrappers end here *********/ /********* User interaction routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* syntax() Print list of command line switches. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY void syntax() { #ifdef CDT_ONLY #ifdef REDUCED printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n"); #else /* not REDUCED */ printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n"); #endif /* not REDUCED */ #else /* not CDT_ONLY */ #ifdef REDUCED printf("triangle [-prq__a__uAcjevngBPNEIOXzo_YS__LlQVh] input_file\n"); #else /* not REDUCED */ printf("triangle [-prq__a__uAcjevngBPNEIOXzo_YS__LiFlsCQVh] input_file\n"); #endif /* not REDUCED */ #endif /* not CDT_ONLY */ printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n"); #ifndef CDT_ONLY printf(" -r Refines a previously generated mesh.\n"); printf( " -q Quality mesh generation. A minimum angle may be specified.\n"); printf(" -a Applies a maximum triangle area constraint.\n"); printf(" -u Applies a user-defined triangle constraint.\n"); #endif /* not CDT_ONLY */ printf( " -A Applies attributes to identify triangles in certain regions.\n"); printf(" -c Encloses the convex hull with segments.\n"); printf(" -w Weighted Delaunay triangulation.\n"); printf(" -W Regular triangulation (lower hull of a height field).\n"); printf(" -j Jettison unused vertices from output .node file.\n"); printf(" -e Generates an edge list.\n"); printf(" -v Generates a Voronoi diagram.\n"); printf(" -n Generates a list of triangle neighbors.\n"); printf(" -g Generates an .off file for Geomview.\n"); printf(" -B Suppresses output of boundary information.\n"); printf(" -P Suppresses output of .poly file.\n"); printf(" -N Suppresses output of .node file.\n"); printf(" -E Suppresses output of .ele file.\n"); printf(" -I Suppresses mesh iteration numbers.\n"); printf(" -O Ignores holes in .poly file.\n"); printf(" -X Suppresses use of exact arithmetic.\n"); printf(" -z Numbers all items starting from zero (rather than one).\n"); printf(" -o2 Generates second-order subparametric elements.\n"); #ifndef CDT_ONLY printf(" -Y Suppresses boundary segment splitting.\n"); printf(" -S Specifies maximum number of added Steiner points.\n"); printf(" -L Uses equatorial circles, not equatorial lenses.\n"); #endif /* not CDT_ONLY */ #ifndef REDUCED printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n"); #endif /* not REDUCED */ printf(" -l Uses vertical cuts only, rather than alternating cuts.\n"); #ifndef REDUCED #ifndef CDT_ONLY printf( " -s Force segments into mesh by splitting (instead of using CDT).\n"); printf(" -L Uses Ruppert's diametral spheres, not diametral lenses.\n"); #endif /* not CDT_ONLY */ printf(" -C Check consistency of final mesh.\n"); #endif /* not REDUCED */ printf(" -Q Quiet: No terminal output except errors.\n"); printf(" -V Verbose: Detailed information on what I'm doing.\n"); printf(" -h Help: Detailed instructions for Triangle.\n"); exit(0); } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* info() Print out complete instructions. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY void info() { printf("Triangle\n"); printf( "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); printf("Version 1.4\n\n"); printf("Copyright 1993, 1995, 1997, 1998, 2002 Jonathan Richard Shewchuk\n"); printf("2360 Woolsey #H / Berkeley, California 94705-1927\n"); printf("Bugs/comments to jrs@cs.berkeley.edu\n"); printf( "Created as part of the Archimedes project (tools for parallel FEM).\n"); printf( "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); printf("There is no warranty whatsoever. Use at your own risk.\n"); #ifdef SINGLE printf("This executable is compiled for single precision arithmetic.\n\n\n"); #else /* not SINGLE */ printf("This executable is compiled for double precision arithmetic.\n\n\n"); #endif /* not SINGLE */ printf( "Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); printf( "triangulations, Voronoi diagrams, and quality conforming Delaunay\n"); printf( "triangulations. The latter can be generated with no small angles, and are\n" ); printf( "thus suitable for finite element analysis. If no command line switches are\n" ); printf( "specified, your .node input file is read, and the Delaunay triangulation is\n" ); printf("returned in .node and .ele output files. The command syntax is:\n"); printf("\n"); printf("triangle [-prq__a__uAcjevngBPNEIOXzo_YS__LiFlsCQVh] input_file\n"); printf("\n"); printf( "Underscores indicate that numbers may optionally follow certain switches.\n"); printf( "Do not leave any space between a switch and its numeric parameter.\n"); printf( "input_file must be a file with extension .node, or extension .poly if the\n"); printf( "-p switch is used. If -r is used, you must supply .node and .ele files,\n"); printf( "and possibly a .poly file and an .area file as well. The formats of these\n" ); printf("files are described below.\n\n"); printf("Command Line Switches:\n\n"); printf( " -p Reads a Planar Straight Line Graph (.poly file), which can specify\n" ); printf(" vertices, segments, holes, regional attributes, and area\n"); printf( " constraints. Generates a constrained Delaunay triangulation (CDT)\n" ); printf( " fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n"); printf( " constrained Delaunay triangulation (CCDT). If -p is not used,\n"); printf(" Triangle reads a .node file by default.\n"); printf( " -r Refines a previously generated mesh. The mesh is read from a .node\n" ); printf( " file and an .ele file. If -p is also used, a .poly file is read\n"); printf( " and used to constrain segments in the mesh. If -a is also used\n"); printf( " (with no number following), an .area file is read and used to\n"); printf( " impose area constraints on the mesh. Further details on refinement\n" ); printf(" are given below.\n"); printf( " -q Quality mesh generation by my variant of Jim Ruppert's Delaunay\n"); printf( " refinement algorithm. Adds vertices to the mesh to ensure that no\n" ); printf( " angles smaller than 20 degrees occur. An alternative minimum angle\n" ); printf( " may be specified after the `q'. If the minimum angle is 20.7\n"); printf( " degrees or smaller, the triangulation algorithm is mathematically\n"); printf( " guaranteed to terminate (assuming infinite precision arithmetic--\n"); printf( " Triangle may fail to terminate if you run out of precision). In\n"); printf( " practice, the algorithm often succeeds for minimum angles up to\n"); printf( " 33.8 degrees. For some meshes, however, it may be necessary to\n"); printf( " reduce the minimum angle to avoid problems associated with\n"); printf( " insufficient floating-point precision. The specified angle may\n"); printf(" include a decimal point.\n"); printf( " -a Imposes a maximum triangle area. If a number follows the `a', no\n"); printf( " triangle is generated whose area is larger than that number. If no\n" ); printf( " number is specified, an .area file (if -r is used) or .poly file\n"); printf( " (if -r is not used) specifies a set of maximum area constraints.\n"); printf( " An .area file contains a separate area constraint for each\n"); printf( " triangle, and is useful for refining a finite element mesh based on\n" ); printf( " a posteriori error estimates. A .poly file can optionally contain\n" ); printf( " an area constraint for each segment-bounded region, thereby\n"); printf( " controlling triangle densities in a first triangulation of a PSLG.\n" ); printf( " You can impose both a fixed area constraint and a varying area\n"); printf( " constraint by invoking the -a switch twice, once with and once\n"); printf( " without a number following. Each area specified may include a\n"); printf(" decimal point.\n"); printf( " -u Imposes a user-defined constraint on triangle size. There are two\n" ); printf( " ways to use this feature. One is to edit the triunsuitable()\n"); printf( " procedure in triangle.c to encode any constraint you like, then\n"); printf( " recompile Triangle. The other is to compile triangle.c with the\n"); printf( " EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n"); printf( " link Triangle against a separate object file that implements\n"); printf( " triunsuitable(). In either case, the -u switch causes the user-\n"); printf(" defined test to be applied to every triangle.\n"); printf( " -A Assigns an additional attribute to each triangle that identifies\n"); printf( " what segment-bounded region each triangle belongs to. Attributes\n"); printf( " are assigned to regions by the .poly file. If a region is not\n"); printf( " explicitly marked by the .poly file, triangles in that region are\n"); printf( " assigned an attribute of zero. The -A switch has an effect only\n"); printf(" when the -p switch is used and the -r switch is not.\n"); printf( " -c Creates segments on the convex hull of the triangulation. If you\n"); printf( " are triangulating a vertex set, this switch causes a .poly file to\n" ); printf( " be written, containing all edges in the convex hull. If you are\n"); printf( " triangulating a PSLG, this switch specifies that the whole convex\n"); printf( " hull of the PSLG should be triangulated, regardless of what\n"); printf( " segments the PSLG has. If you do not use this switch when\n"); printf( " triangulating a PSLG, it is assumed that you have identified the\n"); printf( " region to be triangulated by surrounding it with segments of the\n"); printf( " input PSLG. Beware: if you are not careful, this switch can cause\n" ); printf( " the introduction of an extremely thin angle between a PSLG segment\n" ); printf( " and a convex hull segment, which can cause overrefinement (and\n"); printf( " possibly failure if Triangle runs out of precision). If you are\n"); printf( " refining a mesh, the -c switch works differently; it generates the\n" ); printf( " set of boundary edges of the mesh (useful if no .poly file was\n"); printf(" read).\n"); printf( " -j Jettisons vertices that are not part of the final triangulation\n"); printf( " from the output .node file. By default, Triangle copies all\n"); printf( " vertices in the input .node file to the output .node file, in the\n"); printf( " same order, so their indices do not change. The -j switch prevents\n" ); printf( " duplicated input vertices from appearing in the output .node file;\n" ); printf( " hence, if two input vertices have exactly the same coordinates,\n"); printf( " only the first appears in the output. If any vertices are\n"); printf( " jettisoned, the vertex numbering in the output .node file differs\n"); printf(" from that of the input .node file.\n"); printf( " -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); printf( " -v Outputs the Voronoi diagram associated with the triangulation.\n"); printf( " Does not attempt to detect degeneracies, so some Voronoi vertices\n"); printf( " may be duplicated. See the discussion of Voronoi diagrams below.\n"); printf( " -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); printf(" triangle.\n"); printf( " -g Outputs the mesh to an Object File Format (.off) file, suitable for\n" ); printf(" viewing with the Geometry Center's Geomview package.\n"); printf( " -B No boundary markers in the output .node, .poly, and .edge output\n"); printf( " files. See the detailed discussion of boundary markers below.\n"); printf( " -P No output .poly file. Saves disk space, but you lose the ability\n"); printf( " to maintain constraining segments on later refinements of the mesh.\n" ); printf(" -N No output .node file.\n"); printf(" -E No output .ele file.\n"); printf( " -I No iteration numbers. Suppresses the output of .node and .poly\n"); printf( " files, so your input files won't be overwritten. (If your input is\n" ); printf( " a .poly file only, a .node file is written.) Cannot be used with\n"); printf( " the -r switch, because that would overwrite your input .ele file.\n"); printf( " Shouldn't be used with the -q, -a, -u, or -s switch if you are\n"); printf( " using a .node file for input, because no .node file is written, so\n" ); printf(" there is no record of any added Steiner points.\n"); printf(" -O No holes. Ignores the holes in the .poly file.\n"); printf( " -X No exact arithmetic. Normally, Triangle uses exact floating-point\n" ); printf( " arithmetic for certain tests if it thinks the inexact tests are not\n" ); printf( " accurate enough. Exact arithmetic ensures the robustness of the\n"); printf( " triangulation algorithms, despite floating-point roundoff error.\n"); printf( " Disabling exact arithmetic with the -X switch causes a small\n"); printf( " improvement in speed and creates the possibility (albeit small)\n"); printf( " that Triangle will fail to produce a valid mesh. Not recommended.\n" ); printf( " -z Numbers all items starting from zero (rather than one). Note that\n" ); printf( " this switch is normally overrided by the value used to number the\n"); printf( " first vertex of the input .node or .poly file. However, this\n"); printf( " switch is useful when calling Triangle from another program.\n"); printf( " -o2 Generates second-order subparametric elements with six nodes each.\n" ); printf( " -Y No new vertices on the boundary. This switch is useful when the\n"); printf( " mesh boundary must be preserved so that it conforms to some\n"); printf( " adjacent mesh. Be forewarned that you will probably sacrifice some\n" ); printf( " of the quality of the mesh; Triangle will try, but the resulting\n"); printf( " mesh may contain triangles of poor aspect ratio. Works well if all\n" ); printf( " the boundary vertices are closely spaced. Specify this switch\n"); printf( " twice (`-YY') to prevent all segment splitting, including internal\n" ); printf(" boundaries.\n"); printf( " -S Specifies the maximum number of Steiner points (vertices that are\n"); printf( " not in the input, but are added to meet the constraints on minimum\n" ); printf( " angle and maximum area). The default is to allow an unlimited\n"); printf( " number. If you specify this switch with no number after it,\n"); printf( " the limit is set to zero. Triangle always adds vertices at segment\n" ); printf( " intersections, even if it needs to use more vertices than the limit\n" ); printf( " you set. When Triangle inserts segments by splitting (-s), it\n"); printf( " always adds enough vertices to ensure that all the segments of the\n" ); printf(" PLSG are recovered, ignoring the limit if necessary.\n"); printf( " -L Do not use diametral lenses to determine whether subsegments are\n"); printf( " encroached; use diametral circles instead (as in Ruppert's\n"); printf( " algorithm). Use this switch if you want all triangles in the mesh\n" ); printf( " to be Delaunay, and not just constrained Delaunay; or if you want\n"); printf( " to ensure that all Voronoi vertices lie within the triangulation.\n"); printf( " (Applications such as some finite volume methods may have this\n"); printf( " requirement.) This switch may increase the number of vertices in\n"); printf(" the mesh to meet these constraints.\n"); printf( " -i Uses an incremental rather than divide-and-conquer algorithm to\n"); printf( " form a Delaunay triangulation. Try it if the divide-and-conquer\n"); printf(" algorithm fails.\n"); printf( " -F Uses Steven Fortune's sweepline algorithm to form a Delaunay\n"); printf( " triangulation. Warning: does not use exact arithmetic for all\n"); printf(" calculations. An exact result is not guaranteed.\n"); printf( " -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); printf( " default, Triangle uses alternating vertical and horizontal cuts,\n"); printf( " which usually improve the speed except with vertex sets that are\n"); printf( " small or short and wide. This switch is primarily of theoretical\n"); printf(" interest.\n"); printf( " -s Specifies that segments should be forced into the triangulation by\n" ); printf( " recursively splitting them at their midpoints, rather than by\n"); printf( " generating a constrained Delaunay triangulation. Segment splitting\n" ); printf( " is true to Ruppert's original algorithm, but can create needlessly\n" ); printf( " small triangles. This switch is primarily of theoretical interest.\n" ); printf( " -C Check the consistency of the final mesh. Uses exact arithmetic for\n" ); printf( " checking, even if the -X switch is used. Useful if you suspect\n"); printf(" Triangle is buggy.\n"); printf( " -Q Quiet: Suppresses all explanation of what Triangle is doing,\n"); printf(" unless an error occurs.\n"); printf( " -V Verbose: Gives detailed information about what Triangle is doing.\n" ); printf( " Add more `V's for increasing amount of detail. `-V' gives\n"); printf( " information on algorithmic progress and more detailed statistics.\n"); printf( " `-VV' gives vertex-by-vertex details, and prints so much that\n"); printf( " Triangle runs much more slowly. `-VVVV' gives information only\n"); printf(" a debugger could love.\n"); printf(" -h Help: Displays these instructions.\n"); printf("\n"); printf("Definitions:\n"); printf("\n"); printf( " A Delaunay triangulation of a vertex set is a triangulation whose\n"); printf( " vertices are the vertex set, wherein no vertex in the vertex set falls in\n" ); printf( " the interior of the circumcircle (circle that passes through all three\n"); printf(" vertices) of any triangle in the triangulation.\n\n"); printf( " A Voronoi diagram of a vertex set is a subdivision of the plane into\n"); printf( " polygonal regions (some of which may be infinite), where each region is\n"); printf( " the set of points in the plane that are closer to some input vertex than\n" ); printf( " to any other input vertex. (The Voronoi diagram is the geometric dual of\n" ); printf(" the Delaunay triangulation.)\n\n"); printf( " A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n"); printf( " Segments are simply edges, whose endpoints are vertices in the PSLG.\n"); printf( " Segments may intersect each other only at their endpoints. The file\n"); printf(" format for PSLGs (.poly files) is described below.\n\n"); printf( " A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n"); printf( " Delaunay triangulation, but each PSLG segment is present as a single edge\n" ); printf( " in the triangulation. (A constrained Delaunay triangulation is not truly\n" ); printf( " a Delaunay triangulation.) By definition, a CDT does not have any\n"); printf(" vertices other than those specified in the input PSLG.\n\n"); printf( " A conforming Delaunay triangulation of a PSLG is a true Delaunay\n"); printf( " triangulation in which each PSLG segment is represented by a linear\n"); printf( " contiguous sequence of edges in the triangulation. Each input segment\n"); printf( " may have been subdivided into shorter subsegments by the insertion of\n"); printf( " additional vertices. These inserted vertices are necessary to maintain\n"); printf( " the Delaunay property while ensuring that every segment is represented.\n"); printf("\n"); printf("File Formats:\n"); printf("\n"); printf( " All files may contain comments prefixed by the character '#'. Vertices,\n" ); printf( " triangles, edges, holes, and maximum area constraints must be numbered\n"); printf( " consecutively, starting from either 1 or 0. Whichever you choose, all\n"); printf( " input files must be consistent; if the vertices are numbered from 1, so\n"); printf( " must be all other objects. Triangle automatically detects your choice\n"); printf( " while reading the .node (or .poly) file. (When calling Triangle from\n"); printf( " another program, use the -z switch if you wish to number objects from\n"); printf(" zero.) Examples of these file formats are given below.\n\n"); printf(" .node files:\n"); printf( " First line: <# of vertices> <# of attributes>\n" ); printf( " <# of boundary markers (0 or 1)>\n" ); printf( " Remaining lines: [attributes] [boundary marker]\n"); printf("\n"); printf( " The attributes, which are typically floating-point values of physical\n"); printf( " quantities (such as mass or conductivity) associated with the nodes of\n" ); printf( " a finite element mesh, are copied unchanged to the output mesh. If -q,\n" ); printf( " -a, -u, or -s is selected, each new Steiner point added to the mesh\n"); printf(" has attributes assigned to it by linear interpolation.\n\n"); printf( " If the fourth entry of the first line is `1', the last column of the\n"); printf( " remainder of the file is assumed to contain boundary markers. Boundary\n" ); printf( " markers are used to identify boundary vertices and vertices resting on\n" ); printf( " PSLG segments; a complete description appears in a section below. The\n" ); printf( " .node file produced by Triangle contains boundary markers in the last\n"); printf(" column unless they are suppressed by the -B switch.\n\n"); printf(" .ele files:\n"); printf( " First line: <# of triangles> <# of attributes>\n"); printf( " Remaining lines: ... [attributes]\n"); printf("\n"); printf( " Nodes are indices into the corresponding .node file. The first three\n"); printf( " nodes are the corner vertices, and are listed in counterclockwise order\n" ); printf( " around each triangle. (The remaining nodes, if any, depend on the type\n" ); printf(" of finite element used.)\n\n"); printf( " The attributes are just like those of .node files. Because there is no\n" ); printf( " simple mapping from input to output triangles, an attempt is made to\n"); printf( " interpolate attributes, which may result in a good deal of diffusion of\n" ); printf( " attributes among nearby triangles as the triangulation is refined.\n"); printf( " Attributes do not diffuse across segments, so attributes used to\n"); printf(" identify segment-bounded regions remain intact.\n\n"); printf( " In .ele files produced by Triangle, each triangular element has three\n"); printf( " nodes (vertices) unless the -o2 switch is used, in which case\n"); printf( " subparametric quadratic elements with six nodes each are generated.\n"); printf( " The first three nodes are the corners in counterclockwise order, and\n"); printf( " the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n"); printf( " opposite the first, second, and third vertices, respectively.\n"); printf("\n"); printf(" .poly files:\n"); printf( " First line: <# of vertices> <# of attributes>\n" ); printf( " <# of boundary markers (0 or 1)>\n" ); printf( " Following lines: [attributes] [boundary marker]\n"); printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); printf( " Following lines: [boundary marker]\n"); printf(" One line: <# of holes>\n"); printf(" Following lines: \n"); printf( " Optional line: <# of regional attributes and/or area constraints>\n"); printf( " Optional following lines: \n"); printf("\n"); printf( " A .poly file represents a PSLG, as well as some additional information.\n" ); printf( " The first section lists all the vertices, and is identical to the\n"); printf( " format of .node files. <# of vertices> may be set to zero to indicate\n" ); printf( " that the vertices are listed in a separate .node file; .poly files\n"); printf( " produced by Triangle always have this format. A vertex set represented\n" ); printf( " this way has the advantage that it may easily be triangulated with or\n"); printf( " without segments (depending on whether the .poly or .node file is\n"); printf(" read).\n\n"); printf( " The second section lists the segments. Segments are edges whose\n"); printf( " presence in the triangulation is enforced (although each segment may be\n" ); printf( " subdivided into smaller edges). Each segment is specified by listing\n"); printf( " the indices of its two endpoints. This means that you must include its\n" ); printf( " endpoints in the vertex list. Each segment, like each point, may have\n" ); printf(" a boundary marker.\n\n"); printf( " If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n" ); printf( " Delaunay triangulation (CDT), in which each segment appears as a single\n" ); printf( " edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n" ); printf( " produces a conforming constrained Delaunay triangulation (CCDT), in\n"); printf( " which segments may be subdivided into smaller edges. If -L is selected\n" ); printf( " as well, Triangle produces a conforming Delaunay triangulation, so\n"); printf( " every triangle is Delaunay, and not just constrained Delaunay.\n"); printf("\n"); printf( " The third section lists holes (and concavities, if -c is selected) in\n"); printf( " the triangulation. Holes are specified by identifying a point inside\n"); printf( " each hole. After the triangulation is formed, Triangle creates holes\n"); printf( " by eating triangles, spreading out from each hole point until its\n"); printf( " progress is blocked by PSLG segments; you must be careful to enclose\n"); printf( " each hole in segments, or your whole triangulation might be eaten away.\n" ); printf( " If the two triangles abutting a segment are eaten, the segment itself\n"); printf( " is also eaten. Do not place a hole directly on a segment; if you do,\n"); printf(" Triangle chooses one side of the segment arbitrarily.\n\n"); printf( " The optional fourth section lists regional attributes (to be assigned\n"); printf( " to all triangles in a region) and regional constraints on the maximum\n"); printf( " triangle area. Triangle reads this section only if the -A switch is\n"); printf( " used or the -a switch is used without a number following it, and the -r\n" ); printf( " switch is not used. Regional attributes and area constraints are\n"); printf( " propagated in the same manner as holes; you specify a point for each\n"); printf( " attribute and/or constraint, and the attribute and/or constraint\n"); printf( " affects the whole region (bounded by segments) containing the point.\n"); printf( " If two values are written on a line after the x and y coordinate, the\n"); printf( " first such value is assumed to be a regional attribute (but is only\n"); printf( " applied if the -A switch is selected), and the second value is assumed\n" ); printf( " to be a regional area constraint (but is only applied if the -a switch\n" ); printf( " is selected). You may specify just one value after the coordinates,\n"); printf( " which can serve as both an attribute and an area constraint, depending\n" ); printf( " on the choice of switches. If you are using the -A and -a switches\n"); printf( " simultaneously and wish to assign an attribute to some region without\n"); printf(" imposing an area constraint, use a negative maximum area.\n\n"); printf( " When a triangulation is created from a .poly file, you must either\n"); printf( " enclose the entire region to be triangulated in PSLG segments, or\n"); printf( " use the -c switch, which encloses the convex hull of the input vertex\n"); printf( " set. If you do not use the -c switch, Triangle eats all triangles that\n" ); printf( " are not enclosed by segments; if you are not careful, your whole\n"); printf( " triangulation may be eaten away. If you do use the -c switch, you can\n" ); printf( " still produce concavities by the appropriate placement of holes just\n"); printf(" within the convex hull.\n\n"); printf( " An ideal PSLG has no intersecting segments, nor any vertices that lie\n"); printf( " upon segments (except, of course, the endpoints of each segment.) You\n" ); printf( " aren't required to make your .poly files ideal, but you should be aware\n" ); printf( " of what can go wrong. Segment intersections are relatively safe--\n"); printf( " Triangle calculates the intersection points for you and adds them to\n"); printf( " the triangulation--as long as your machine's floating-point precision\n"); printf( " doesn't become a problem. You are tempting the fates if you have three\n" ); printf( " segments that cross at the same location, and expect Triangle to figure\n" ); printf( " out where the intersection point is. Thanks to floating-point roundoff\n" ); printf( " error, Triangle will probably decide that the three segments intersect\n" ); printf( " at three different points, and you will find a minuscule triangle in\n"); printf( " your output--unless Triangle tries to refine the tiny triangle, uses\n"); printf( " up the last bit of machine precision, and fails to terminate at all.\n"); printf( " You're better off putting the intersection point in the input files,\n"); printf( " and manually breaking up each segment into two. Similarly, if you\n"); printf( " place a vertex at the middle of a segment, and hope that Triangle will\n" ); printf( " break up the segment at that vertex, you might get lucky. On the other\n" ); printf( " hand, Triangle might decide that the vertex doesn't lie precisely on\n"); printf( " the segment, and you'll have a needle-sharp triangle in your output--or\n" ); printf(" a lot of tiny triangles if you're generating a quality mesh.\n"); printf("\n"); printf( " When Triangle reads a .poly file, it also writes a .poly file, which\n"); printf( " includes all edges that are parts of input segments. If the -c switch\n" ); printf( " is used, the output .poly file also includes all of the edges on the\n"); printf( " convex hull. Hence, the output .poly file is useful for finding edges\n" ); printf( " associated with input segments and for setting boundary conditions in\n"); printf( " finite element simulations. Moreover, you will need it if you plan to\n" ); printf( " refine the output mesh, and don't want segments to be missing in later\n" ); printf(" triangulations.\n\n"); printf(" .area files:\n"); printf(" First line: <# of triangles>\n"); printf(" Following lines: \n\n"); printf( " An .area file associates with each triangle a maximum area that is used\n" ); printf( " for mesh refinement. As with other file formats, every triangle must\n"); printf( " be represented, and they must be numbered consecutively. A triangle\n"); printf( " may be left unconstrained by assigning it a negative maximum area.\n"); printf("\n"); printf(" .edge files:\n"); printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); printf( " Following lines: [boundary marker]\n"); printf("\n"); printf( " Endpoints are indices into the corresponding .node file. Triangle can\n" ); printf( " produce .edge files (use the -e switch), but cannot read them. The\n"); printf( " optional column of boundary markers is suppressed by the -B switch.\n"); printf("\n"); printf( " In Voronoi diagrams, one also finds a special kind of edge that is an\n"); printf( " infinite ray with only one endpoint. For these edges, a different\n"); printf(" format is used:\n\n"); printf(" -1 \n\n"); printf( " The `direction' is a floating-point vector that indicates the direction\n" ); printf(" of the infinite ray.\n\n"); printf(" .neigh files:\n"); printf( " First line: <# of triangles> <# of neighbors per triangle (always 3)>\n" ); printf( " Following lines: \n"); printf("\n"); printf( " Neighbors are indices into the corresponding .ele file. An index of -1\n" ); printf( " indicates no neighbor (because the triangle is on an exterior\n"); printf( " boundary). The first neighbor of triangle i is opposite the first\n"); printf(" corner of triangle i, and so on.\n\n"); printf( " Triangle can produce .neigh files (use the -n switch), but cannot read\n" ); printf(" them.\n\n"); printf("Boundary Markers:\n\n"); printf( " Boundary markers are tags used mainly to identify which output vertices\n"); printf( " and edges are associated with which PSLG segment, and to identify which\n"); printf( " vertices and edges occur on a boundary of the triangulation. A common\n"); printf( " use is to determine where boundary conditions should be applied to a\n"); printf( " finite element mesh. You can prevent boundary markers from being written\n" ); printf(" into files produced by Triangle by using the -B switch.\n\n"); printf( " The boundary marker associated with each segment in an output .poly file\n" ); printf(" and each edge in an output .edge file is chosen as follows:\n"); printf( " - If an output edge is part or all of a PSLG segment with a nonzero\n"); printf( " boundary marker, then the edge is assigned the same marker.\n"); printf( " - Otherwise, if the edge occurs on a boundary of the triangulation\n"); printf( " (including boundaries of holes), then the edge is assigned the marker\n" ); printf(" one (1).\n"); printf(" - Otherwise, the edge is assigned the marker zero (0).\n"); printf( " The boundary marker associated with each vertex in an output .node file\n"); printf(" is chosen as follows:\n"); printf( " - If a vertex is assigned a nonzero boundary marker in the input file,\n" ); printf( " then it is assigned the same marker in the output .node file.\n"); printf( " - Otherwise, if the vertex lies on a PSLG segment (including the\n"); printf( " segment's endpoints) with a nonzero boundary marker, then the vertex\n" ); printf( " is assigned the same marker. If the vertex lies on several such\n"); printf(" segments, one of the markers is chosen arbitrarily.\n"); printf( " - Otherwise, if the vertex occurs on a boundary of the triangulation,\n"); printf(" then the vertex is assigned the marker one (1).\n"); printf(" - Otherwise, the vertex is assigned the marker zero (0).\n"); printf("\n"); printf( " If you want Triangle to determine for you which vertices and edges are on\n" ); printf( " the boundary, assign them the boundary marker zero (or use no markers at\n" ); printf( " all) in your input files. In the output files, all boundary vertices,\n"); printf(" edges, and segments are assigned the value one.\n\n"); printf("Triangulation Iteration Numbers:\n\n"); printf( " Because Triangle can read and refine its own triangulations, input\n"); printf( " and output files have iteration numbers. For instance, Triangle might\n"); printf( " read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); printf( " triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); printf( " their iteration number is zero; hence, Triangle might read the file\n"); printf( " points.node, triangulate it, and produce the files points.1.node and\n"); printf(" points.1.ele.\n\n"); printf( " Iteration numbers allow you to create a sequence of successively finer\n"); printf( " meshes suitable for multigrid methods. They also allow you to produce a\n" ); printf( " sequence of meshes using error estimate-driven mesh refinement.\n"); printf("\n"); printf( " If you're not using refinement or quality meshing, and you don't like\n"); printf( " iteration numbers, use the -I switch to disable them. This switch also\n"); printf( " disables output of .node and .poly files to prevent your input files from\n" ); printf( " being overwritten. (If the input is a .poly file that contains its own\n"); printf(" points, a .node file is written.)\n\n"); printf("Examples of How to Use Triangle:\n\n"); printf( " `triangle dots' reads vertices from dots.node, and writes their Delaunay\n" ); printf( " triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n"); printf( " to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n"); printf( " instead. (No additional .node file is needed, so none is written.)\n"); printf("\n"); printf( " `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n"); printf( " object.1.node, if the vertices are omitted from object.1.poly) and writes\n" ); printf( " its constrained Delaunay triangulation to object.2.node and object.2.ele.\n" ); printf( " The segments are copied to object.2.poly, and all edges are written to\n"); printf(" object.2.edge.\n\n"); printf( " `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n" ); printf( " object.node), generates a mesh whose angles are all 31.5 degrees or\n"); printf( " greater and whose triangles all have areas of 0.1 or less, and writes the\n" ); printf( " mesh to object.1.node and object.1.ele. Each segment may be broken up\n"); printf(" into multiple subsegments; these are written to object.1.poly.\n"); printf("\n"); printf( " Here is a sample file `box.poly' describing a square with a square hole:\n" ); printf("\n"); printf( " # A box with eight vertices in 2D, no attributes, one boundary marker.\n" ); printf(" 8 2 0 1\n"); printf(" # Outer box has these vertices:\n"); printf(" 1 0 0 0\n"); printf(" 2 0 3 0\n"); printf(" 3 3 0 0\n"); printf(" 4 3 3 33 # A special marker for this vertex.\n"); printf(" # Inner square has these vertices:\n"); printf(" 5 1 1 0\n"); printf(" 6 1 2 0\n"); printf(" 7 2 1 0\n"); printf(" 8 2 2 0\n"); printf(" # Five segments with boundary markers.\n"); printf(" 5 1\n"); printf(" 1 1 2 5 # Left side of outer box.\n"); printf(" # Square hole has these segments:\n"); printf(" 2 5 7 0\n"); printf(" 3 7 8 0\n"); printf(" 4 8 6 10\n"); printf(" 5 6 5 0\n"); printf(" # One hole in the middle of the inner square.\n"); printf(" 1\n"); printf(" 1 1.5 1.5\n"); printf("\n"); printf( " Note that some segments are missing from the outer square, so one must\n"); printf( " use the `-c' switch. After `triangle -pqc box.poly', here is the output\n" ); printf( " file `box.1.node', with twelve vertices. The last four vertices were\n"); printf( " added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n"); printf( " from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n"); printf( " other vertices but 4 have been marked to indicate that they lie on a\n"); printf(" boundary.\n\n"); printf(" 12 2 0 1\n"); printf(" 1 0 0 5\n"); printf(" 2 0 3 5\n"); printf(" 3 3 0 1\n"); printf(" 4 3 3 33\n"); printf(" 5 1 1 1\n"); printf(" 6 1 2 10\n"); printf(" 7 2 1 1\n"); printf(" 8 2 2 10\n"); printf(" 9 0 1.5 5\n"); printf(" 10 1.5 0 1\n"); printf(" 11 3 1.5 1\n"); printf(" 12 1.5 3 1\n"); printf(" # Generated by triangle -pqc box.poly\n"); printf("\n"); printf(" Here is the output file `box.1.ele', with twelve triangles.\n"); printf("\n"); printf(" 12 3 0\n"); printf(" 1 5 6 9\n"); printf(" 2 10 3 7\n"); printf(" 3 6 8 12\n"); printf(" 4 9 1 5\n"); printf(" 5 6 2 9\n"); printf(" 6 7 3 11\n"); printf(" 7 11 4 8\n"); printf(" 8 7 5 10\n"); printf(" 9 12 2 6\n"); printf(" 10 8 7 11\n"); printf(" 11 5 1 10\n"); printf(" 12 8 4 12\n"); printf(" # Generated by triangle -pqc box.poly\n\n"); printf( " Here is the output file `box.1.poly'. Note that segments have been added\n" ); printf( " to represent the convex hull, and some segments have been split by newly\n" ); printf( " added vertices. Note also that <# of vertices> is set to zero to\n"); printf(" indicate that the vertices should be read from the .node file.\n"); printf("\n"); printf(" 0 2 0 1\n"); printf(" 12 1\n"); printf(" 1 1 9 5\n"); printf(" 2 5 7 1\n"); printf(" 3 8 7 1\n"); printf(" 4 6 8 10\n"); printf(" 5 5 6 1\n"); printf(" 6 3 10 1\n"); printf(" 7 4 11 1\n"); printf(" 8 2 12 1\n"); printf(" 9 9 2 5\n"); printf(" 10 10 1 1\n"); printf(" 11 11 3 1\n"); printf(" 12 12 4 1\n"); printf(" 1\n"); printf(" 1 1.5 1.5\n"); printf(" # Generated by triangle -pqc box.poly\n"); printf("\n"); printf("Refinement and Area Constraints:\n"); printf("\n"); printf( " The -r switch causes a mesh (.node and .ele files) to be read and\n"); printf( " refined. If the -p switch is also used, a .poly file is read and used to\n" ); printf( " specify edges that are constrained and cannot be eliminated (although\n"); printf( " they can be divided into smaller edges) by the refinement process.\n"); printf("\n"); printf( " When you refine a mesh, you generally want to impose tighter quality\n"); printf( " constraints. One way to accomplish this is to use -q with a larger\n"); printf( " angle, or -a followed by a smaller area than you used to generate the\n"); printf( " mesh you are refining. Another way to do this is to create an .area\n"); printf( " file, which specifies a maximum area for each triangle, and use the -a\n"); printf( " switch (without a number following). Each triangle's area constraint is\n" ); printf( " applied to that triangle. Area constraints tend to diffuse as the mesh\n"); printf( " is refined, so if there are large variations in area constraint between\n"); printf(" adjacent triangles, you may not get the results you want.\n\n"); printf( " If you are refining a mesh composed of linear (three-node) elements, the\n" ); printf( " output mesh contains all the nodes present in the input mesh, in the same\n" ); printf( " order, with new nodes added at the end of the .node file. However, the\n"); printf( " refinement is not hierarchical: there is no guarantee that each output\n"); printf( " element is contained in a single input element. Often, output elements\n"); printf( " overlap two input elements, and some input edges are not present in the\n"); printf( " output mesh. Hence, a sequence of refined meshes forms a hierarchy of\n"); printf( " nodes, but not a hierarchy of elements. If you refine a mesh of higher-\n" ); printf( " order elements, the hierarchical property applies only to the nodes at\n"); printf( " the corners of an element; other nodes may not be present in the refined\n" ); printf(" mesh.\n\n"); printf( " Maximum area constraints in .poly files operate differently from those in\n" ); printf( " .area files. A maximum area in a .poly file applies to the whole\n"); printf( " (segment-bounded) region in which a point falls, whereas a maximum area\n"); printf( " in an .area file applies to only one triangle. Area constraints in .poly\n" ); printf( " files are used only when a mesh is first generated, whereas area\n"); printf( " constraints in .area files are used only to refine an existing mesh, and\n" ); printf( " are typically based on a posteriori error estimates resulting from a\n"); printf(" finite element simulation on that mesh.\n\n"); printf( " `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n"); printf( " refines the triangulation to enforce a 25 degree minimum angle, and then\n" ); printf( " writes the refined triangulation to object.2.node and object.2.ele.\n"); printf("\n"); printf( " `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n" ); printf( " After reconstructing the mesh and its subsegments, Triangle refines the\n"); printf( " mesh so that no triangle has area greater than 6.2, and furthermore the\n"); printf( " triangles satisfy the maximum area constraints in z.3.area. No angle\n"); printf( " bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n" ); printf(" z.4.poly.\n\n"); printf( " The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); printf( " x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n"); printf(" suitable for multigrid.\n\n"); printf("Convex Hulls and Mesh Boundaries:\n\n"); printf( " If the input is a vertex set (rather than a PSLG), Triangle produces its\n" ); printf( " convex hull as a by-product in the output .poly file if you use the -c\n"); printf( " switch. There are faster algorithms for finding a two-dimensional convex\n" ); printf( " hull than triangulation, of course, but this one comes for free.\n"); printf("\n"); printf( " If the input is an unconstrained mesh (you are using the -r switch but\n"); printf( " not the -p switch), Triangle produces a list of its boundary edges\n"); printf( " (including hole boundaries) as a by-product when you use the -c switch.\n"); printf( " If you also use the -p switch, the output .poly file contains all the\n"); printf(" segments from the input .poly file as well.\n\n"); printf("Voronoi Diagrams:\n\n"); printf( " The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); printf( " .v.edge. For example, `triangle -v points' reads points.node, produces\n"); printf( " its Delaunay triangulation in points.1.node and points.1.ele, and\n"); printf( " produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n" ); printf( " .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"); printf( " file contains a list of all Voronoi edges, some of which may be infinite\n" ); printf( " rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); printf(" vertices through Triangle, if so desired.)\n\n"); printf( " This implementation does not use exact arithmetic to compute the Voronoi\n" ); printf( " vertices, and does not check whether neighboring vertices are identical.\n" ); printf( " Be forewarned that if the Delaunay triangulation is degenerate or\n"); printf( " near-degenerate, the Voronoi diagram may have duplicate vertices,\n"); printf( " crossing edges, or infinite rays whose direction vector is zero.\n"); printf("\n"); printf( " The result is a valid Voronoi diagram only if Triangle's output is a true\n" ); printf( " Delaunay triangulation. The Voronoi output is usually meaningless (and\n"); printf( " may contain crossing edges and other pathology) if the output is a CDT or\n" ); printf( " CCDT, or if it has holes or concavities. If the triangulation is convex\n" ); printf( " and has no holes, this can be fixed by using the -L switch to ensure a\n"); printf(" conforming Delaunay triangulation is constructed.\n\n"); printf("Mesh Topology:\n\n"); printf( " You may wish to know which triangles are adjacent to a certain Delaunay\n"); printf( " edge in an .edge file, which Voronoi regions are adjacent to a certain\n"); printf( " Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n" ); printf( " each other. All of this information can be found by cross-referencing\n"); printf( " output files with the recollection that the Delaunay triangulation and\n"); printf(" the Voronoi diagram are planar duals.\n\n"); printf( " Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); printf( " the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); printf( " wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); printf( " vertex j of the corresponding .v.node file. Voronoi region k is the dual\n" ); printf(" of vertex k of the corresponding .node file.\n\n"); printf( " Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); printf( " vertices of the corresponding Voronoi edge. If the endpoints of a\n"); printf( " Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n" ); printf( " and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n" ); printf( " respectively. To find the Voronoi regions adjacent to a Voronoi edge,\n"); printf( " look at the endpoints of the corresponding Delaunay edge. If the\n"); printf( " endpoints of a Delaunay edge are input vertices 7 and 12, then Voronoi\n"); printf( " regions 7 and 12 adjoin the right and left sides of the corresponding\n"); printf( " Voronoi edge, respectively. To find which Voronoi regions are adjacent\n"); printf(" to each other, just read the list of Delaunay edges.\n\n"); printf( " Triangle does not write a list of Voronoi regions, but one can be\n"); printf( " reconstructed straightforwardly. For instance, to find all the edges of\n" ); printf( " Voronoi region 1, search the output .edge file for every edge that has\n"); printf( " input vertex 1 as an endpoint. The corresponding dual edges in the\n"); printf(" output .v.edge file form the boundary of Voronoi region 1.\n\n"); printf("Quadratic Elements:\n\n"); printf( " Triangle generates meshes with subparametric quadratic elements if the\n"); printf( " -o2 switch is specified. Quadratic elements have six nodes per element,\n" ); printf( " rather than three. `Subparametric' means that the edges of the triangles\n" ); printf( " are always straight, so that subparametric quadratic elements are\n"); printf( " geometrically identical to linear elements, even though they can be used\n" ); printf( " with quadratic interpolating functions. The three extra nodes of an\n"); printf( " element fall at the midpoints of the three edges, with the fourth, fifth,\n" ); printf( " and sixth nodes appearing opposite the first, second, and third corners\n"); printf(" respectively.\n\n"); printf("Statistics:\n\n"); printf( " After generating a mesh, Triangle prints a count of the number of\n"); printf( " vertices, triangles, edges, exterior boundary edges (including hole\n"); printf( " boundaries), interior boundary edges, and segments in the output mesh.\n"); printf( " If you've forgotten the statistics for an existing mesh, run Triangle on\n" ); printf( " that mesh with the -rNEP switches to read the mesh and print the\n"); printf( " statistics without writing any files. Use -rpNEP if you've got a .poly\n"); printf(" file for the mesh.\n\n"); printf( " The -V switch produces extended statistics, including a rough estimate\n"); printf( " of memory use, the number of calls to geometric predicates, and\n"); printf(" histograms of triangle aspect ratios and angles in the mesh.\n\n"); printf("Exact Arithmetic:\n\n"); printf( " Triangle uses adaptive exact arithmetic to perform what computational\n"); printf( " geometers call the `orientation' and `incircle' tests. If the floating-\n" ); printf( " point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); printf( " most workstations do), and does not use extended precision internal\n"); printf( " floating-point registers, then your output is guaranteed to be an\n"); printf( " absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n" ); printf( " error notwithstanding. The word `adaptive' implies that these arithmetic\n" ); printf( " routines compute the result only to the precision necessary to guarantee\n" ); printf( " correctness, so they are usually nearly as fast as their approximate\n"); printf(" counterparts.\n\n"); printf( " Pentiums have extended precision floating-point registers. These must be\n" ); printf( " reconfigured so their precision is reduced to memory precision. Triangle\n" ); printf( " does this if it is compiled correctly. See the makefile for details.\n"); printf("\n"); printf( " The exact tests can be disabled with the -X switch. On most inputs, this\n" ); printf( " switch reduces the computation time by about eight percent--it's not\n"); printf( " worth the risk. There are rare difficult inputs (having many collinear\n"); printf( " and cocircular vertices), however, for which the difference in speed\n"); printf( " could be a factor of two. Be forewarned that these are precisely the\n"); printf( " inputs most likely to cause errors if you use the -X switch. Hence, the\n" ); printf(" -X switch is not recommended.\n\n"); printf( " Unfortunately, the exact tests don't solve every numerical problem.\n"); printf( " Exact arithmetic is not used to compute the positions of new vertices,\n"); printf( " because the bit complexity of vertex coordinates would grow without\n"); printf( " bound. Hence, segment intersections aren't computed exactly; in very\n"); printf( " unusual cases, roundoff error in computing an intersection point might\n"); printf( " actually lead to an inverted triangle and an invalid triangulation.\n"); printf( " (This is one reason to compute your own intersection points in your .poly\n" ); printf( " files.) Similarly, exact arithmetic is not used to compute the vertices\n" ); printf(" of the Voronoi diagram.\n\n"); printf( " Another pair of problems not solved by the exact arithmetic routines is\n"); printf( " underflow and overflow. If Triangle is compiled for double precision\n"); printf( " arithmetic, I believe that Triangle's geometric predicates work correctly\n" ); printf( " if the exponent of every input coordinate falls in the range [-148, 201].\n" ); printf( " Underflow can silently prevent the orientation and incircle tests from\n"); printf( " being performed exactly, while overflow typically causes a floating\n"); printf(" exception.\n\n"); printf("Calling Triangle from Another Program:\n\n"); printf(" Read the file triangle.h for details.\n\n"); printf("Troubleshooting:\n\n"); printf(" Please read this section before mailing me bugs.\n\n"); printf(" `My output mesh has no triangles!'\n\n"); printf( " If you're using a PSLG, you've probably failed to specify a proper set\n" ); printf( " of bounding segments, or forgotten to use the -c switch. Or you may\n"); printf( " have placed a hole badly, thereby eating all your triangles. To test\n"); printf(" these possibilities, try again with the -c and -O switches.\n"); printf( " Alternatively, all your input vertices may be collinear, in which case\n" ); printf(" you can hardly expect to triangulate them.\n\n"); printf(" `Triangle doesn't terminate, or just crashes.'\n\n"); printf( " Bad things can happen when triangles get so small that the distance\n"); printf( " between their vertices isn't much larger than the precision of your\n"); printf( " machine's arithmetic. If you've compiled Triangle for single-precision\n" ); printf( " arithmetic, you might do better by recompiling it for double-precision.\n" ); printf( " Then again, you might just have to settle for more lenient constraints\n" ); printf( " on the minimum angle and the maximum area than you had planned.\n"); printf("\n"); printf( " You can minimize precision problems by ensuring that the origin lies\n"); printf( " inside your vertex set, or even inside the densest part of your\n"); printf( " mesh. If you're triangulating an object whose x coordinates all fall\n"); printf( " between 6247133 and 6247134, you're not leaving much floating-point\n"); printf(" precision for Triangle to work with.\n\n"); printf( " Precision problems can occur covertly if the input PSLG contains two\n"); printf( " segments that meet (or intersect) at an extremely small angle, or if\n"); printf( " such an angle is introduced by the -c switch. If you don't realize\n"); printf( " that a tiny angle is being formed, you might never discover why\n"); printf( " Triangle is crashing. To check for this possibility, use the -S switch\n" ); printf( " (with an appropriate limit on the number of Steiner points, found by\n"); printf( " trial-and-error) to stop Triangle early, and view the output .poly file\n" ); printf( " with Show Me (described below). Look carefully for regions where dense\n" ); printf( " clusters of vertices are forming and for small angles between segments.\n" ); printf( " Zoom in closely, as such segments might look like a single segment from\n" ); printf(" a distance.\n\n"); printf( " If some of the input values are too large, Triangle may suffer a\n"); printf( " floating exception due to overflow when attempting to perform an\n"); printf( " orientation or incircle test. (Read the section on exact arithmetic\n"); printf( " above.) Again, I recommend compiling Triangle for double (rather\n"); printf(" than single) precision arithmetic.\n\n"); printf( " Unexpected problems can arise if you use quality meshing (-q, -a, or\n"); printf( " -u) with an input that is not segment-bounded--that is, if your input\n"); printf( " is a vertex set, or you're using the -c switch. If the convex hull of\n" ); printf( " your input vertices has collinear vertices on its boundary, an input\n"); printf( " vertex that you think lies on the convex hull might actually lie just\n"); printf( " inside the convex hull. If so, an extremely thin triangle is formed by\n" ); printf( " the vertex and the convex hull edge beside it. When Triangle tries to\n" ); printf( " refine the mesh to enforce angle and area constraints, extremely tiny\n"); printf( " triangles may be formed, or Triangle may fail because of insufficient\n"); printf(" floating-point precision.\n\n"); printf( " `The numbering of the output vertices doesn't match the input vertices.'\n" ); printf("\n"); printf( " You may have had duplicate input vertices, or you may have eaten some\n"); printf( " of your input vertices with a hole, or by placing them outside the area\n" ); printf( " enclosed by segments. In any case, you can solve the problem by not\n"); printf(" using the -j switch.\n\n"); printf( " `Triangle executes without incident, but when I look at the resulting\n"); printf( " mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); printf("\n"); printf( " If you select the -X switch, Triangle occasionally makes mistakes due\n"); printf( " to floating-point roundoff error. Although these errors are rare,\n"); printf( " don't use the -X switch. If you still have problems, please report the\n" ); printf(" bug.\n\n"); printf( " Strange things can happen if you've taken liberties with your PSLG. Do\n"); printf( " you have a vertex lying in the middle of a segment? Triangle sometimes\n"); printf( " copes poorly with that sort of thing. Do you want to lay out a collinear\n" ); printf( " row of evenly spaced, segment-connected vertices? Have you simply\n"); printf( " defined one long segment connecting the leftmost vertex to the rightmost\n" ); printf( " vertex, and a bunch of vertices lying along it? This method occasionally\n" ); printf( " works, especially with horizontal and vertical lines, but often it\n"); printf( " doesn't, and you'll have to connect each adjacent pair of vertices with a\n" ); printf(" separate segment. If you don't like it, tough.\n\n"); printf( " Furthermore, if you have segments that intersect other than at their\n"); printf( " endpoints, try not to let the intersections fall extremely close to PSLG\n" ); printf(" vertices or each other.\n\n"); printf( " If you have problems refining a triangulation not produced by Triangle:\n"); printf( " Are you sure the triangulation is geometrically valid? Is it formatted\n"); printf( " correctly for Triangle? Are the triangles all listed so the first three\n" ); printf( " vertices are their corners in counterclockwise order? Are all of the\n"); printf( " triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n" ); printf(" assumes that it starts with a CDT.\n\n"); printf("Show Me:\n\n"); printf( " Triangle comes with a separate program named `Show Me', whose primary\n"); printf( " purpose is to draw meshes on your screen or in PostScript. Its secondary\n" ); printf( " purpose is to check the validity of your input files, and do so more\n"); printf( " thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n"); printf(" you have the X Windows system.\n\n"); printf("Triangle on the Web:\n\n"); printf( " To see an illustrated, updated version of these instructions, check out\n"); printf("\n"); printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); printf("\n"); printf("A Brief Plea:\n"); printf("\n"); printf( " If you use Triangle, and especially if you use it to accomplish real\n"); printf( " work, I would like very much to hear from you. A short letter or email\n"); printf( " (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n" ); printf( " to me. The more people I know are using this program, the more easily I\n" ); printf( " can justify spending time on improvements, which in turn will benefit\n"); printf( " you. Also, I can put you on a list to receive email whenever a new\n"); printf(" version of Triangle is available.\n\n"); printf( " If you use a mesh generated by Triangle in a publication, please include\n" ); printf(" an acknowledgment as well.\n\n"); printf("Research credit:\n\n"); printf( " Of course, I can take credit for only a fraction of the ideas that made\n"); printf( " this mesh generator possible. Triangle owes its existence to the efforts\n" ); printf( " of many fine computational geometers and other researchers, including\n"); printf( " Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n"); printf( " Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n"); printf( " Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n"); printf( " Isaac Saias, Bruce J. Schachter, Micha Sharir, Daniel D. Sleator, Jorge\n"); printf( " Stolfi, Robert E. Tarjan, Christopher J. Van Wyk, and Binhai Zhu. See\n"); printf( " the comments at the beginning of the source code for references.\n"); exit(0); } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* internalerror() Ask the user to send me the defective product. Exit. */ /* */ /*****************************************************************************/ void internalerror(void) { printf(" Please report this bug to jrs@cs.berkeley.edu\n"); printf(" Include the message above, your input data set, and the exact\n"); printf(" command line you used to run Triangle.\n"); exit(1); } /*****************************************************************************/ /* */ /* parsecommandline() Read the command line, identify switches, and set */ /* up options and file names. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void parsecommandline(int argc, char **argv, struct behavior *b) #else /* not ANSI_DECLARATORS */ void parsecommandline(argc, argv, b) int argc; char **argv; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { #ifdef TRILIBRARY #define STARTINDEX 0 #else /* not TRILIBRARY */ #define STARTINDEX 1 int increment; int meshnumber; #endif /* not TRILIBRARY */ int i, j, k; char workstring[FILENAMESIZE]; b->poly = b->refine = b->quality = 0; b->vararea = b->fixedarea = b->usertest = 0; b->regionattrib = b->convex = b->weighted = b->jettison = 0; b->firstnumber = 1; b->edgesout = b->voronoi = b->neighbors = b->geomview = 0; b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0; b->noiterationnum = 0; b->noholes = b->noexact = 0; b->incremental = b->sweepline = 0; b->dwyer = 1; b->splitseg = 0; b->docheck = 0; b->nobisect = 0; b->nolenses = 0; b->steiner = -1; b->order = 1; b->minangle = 0.0; b->maxarea = -1.0; b->quiet = b->verbose = 0; #ifndef TRILIBRARY b->innodefilename[0] = '\0'; #endif /* not TRILIBRARY */ for (i = STARTINDEX; i < argc; i++) { #ifndef TRILIBRARY if (argv[i][0] == '-') { #endif /* not TRILIBRARY */ for (j = STARTINDEX; argv[i][j] != '\0'; j++) { if (argv[i][j] == 'p') { b->poly = 1; } #ifndef CDT_ONLY if (argv[i][j] == 'r') { b->refine = 1; } if (argv[i][j] == 'q') { b->quality = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; b->minangle = (REAL) strtod(workstring, (char **) NULL); } else { b->minangle = 20.0; } } if (argv[i][j] == 'a') { b->quality = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { b->fixedarea = 1; k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; b->maxarea = (REAL) strtod(workstring, (char **) NULL); if (b->maxarea <= 0.0) { printf("Error: Maximum area must be greater than zero.\n"); exit(1); } } else { b->vararea = 1; } } if (argv[i][j] == 'u') { b->quality = 1; b->usertest = 1; } #endif /* not CDT_ONLY */ if (argv[i][j] == 'A') { b->regionattrib = 1; } if (argv[i][j] == 'c') { b->convex = 1; } if (argv[i][j] == 'w') { b->weighted = 1; } if (argv[i][j] == 'W') { b->weighted = 2; } if (argv[i][j] == 'j') { b->jettison = 1; } if (argv[i][j] == 'z') { b->firstnumber = 0; } if (argv[i][j] == 'e') { b->edgesout = 1; } if (argv[i][j] == 'v') { b->voronoi = 1; } if (argv[i][j] == 'n') { b->neighbors = 1; } if (argv[i][j] == 'g') { b->geomview = 1; } if (argv[i][j] == 'B') { b->nobound = 1; } if (argv[i][j] == 'P') { b->nopolywritten = 1; } if (argv[i][j] == 'N') { b->nonodewritten = 1; } if (argv[i][j] == 'E') { b->noelewritten = 1; } #ifndef TRILIBRARY if (argv[i][j] == 'I') { b->noiterationnum = 1; } #endif /* not TRILIBRARY */ if (argv[i][j] == 'O') { b->noholes = 1; } if (argv[i][j] == 'X') { b->noexact = 1; } if (argv[i][j] == 'o') { if (argv[i][j + 1] == '2') { j++; b->order = 2; } } #ifndef CDT_ONLY if (argv[i][j] == 'Y') { b->nobisect++; } if (argv[i][j] == 'S') { b->steiner = 0; while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { j++; b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0'); } } #endif /* not CDT_ONLY */ #ifndef REDUCED if (argv[i][j] == 'i') { b->incremental = 1; } if (argv[i][j] == 'F') { b->sweepline = 1; } #endif /* not REDUCED */ if (argv[i][j] == 'l') { b->dwyer = 0; } #ifndef REDUCED #ifndef CDT_ONLY if (argv[i][j] == 's') { b->splitseg = 1; } if (argv[i][j] == 'L') { b->nolenses = 1; } #endif /* not CDT_ONLY */ if (argv[i][j] == 'C') { b->docheck = 1; } #endif /* not REDUCED */ if (argv[i][j] == 'Q') { b->quiet = 1; } if (argv[i][j] == 'V') { b->verbose++; } #ifndef TRILIBRARY if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || (argv[i][j] == '?')) { info(); } #endif /* not TRILIBRARY */ } #ifndef TRILIBRARY } else { strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1); b->innodefilename[FILENAMESIZE - 1] = '\0'; } #endif /* not TRILIBRARY */ } #ifndef TRILIBRARY if (b->innodefilename[0] == '\0') { syntax(); } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; b->poly = 1; } #ifndef CDT_ONLY if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) { b->innodefilename[strlen(b->innodefilename) - 4] = '\0'; b->refine = 1; } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; b->refine = 1; b->quality = 1; b->vararea = 1; } #endif /* not CDT_ONLY */ #endif /* not TRILIBRARY */ b->usesegments = b->poly || b->refine || b->quality || b->convex; b->goodangle = cos(b->minangle * PI / 180.0); b->goodangle *= b->goodangle; if (b->refine && b->noiterationnum) { printf( "Error: You cannot use the -I switch when refining a triangulation.\n"); exit(1); } /* Be careful not to allocate space for element area constraints that */ /* will never be assigned any value (other than the default -1.0). */ if (!b->refine && !b->poly) { b->vararea = 0; } /* Be careful not to add an extra attribute to each element unless the */ /* input supports it (PSLG in, but not refining a preexisting mesh). */ if (b->refine || !b->poly) { b->regionattrib = 0; } /* Regular/weighted triangulations are incompatible with PSLGs */ /* and meshing. */ if (b->weighted && (b->poly || b->quality)) { b->weighted = 0; if (!b->quiet) { printf("Warning: weighted triangulations (-w, -W) are incompatible\n"); printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n" ); } } if (b->jettison && b->nonodewritten && !b->quiet) { printf("Warning: -j and -N switches are somewhat incompatible.\n"); printf(" If any vertices are jettisoned, you will need the output\n"); printf(" .node file to reconstruct the new node indices."); } #ifndef TRILIBRARY strcpy(b->inpolyfilename, b->innodefilename); strcpy(b->inelefilename, b->innodefilename); strcpy(b->areafilename, b->innodefilename); increment = 0; strcpy(workstring, b->innodefilename); j = 1; while (workstring[j] != '\0') { if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { increment = j + 1; } j++; } meshnumber = 0; if (increment > 0) { j = increment; do { if ((workstring[j] >= '0') && (workstring[j] <= '9')) { meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); } else { increment = 0; } j++; } while (workstring[j] != '\0'); } if (b->noiterationnum) { strcpy(b->outnodefilename, b->innodefilename); strcpy(b->outelefilename, b->innodefilename); strcpy(b->edgefilename, b->innodefilename); strcpy(b->vnodefilename, b->innodefilename); strcpy(b->vedgefilename, b->innodefilename); strcpy(b->neighborfilename, b->innodefilename); strcpy(b->offfilename, b->innodefilename); strcat(b->outnodefilename, ".node"); strcat(b->outelefilename, ".ele"); strcat(b->edgefilename, ".edge"); strcat(b->vnodefilename, ".v.node"); strcat(b->vedgefilename, ".v.edge"); strcat(b->neighborfilename, ".neigh"); strcat(b->offfilename, ".off"); } else if (increment == 0) { strcpy(b->outnodefilename, b->innodefilename); strcpy(b->outpolyfilename, b->innodefilename); strcpy(b->outelefilename, b->innodefilename); strcpy(b->edgefilename, b->innodefilename); strcpy(b->vnodefilename, b->innodefilename); strcpy(b->vedgefilename, b->innodefilename); strcpy(b->neighborfilename, b->innodefilename); strcpy(b->offfilename, b->innodefilename); strcat(b->outnodefilename, ".1.node"); strcat(b->outpolyfilename, ".1.poly"); strcat(b->outelefilename, ".1.ele"); strcat(b->edgefilename, ".1.edge"); strcat(b->vnodefilename, ".1.v.node"); strcat(b->vedgefilename, ".1.v.edge"); strcat(b->neighborfilename, ".1.neigh"); strcat(b->offfilename, ".1.off"); } else { workstring[increment] = '%'; workstring[increment + 1] = 'd'; workstring[increment + 2] = '\0'; sprintf(b->outnodefilename, workstring, meshnumber + 1); strcpy(b->outpolyfilename, b->outnodefilename); strcpy(b->outelefilename, b->outnodefilename); strcpy(b->edgefilename, b->outnodefilename); strcpy(b->vnodefilename, b->outnodefilename); strcpy(b->vedgefilename, b->outnodefilename); strcpy(b->neighborfilename, b->outnodefilename); strcpy(b->offfilename, b->outnodefilename); strcat(b->outnodefilename, ".node"); strcat(b->outpolyfilename, ".poly"); strcat(b->outelefilename, ".ele"); strcat(b->edgefilename, ".edge"); strcat(b->vnodefilename, ".v.node"); strcat(b->vedgefilename, ".v.edge"); strcat(b->neighborfilename, ".neigh"); strcat(b->offfilename, ".off"); } strcat(b->innodefilename, ".node"); strcat(b->inpolyfilename, ".poly"); strcat(b->inelefilename, ".ele"); strcat(b->areafilename, ".area"); #endif /* not TRILIBRARY */ } /** **/ /** **/ /********* User interaction routines begin here *********/ /********* Debugging routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* printtriangle() Print out the details of an oriented triangle. */ /* */ /* I originally wrote this procedure to simplify debugging; it can be */ /* called directly from the debugger, and presents information about an */ /* oriented triangle in digestible form. It's also used when the */ /* highest level of verbosity (`-VVV') is specified. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void printtriangle(struct mesh *m, struct behavior *b, struct otri *t) #else /* not ANSI_DECLARATORS */ void printtriangle(m, b, t) struct mesh *m; struct behavior *b; struct otri *t; #endif /* not ANSI_DECLARATORS */ { struct otri printtri; struct osub printsh; vertex printvertex; printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri, t->orient); decode(t->tri[0], printtri); if (printtri.tri == m->dummytri) { printf(" [0] = Outer space\n"); } else { printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(t->tri[1], printtri); if (printtri.tri == m->dummytri) { printf(" [1] = Outer space\n"); } else { printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(t->tri[2], printtri); if (printtri.tri == m->dummytri) { printf(" [2] = Outer space\n"); } else { printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } org(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); else printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", (t->orient + 1) % 3 + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); dest(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); else printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", (t->orient + 2) % 3 + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); apex(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Apex [%d] = NULL\n", t->orient + 3); else printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", t->orient + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); if (b->usesegments) { sdecode(t->tri[6], printsh); if (printsh.ss != m->dummysub) { printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(t->tri[7], printsh); if (printsh.ss != m->dummysub) { printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(t->tri[8], printsh); if (printsh.ss != m->dummysub) { printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } } if (b->vararea) { printf(" Area constraint: %.4g\n", areabound(*t)); } } /*****************************************************************************/ /* */ /* printsubseg() Print out the details of an oriented subsegment. */ /* */ /* I originally wrote this procedure to simplify debugging; it can be */ /* called directly from the debugger, and presents information about an */ /* oriented subsegment in digestible form. It's also used when the highest */ /* level of verbosity (`-VVV') is specified. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void printsubseg(struct mesh *m, struct behavior *b, struct osub *s) #else /* not ANSI_DECLARATORS */ void printsubseg(m, b, s) struct mesh *m; struct behavior *b; struct osub *s; #endif /* not ANSI_DECLARATORS */ { struct osub printsh; struct otri printtri; vertex printvertex; printf("subsegment x%lx with orientation %d and mark %d:\n", (unsigned long) s->ss, s->ssorient, mark(*s)); sdecode(s->ss[0], printsh); if (printsh.ss == m->dummysub) { printf(" [0] = No subsegment\n"); } else { printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(s->ss[1], printsh); if (printsh.ss == m->dummysub) { printf(" [1] = No subsegment\n"); } else { printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sorg(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Origin[%d] = NULL\n", 2 + s->ssorient); else printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", 2 + s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]); sdest(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Dest [%d] = NULL\n", 3 - s->ssorient); else printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", 3 - s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]); decode(s->ss[4], printtri); if (printtri.tri == m->dummytri) { printf(" [4] = Outer space\n"); } else { printf(" [4] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(s->ss[5], printtri); if (printtri.tri == m->dummytri) { printf(" [5] = Outer space\n"); } else { printf(" [5] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } } /** **/ /** **/ /********* Debugging routines end here *********/ /********* Memory management routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* poolrestart() Deallocate all items in a pool. */ /* */ /* The pool is returned to its starting state, except that no memory is */ /* freed to the operating system. Rather, the previously allocated blocks */ /* are ready to be reused. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void poolrestart(struct memorypool *pool) #else /* not ANSI_DECLARATORS */ void poolrestart(pool) struct memorypool *pool; #endif /* not ANSI_DECLARATORS */ { unsigned long alignptr; pool->items = 0; pool->maxitems = 0; /* Set the currently active block. */ pool->nowblock = pool->firstblock; /* Find the first item in the pool. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->nowblock + 1); /* Align the item on an `alignbytes'-byte boundary. */ pool->nextitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* There are lots of unallocated items left in this block. */ pool->unallocateditems = pool->itemsperblock; /* The stack of deallocated items is empty. */ pool->deaditemstack = (VOID *) NULL; } /*****************************************************************************/ /* */ /* poolinit() Initialize a pool of memory for allocation of items. */ /* */ /* This routine initializes the machinery for allocating items. A `pool' */ /* is created whose records have size at least `bytecount'. Items will be */ /* allocated in `itemcount'-item blocks. Each item is assumed to be a */ /* collection of words, and either pointers or floating-point values are */ /* assumed to be the "primary" word type. (The "primary" word type is used */ /* to determine alignment of items.) If `alignment' isn't zero, all items */ /* will be `alignment'-byte aligned in memory. `alignment' must be either */ /* a multiple or a factor of the primary word size; powers of two are safe. */ /* `alignment' is normally used to create a few unused bits at the bottom */ /* of each item's pointer, in which information may be stored. */ /* */ /* Don't change this routine unless you understand it. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void poolinit(struct memorypool *pool, int bytecount, int itemcount, enum wordtype wtype, int alignment) #else /* not ANSI_DECLARATORS */ void poolinit(pool, bytecount, itemcount, wtype, alignment) struct memorypool *pool; int bytecount; int itemcount; enum wordtype wtype; int alignment; #endif /* not ANSI_DECLARATORS */ { int wordsize; /* Initialize values in the pool. */ pool->itemwordtype = wtype; wordsize = (pool->itemwordtype == POINTER) ? sizeof(VOID *) : sizeof(REAL); /* Find the proper alignment, which must be at least as large as: */ /* - The parameter `alignment'. */ /* - The primary word type, to avoid unaligned accesses. */ /* - sizeof(VOID *), so the stack of dead items can be maintained */ /* without unaligned accesses. */ if (alignment > wordsize) { pool->alignbytes = alignment; } else { pool->alignbytes = wordsize; } if (sizeof(VOID *) > pool->alignbytes) { pool->alignbytes = sizeof(VOID *); } pool->itemwords = ((bytecount + pool->alignbytes - 1) / pool->alignbytes) * (pool->alignbytes / wordsize); pool->itembytes = pool->itemwords * wordsize; pool->itemsperblock = itemcount; /* Allocate a block of items. Space for `itemsperblock' items and one */ /* pointer (to point to the next block) are allocated, as well as space */ /* to ensure alignment of the items. */ pool->firstblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes + sizeof(VOID *) + pool->alignbytes); /* Set the next block pointer to NULL. */ *(pool->firstblock) = (VOID *) NULL; poolrestart(pool); } /*****************************************************************************/ /* */ /* pooldeinit() Free to the operating system all memory taken by a pool. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void pooldeinit(struct memorypool *pool) #else /* not ANSI_DECLARATORS */ void pooldeinit(pool) struct memorypool *pool; #endif /* not ANSI_DECLARATORS */ { while (pool->firstblock != (VOID **) NULL) { pool->nowblock = (VOID **) *(pool->firstblock); trifree((VOID *) pool->firstblock); pool->firstblock = pool->nowblock; } } /*****************************************************************************/ /* */ /* poolalloc() Allocate space for an item. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS VOID *poolalloc(struct memorypool *pool) #else /* not ANSI_DECLARATORS */ VOID *poolalloc(pool) struct memorypool *pool; #endif /* not ANSI_DECLARATORS */ { VOID *newitem; VOID **newblock; unsigned long alignptr; /* First check the linked list of dead items. If the list is not */ /* empty, allocate an item from the list rather than a fresh one. */ if (pool->deaditemstack != (VOID *) NULL) { newitem = pool->deaditemstack; /* Take first item in list. */ pool->deaditemstack = * (VOID **) pool->deaditemstack; } else { /* Check if there are any free items left in the current block. */ if (pool->unallocateditems == 0) { /* Check if another block must be allocated. */ if (*(pool->nowblock) == (VOID *) NULL) { /* Allocate a new block of items, pointed to by the previous block. */ newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes + sizeof(VOID *) + pool->alignbytes); *(pool->nowblock) = (VOID *) newblock; /* The next block pointer is NULL. */ *newblock = (VOID *) NULL; } /* Move to the new block. */ pool->nowblock = (VOID **) *(pool->nowblock); /* Find the first item in the block. */ /* Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->nowblock + 1); /* Align the item on an `alignbytes'-byte boundary. */ pool->nextitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* There are lots of unallocated items left in this block. */ pool->unallocateditems = pool->itemsperblock; } /* Allocate a new item. */ newitem = pool->nextitem; /* Advance `nextitem' pointer to next free item in block. */ if (pool->itemwordtype == POINTER) { pool->nextitem = (VOID *) ((VOID **) pool->nextitem + pool->itemwords); } else { pool->nextitem = (VOID *) ((REAL *) pool->nextitem + pool->itemwords); } pool->unallocateditems--; pool->maxitems++; } pool->items++; return newitem; } /*****************************************************************************/ /* */ /* pooldealloc() Deallocate space for an item. */ /* */ /* The deallocated space is stored in a queue for later reuse. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void pooldealloc(struct memorypool *pool, VOID *dyingitem) #else /* not ANSI_DECLARATORS */ void pooldealloc(pool, dyingitem) struct memorypool *pool; VOID *dyingitem; #endif /* not ANSI_DECLARATORS */ { /* Push freshly killed item onto stack. */ *((VOID **) dyingitem) = pool->deaditemstack; pool->deaditemstack = dyingitem; pool->items--; } /*****************************************************************************/ /* */ /* traversalinit() Prepare to traverse the entire list of items. */ /* */ /* This routine is used in conjunction with traverse(). */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void traversalinit(struct memorypool *pool) #else /* not ANSI_DECLARATORS */ void traversalinit(pool) struct memorypool *pool; #endif /* not ANSI_DECLARATORS */ { unsigned long alignptr; /* Begin the traversal in the first block. */ pool->pathblock = pool->firstblock; /* Find the first item in the block. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->pathblock + 1); /* Align with item on an `alignbytes'-byte boundary. */ pool->pathitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* Set the number of items left in the current block. */ pool->pathitemsleft = pool->itemsperblock; } /*****************************************************************************/ /* */ /* traverse() Find the next item in the list. */ /* */ /* This routine is used in conjunction with traversalinit(). Be forewarned */ /* that this routine successively returns all items in the list, including */ /* deallocated ones on the deaditemqueue. It's up to you to figure out */ /* which ones are actually dead. Why? I don't want to allocate extra */ /* space just to demarcate dead items. It can usually be done more */ /* space-efficiently by a routine that knows something about the structure */ /* of the item. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS VOID *traverse(struct memorypool *pool) #else /* not ANSI_DECLARATORS */ VOID *traverse(pool) struct memorypool *pool; #endif /* not ANSI_DECLARATORS */ { VOID *newitem; unsigned long alignptr; /* Stop upon exhausting the list of items. */ if (pool->pathitem == pool->nextitem) { return (VOID *) NULL; } /* Check whether any untraversed items remain in the current block. */ if (pool->pathitemsleft == 0) { /* Find the next block. */ pool->pathblock = (VOID **) *(pool->pathblock); /* Find the first item in the block. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->pathblock + 1); /* Align with item on an `alignbytes'-byte boundary. */ pool->pathitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* Set the number of items left in the current block. */ pool->pathitemsleft = pool->itemsperblock; } newitem = pool->pathitem; /* Find the next item in the block. */ if (pool->itemwordtype == POINTER) { pool->pathitem = (VOID *) ((VOID **) pool->pathitem + pool->itemwords); } else { pool->pathitem = (VOID *) ((REAL *) pool->pathitem + pool->itemwords); } pool->pathitemsleft--; return newitem; } /*****************************************************************************/ /* */ /* dummyinit() Initialize the triangle that fills "outer space" and the */ /* omnipresent subsegment. */ /* */ /* The triangle that fills "outer space," called `dummytri', is pointed to */ /* by every triangle and subsegment on a boundary (be it outer or inner) of */ /* the triangulation. Also, `dummytri' points to one of the triangles on */ /* the convex hull (until the holes and concavities are carved), making it */ /* possible to find a starting triangle for point location. */ /* */ /* The omnipresent subsegment, `dummysub', is pointed to by every triangle */ /* or subsegment that doesn't have a full complement of real subsegments */ /* to point to. */ /* */ /* `dummytri' and `dummysub' are generally required to fulfill only a few */ /* invariants: their vertices must remain NULL and `dummytri' must always */ /* be bonded (at offset zero) to some triangle on the convex hull of the */ /* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */ /* `dummysub' may change willy-nilly. This makes it possible to avoid */ /* writing a good deal of special-case code (in the edge flip, for example) */ /* for dealing with the boundary of the mesh, places where no subsegment is */ /* present, and so forth. Other entities are frequently bonded to */ /* `dummytri' and `dummysub' as if they were real mesh entities, with no */ /* harm done. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void dummyinit(struct mesh *m, struct behavior *b, int trianglewords, int subsegwords) #else /* not ANSI_DECLARATORS */ void dummyinit(m, b, trianglewords, subsegwords) struct mesh *m; struct behavior *b; int trianglewords; int subsegwords; #endif /* not ANSI_DECLARATORS */ { unsigned long alignptr; /* Set up `dummytri', the `triangle' that occupies "outer space." */ m->dummytribase = (triangle *) trimalloc(trianglewords * sizeof(triangle) + m->triangles.alignbytes); /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ alignptr = (unsigned long) m->dummytribase; m->dummytri = (triangle *) (alignptr + (unsigned long) m->triangles.alignbytes - (alignptr % (unsigned long) m->triangles.alignbytes)); /* Initialize the three adjoining triangles to be "outer space." These */ /* will eventually be changed by various bonding operations, but their */ /* values don't really matter, as long as they can legally be */ /* dereferenced. */ m->dummytri[0] = (triangle) m->dummytri; m->dummytri[1] = (triangle) m->dummytri; m->dummytri[2] = (triangle) m->dummytri; /* Three NULL vertices. */ m->dummytri[3] = (triangle) NULL; m->dummytri[4] = (triangle) NULL; m->dummytri[5] = (triangle) NULL; if (b->usesegments) { /* Set up `dummysub', the omnipresent subsegment pointed to by any */ /* triangle side or subsegment end that isn't attached to a real */ /* subsegment. */ m->dummysubbase = (subseg *) trimalloc(subsegwords * sizeof(subseg) + m->subsegs.alignbytes); /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */ alignptr = (unsigned long) m->dummysubbase; m->dummysub = (subseg *) (alignptr + (unsigned long) m->subsegs.alignbytes - (alignptr % (unsigned long) m->subsegs.alignbytes)); /* Initialize the two adjoining subsegments to be the omnipresent */ /* subsegment. These will eventually be changed by various bonding */ /* operations, but their values don't really matter, as long as they */ /* can legally be dereferenced. */ m->dummysub[0] = (subseg) m->dummysub; m->dummysub[1] = (subseg) m->dummysub; /* Two NULL vertices. */ m->dummysub[2] = (subseg) NULL; m->dummysub[3] = (subseg) NULL; /* Initialize the two adjoining triangles to be "outer space." */ m->dummysub[4] = (subseg) m->dummytri; m->dummysub[5] = (subseg) m->dummytri; /* Set the boundary marker to zero. */ * (int *) (m->dummysub + 6) = 0; /* Initialize the three adjoining subsegments of `dummytri' to be */ /* the omnipresent subsegment. */ m->dummytri[6] = (triangle) m->dummysub; m->dummytri[7] = (triangle) m->dummysub; m->dummytri[8] = (triangle) m->dummysub; } } /*****************************************************************************/ /* */ /* initializevertexpool() Calculate the size of the vertex data structure */ /* and initialize its memory pool. */ /* */ /* This routine also computes the `vertexmarkindex' and `vertex2triindex' */ /* indices used to find values within each vertex. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void initializevertexpool(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void initializevertexpool(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { int vertexsize; /* The index within each vertex at which the boundary marker is found, */ /* followed by the vertex type. Ensure the vertex marker is aligned to */ /* a sizeof(int)-byte address. */ m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) + sizeof(int) - 1) / sizeof(int); vertexsize = (m->vertexmarkindex + 2) * sizeof(int); if (b->poly) { /* The index within each vertex at which a triangle pointer is found. */ /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) / sizeof(triangle); vertexsize = (m->vertex2triindex + 1) * sizeof(triangle); } /* Initialize the pool of vertices. */ poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK, (sizeof(REAL) >= sizeof(triangle)) ? FLOATINGPOINT : POINTER, 0); } /*****************************************************************************/ /* */ /* initializetrisubpools() Calculate the sizes of the triangle and */ /* subsegment data structures and initialize */ /* their memory pools. */ /* */ /* This routine also computes the `highorderindex', `elemattribindex', and */ /* `areaboundindex' indices used to find values within each triangle. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void initializetrisubpools(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void initializetrisubpools(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { int trisize; /* The index within each triangle at which the extra nodes (above three) */ /* associated with high order elements are found. There are three */ /* pointers to other triangles, three pointers to corners, and possibly */ /* three pointers to subsegments before the extra nodes. */ m->highorderindex = 6 + (b->usesegments * 3); /* The number of bytes occupied by a triangle. */ trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) * sizeof(triangle); /* The index within each triangle at which its attributes are found, */ /* where the index is measured in REALs. */ m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL); /* The index within each triangle at which the maximum area constraint */ /* is found, where the index is measured in REALs. Note that if the */ /* `regionattrib' flag is set, an additional attribute will be added. */ m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib; /* If triangle attributes or an area bound are needed, increase the number */ /* of bytes occupied by a triangle. */ if (b->vararea) { trisize = (m->areaboundindex + 1) * sizeof(REAL); } else if (m->eextras + b->regionattrib > 0) { trisize = m->areaboundindex * sizeof(REAL); } /* If a Voronoi diagram or triangle neighbor graph is requested, make */ /* sure there's room to store an integer index in each triangle. This */ /* integer index can occupy the same space as the subsegment pointers */ /* or attributes or area constraint or extra nodes. */ if ((b->voronoi || b->neighbors) && (trisize < 6 * sizeof(triangle) + sizeof(int))) { trisize = 6 * sizeof(triangle) + sizeof(int); } /* Having determined the memory size of a triangle, initialize the pool. */ poolinit(&m->triangles, trisize, TRIPERBLOCK, POINTER, 4); if (b->usesegments) { /* Initialize the pool of subsegments. Take into account all six */ /* pointers and one boundary marker. */ poolinit(&m->subsegs, 6 * sizeof(triangle) + sizeof(int), SUBSEGPERBLOCK, POINTER, 4); /* Initialize the "outer space" triangle and omnipresent subsegment. */ dummyinit(m, b, m->triangles.itemwords, m->subsegs.itemwords); } else { /* Initialize the "outer space" triangle. */ dummyinit(m, b, m->triangles.itemwords, 0); } } /*****************************************************************************/ /* */ /* triangledealloc() Deallocate space for a triangle, marking it dead. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void triangledealloc(struct mesh *m, triangle *dyingtriangle) #else /* not ANSI_DECLARATORS */ void triangledealloc(m, dyingtriangle) struct mesh *m; triangle *dyingtriangle; #endif /* not ANSI_DECLARATORS */ { /* Mark the triangle as dead. This makes it possible to detect dead */ /* triangles when traversing the list of all triangles. */ killtri(dyingtriangle); pooldealloc(&m->triangles, (VOID *) dyingtriangle); } /*****************************************************************************/ /* */ /* triangletraverse() Traverse the triangles, skipping dead ones. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS triangle *triangletraverse(struct mesh *m) #else /* not ANSI_DECLARATORS */ triangle *triangletraverse(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { triangle *newtriangle; do { newtriangle = (triangle *) traverse(&m->triangles); if (newtriangle == (triangle *) NULL) { return (triangle *) NULL; } } while (deadtri(newtriangle)); /* Skip dead ones. */ return newtriangle; } /*****************************************************************************/ /* */ /* subsegdealloc() Deallocate space for a subsegment, marking it dead. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void subsegdealloc(struct mesh *m, subseg *dyingsubseg) #else /* not ANSI_DECLARATORS */ void subsegdealloc(m, dyingsubseg) struct mesh *m; subseg *dyingsubseg; #endif /* not ANSI_DECLARATORS */ { /* Mark the subsegment as dead. This makes it possible to detect dead */ /* subsegments when traversing the list of all subsegments. */ killsubseg(dyingsubseg); pooldealloc(&m->subsegs, (VOID *) dyingsubseg); } /*****************************************************************************/ /* */ /* subsegtraverse() Traverse the subsegments, skipping dead ones. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS subseg *subsegtraverse(struct mesh *m) #else /* not ANSI_DECLARATORS */ subseg *subsegtraverse(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { subseg *newsubseg; do { newsubseg = (subseg *) traverse(&m->subsegs); if (newsubseg == (subseg *) NULL) { return (subseg *) NULL; } } while (deadsubseg(newsubseg)); /* Skip dead ones. */ return newsubseg; } /*****************************************************************************/ /* */ /* vertexdealloc() Deallocate space for a vertex, marking it dead. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void vertexdealloc(struct mesh *m, vertex dyingvertex) #else /* not ANSI_DECLARATORS */ void vertexdealloc(m, dyingvertex) struct mesh *m; vertex dyingvertex; #endif /* not ANSI_DECLARATORS */ { /* Mark the vertex as dead. This makes it possible to detect dead */ /* vertices when traversing the list of all vertices. */ setvertextype(dyingvertex, DEADVERTEX); pooldealloc(&m->vertices, (VOID *) dyingvertex); } /*****************************************************************************/ /* */ /* vertextraverse() Traverse the vertices, skipping dead ones. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS vertex vertextraverse(struct mesh *m) #else /* not ANSI_DECLARATORS */ vertex vertextraverse(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { vertex newvertex; do { newvertex = (vertex) traverse(&m->vertices); if (newvertex == (vertex) NULL) { return (vertex) NULL; } } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */ return newvertex; } /*****************************************************************************/ /* */ /* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */ /* dead. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg) #else /* not ANSI_DECLARATORS */ void badsubsegdealloc(m, dyingseg) struct mesh *m; struct badsubseg *dyingseg; #endif /* not ANSI_DECLARATORS */ { /* Set subsegment's origin to NULL. This makes it possible to detect dead */ /* subsegments when traversing the list of all encroached subsegments. */ dyingseg->subsegorg = (vertex) NULL; pooldealloc(&m->badsubsegs, (VOID *) dyingseg); } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS struct badsubseg *badsubsegtraverse(struct mesh *m) #else /* not ANSI_DECLARATORS */ struct badsubseg *badsubsegtraverse(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { struct badsubseg *newseg; do { newseg = (struct badsubseg *) traverse(&m->badsubsegs); if (newseg == (struct badsubseg *) NULL) { return (struct badsubseg *) NULL; } } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */ return newseg; } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* getvertex() Get a specific vertex, by number, from the list. */ /* */ /* The first vertex is number 'firstnumber'. */ /* */ /* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */ /* is large). I don't care to take the trouble to make it work in constant */ /* time. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS vertex getvertex(struct mesh *m, struct behavior *b, int number) #else /* not ANSI_DECLARATORS */ vertex getvertex(m, b, number) struct mesh *m; struct behavior *b; int number; #endif /* not ANSI_DECLARATORS */ { VOID **getblock; vertex foundvertex; unsigned long alignptr; int current; getblock = m->vertices.firstblock; current = b->firstnumber; /* Find the right block. */ while (current + m->vertices.itemsperblock <= number) { getblock = (VOID **) *getblock; current += m->vertices.itemsperblock; } /* Now find the right vertex. */ alignptr = (unsigned long) (getblock + 1); foundvertex = (vertex) (alignptr + (unsigned long) m->vertices.alignbytes - (alignptr % (unsigned long) m->vertices.alignbytes)); while (current < number) { foundvertex += m->vertices.itemwords; current++; } return foundvertex; } /*****************************************************************************/ /* */ /* triangledeinit() Free all remaining allocated memory. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void triangledeinit(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void triangledeinit(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { pooldeinit(&m->triangles); trifree((VOID *) m->dummytribase); if (b->usesegments) { pooldeinit(&m->subsegs); trifree((VOID *) m->dummysubbase); } pooldeinit(&m->vertices); #ifndef CDT_ONLY if (b->quality) { pooldeinit(&m->badsubsegs); if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { pooldeinit(&m->badtriangles); pooldeinit(&m->flipstackers); } } #endif /* not CDT_ONLY */ } /** **/ /** **/ /********* Memory management routines end here *********/ /********* Constructors begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* maketriangle() Create a new triangle with orientation zero. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri) #else /* not ANSI_DECLARATORS */ void maketriangle(m, b, newotri) struct mesh *m; struct behavior *b; struct otri *newotri; #endif /* not ANSI_DECLARATORS */ { int i; newotri->tri = (triangle *) poolalloc(&m->triangles); /* Initialize the three adjoining triangles to be "outer space". */ newotri->tri[0] = (triangle) m->dummytri; newotri->tri[1] = (triangle) m->dummytri; newotri->tri[2] = (triangle) m->dummytri; /* Three NULL vertices. */ newotri->tri[3] = (triangle) NULL; newotri->tri[4] = (triangle) NULL; newotri->tri[5] = (triangle) NULL; if (b->usesegments) { /* Initialize the three adjoining subsegments to be the omnipresent */ /* subsegment. */ newotri->tri[6] = (triangle) m->dummysub; newotri->tri[7] = (triangle) m->dummysub; newotri->tri[8] = (triangle) m->dummysub; } for (i = 0; i < m->eextras; i++) { setelemattribute(*newotri, i, 0.0); } if (b->vararea) { setareabound(*newotri, -1.0); } newotri->orient = 0; } /*****************************************************************************/ /* */ /* makesubseg() Create a new subsegment with orientation zero. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void makesubseg(struct mesh *m, struct osub *newsubseg) #else /* not ANSI_DECLARATORS */ void makesubseg(m, newsubseg) struct mesh *m; struct osub *newsubseg; #endif /* not ANSI_DECLARATORS */ { newsubseg->ss = (subseg *) poolalloc(&m->subsegs); /* Initialize the two adjoining subsegments to be the omnipresent */ /* subsegment. */ newsubseg->ss[0] = (subseg) m->dummysub; newsubseg->ss[1] = (subseg) m->dummysub; /* Two NULL vertices. */ newsubseg->ss[2] = (subseg) NULL; newsubseg->ss[3] = (subseg) NULL; /* Initialize the two adjoining triangles to be "outer space." */ newsubseg->ss[4] = (subseg) m->dummytri; newsubseg->ss[5] = (subseg) m->dummytri; /* Set the boundary marker to zero. */ setmark(*newsubseg, 0); newsubseg->ssorient = 0; } /** **/ /** **/ /********* Constructors end here *********/ /********* Geometric primitives begin here *********/ /** **/ /** **/ /* The adaptive exact arithmetic geometric predicates implemented herein are */ /* described in detail in my paper, "Adaptive Precision Floating-Point */ /* Arithmetic and Fast Robust Geometric Predicates." See the header for a */ /* full citation. */ /* Which of the following two methods of finding the absolute values is */ /* fastest is compiler-dependent. A few compilers can inline and optimize */ /* the fabs() call; but most will incur the overhead of a function call, */ /* which is disastrously slow. A faster way on IEEE machines might be to */ /* mask the appropriate bit, but that's difficult to do in C without */ /* forcing the value to be stored to memory (rather than be kept in the */ /* register to which the optimizer assigned it). */ #define Absolute(a) ((a) >= 0.0 ? (a) : -(a)) /* #define Absolute(a) fabs(a) */ /* Many of the operations are broken up into two pieces, a main part that */ /* performs an approximate operation, and a "tail" that computes the */ /* roundoff error of that operation. */ /* */ /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */ /* Split(), and Two_Product() are all implemented as described in the */ /* reference. Each of these macros requires certain variables to be */ /* defined in the calling routine. The variables `bvirt', `c', `abig', */ /* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */ /* they store the result of an operation that may incur roundoff error. */ /* The input parameter `x' (or the highest numbered `x_' parameter) must */ /* also be declared `INEXACT'. */ #define Fast_Two_Sum_Tail(a, b, x, y) \ bvirt = x - a; \ y = b - bvirt #define Fast_Two_Sum(a, b, x, y) \ x = (REAL) (a + b); \ Fast_Two_Sum_Tail(a, b, x, y) #define Two_Sum_Tail(a, b, x, y) \ bvirt = (REAL) (x - a); \ avirt = x - bvirt; \ bround = b - bvirt; \ around = a - avirt; \ y = around + bround #define Two_Sum(a, b, x, y) \ x = (REAL) (a + b); \ Two_Sum_Tail(a, b, x, y) #define Two_Diff_Tail(a, b, x, y) \ bvirt = (REAL) (a - x); \ avirt = x + bvirt; \ bround = bvirt - b; \ around = a - avirt; \ y = around + bround #define Two_Diff(a, b, x, y) \ x = (REAL) (a - b); \ Two_Diff_Tail(a, b, x, y) #define Split(a, ahi, alo) \ c = (REAL) (splitter * a); \ abig = (REAL) (c - a); \ ahi = c - abig; \ alo = a - ahi #define Two_Product_Tail(a, b, x, y) \ Split(a, ahi, alo); \ Split(b, bhi, blo); \ err1 = x - (ahi * bhi); \ err2 = err1 - (alo * bhi); \ err3 = err2 - (ahi * blo); \ y = (alo * blo) - err3 #define Two_Product(a, b, x, y) \ x = (REAL) (a * b); \ Two_Product_Tail(a, b, x, y) /* Two_Product_Presplit() is Two_Product() where one of the inputs has */ /* already been split. Avoids redundant splitting. */ #define Two_Product_Presplit(a, b, bhi, blo, x, y) \ x = (REAL) (a * b); \ Split(a, ahi, alo); \ err1 = x - (ahi * bhi); \ err2 = err1 - (alo * bhi); \ err3 = err2 - (ahi * blo); \ y = (alo * blo) - err3 /* Square() can be done more quickly than Two_Product(). */ #define Square_Tail(a, x, y) \ Split(a, ahi, alo); \ err1 = x - (ahi * ahi); \ err3 = err1 - ((ahi + ahi) * alo); \ y = (alo * alo) - err3 #define Square(a, x, y) \ x = (REAL) (a * a); \ Square_Tail(a, x, y) /* Macros for summing expansions of various fixed lengths. These are all */ /* unrolled versions of Expansion_Sum(). */ #define Two_One_Sum(a1, a0, b, x2, x1, x0) \ Two_Sum(a0, b , _i, x0); \ Two_Sum(a1, _i, x2, x1) #define Two_One_Diff(a1, a0, b, x2, x1, x0) \ Two_Diff(a0, b , _i, x0); \ Two_Sum( a1, _i, x2, x1) #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ Two_One_Sum(a1, a0, b0, _j, _0, x0); \ Two_One_Sum(_j, _0, b1, x3, x2, x1) #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ Two_One_Diff(a1, a0, b0, _j, _0, x0); \ Two_One_Diff(_j, _0, b1, x3, x2, x1) /* Macro for multiplying a two-component expansion by a single component. */ #define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \ Split(b, bhi, blo); \ Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \ Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ Two_Sum(_i, _0, _k, x1); \ Fast_Two_Sum(_j, _k, x3, x2) /*****************************************************************************/ /* */ /* exactinit() Initialize the variables used for exact arithmetic. */ /* */ /* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */ /* floating-point arithmetic. `epsilon' bounds the relative roundoff */ /* error. It is used for floating-point error analysis. */ /* */ /* `splitter' is used to split floating-point numbers into two half- */ /* length significands for exact multiplication. */ /* */ /* I imagine that a highly optimizing compiler might be too smart for its */ /* own good, and somehow cause this routine to fail, if it pretends that */ /* floating-point arithmetic is too much like real arithmetic. */ /* */ /* Don't change this routine unless you fully understand it. */ /* */ /*****************************************************************************/ void exactinit(void) { REAL half; REAL check, lastcheck; int every_other; #ifdef LINUX int cword; #endif /* LINUX */ #ifdef CPU86 #ifdef SINGLE _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */ #else /* not SINGLE */ _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */ #endif /* not SINGLE */ #endif /* CPU86 */ #ifdef LINUX #ifdef SINGLE /* cword = 4223; */ cword = 4210; /* set FPU control word for single precision */ #else /* not SINGLE */ /* cword = 4735; */ cword = 4722; /* set FPU control word for double precision */ #endif /* not SINGLE */ _FPU_SETCW(cword); #endif /* LINUX */ every_other = 1; half = 0.5; epsilon = 1.0; splitter = 1.0; check = 1.0; /* Repeatedly divide `epsilon' by two until it is too small to add to */ /* one without causing roundoff. (Also check if the sum is equal to */ /* the previous sum, for machines that round up instead of using exact */ /* rounding. Not that these routines will work on such machines.) */ do { lastcheck = check; epsilon *= half; if (every_other) { splitter *= 2.0; } every_other = !every_other; check = 1.0 + epsilon; } while ((check != 1.0) && (check != lastcheck)); splitter += 1.0; /* Error bounds for orientation and incircle tests. */ resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon; o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon; o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon; } /*****************************************************************************/ /* */ /* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */ /* components from the output expansion. */ /* */ /* Sets h = e + f. See my Robust Predicates paper for details. */ /* */ /* If round-to-even is used (as with IEEE 754), maintains the strongly */ /* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */ /* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */ /* properties. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h) #else /* not ANSI_DECLARATORS */ int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */ int elen; REAL *e; int flen; REAL *f; REAL *h; #endif /* not ANSI_DECLARATORS */ { REAL Q; INEXACT REAL Qnew; INEXACT REAL hh; INEXACT REAL bvirt; REAL avirt, bround, around; int eindex, findex, hindex; REAL enow, fnow; enow = e[0]; fnow = f[0]; eindex = findex = 0; if ((fnow > enow) == (fnow > -enow)) { Q = enow; enow = e[++eindex]; } else { Q = fnow; fnow = f[++findex]; } hindex = 0; if ((eindex < elen) && (findex < flen)) { if ((fnow > enow) == (fnow > -enow)) { Fast_Two_Sum(enow, Q, Qnew, hh); enow = e[++eindex]; } else { Fast_Two_Sum(fnow, Q, Qnew, hh); fnow = f[++findex]; } Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } while ((eindex < elen) && (findex < flen)) { if ((fnow > enow) == (fnow > -enow)) { Two_Sum(Q, enow, Qnew, hh); enow = e[++eindex]; } else { Two_Sum(Q, fnow, Qnew, hh); fnow = f[++findex]; } Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } } while (eindex < elen) { Two_Sum(Q, enow, Qnew, hh); enow = e[++eindex]; Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } while (findex < flen) { Two_Sum(Q, fnow, Qnew, hh); fnow = f[++findex]; Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } if ((Q != 0.0) || (hindex == 0)) { h[hindex++] = Q; } return hindex; } /*****************************************************************************/ /* */ /* scale_expansion_zeroelim() Multiply an expansion by a scalar, */ /* eliminating zero components from the */ /* output expansion. */ /* */ /* Sets h = be. See my Robust Predicates paper for details. */ /* */ /* Maintains the nonoverlapping property. If round-to-even is used (as */ /* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */ /* properties as well. (That is, if e has one of these properties, so */ /* will h.) */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h) #else /* not ANSI_DECLARATORS */ int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */ int elen; REAL *e; REAL b; REAL *h; #endif /* not ANSI_DECLARATORS */ { INEXACT REAL Q, sum; REAL hh; INEXACT REAL product1; REAL product0; int eindex, hindex; REAL enow; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; Split(b, bhi, blo); Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); hindex = 0; if (hh != 0) { h[hindex++] = hh; } for (eindex = 1; eindex < elen; eindex++) { enow = e[eindex]; Two_Product_Presplit(enow, b, bhi, blo, product1, product0); Two_Sum(Q, product0, sum, hh); if (hh != 0) { h[hindex++] = hh; } Fast_Two_Sum(product1, sum, Q, hh); if (hh != 0) { h[hindex++] = hh; } } if ((Q != 0.0) || (hindex == 0)) { h[hindex++] = Q; } return hindex; } /*****************************************************************************/ /* */ /* estimate() Produce a one-word estimate of an expansion's value. */ /* */ /* See my Robust Predicates paper for details. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS REAL estimate(int elen, REAL *e) #else /* not ANSI_DECLARATORS */ REAL estimate(elen, e) int elen; REAL *e; #endif /* not ANSI_DECLARATORS */ { REAL Q; int eindex; Q = e[0]; for (eindex = 1; eindex < elen; eindex++) { Q += e[eindex]; } return Q; } /*****************************************************************************/ /* */ /* counterclockwise() Return a positive value if the points pa, pb, and */ /* pc occur in counterclockwise order; a negative */ /* value if they occur in clockwise order; and zero */ /* if they are collinear. The result is also a rough */ /* approximation of twice the signed area of the */ /* triangle defined by the three points. */ /* */ /* Uses exact arithmetic if necessary to ensure a correct answer. The */ /* result returned is the determinant of a matrix. This determinant is */ /* computed adaptively, in the sense that exact arithmetic is used only to */ /* the degree it is needed to ensure that the returned value has the */ /* correct sign. Hence, this function is usually quite fast, but will run */ /* more slowly when the input points are collinear or nearly so. */ /* */ /* See my Robust Predicates paper for details. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum) #else /* not ANSI_DECLARATORS */ REAL counterclockwiseadapt(pa, pb, pc, detsum) vertex pa; vertex pb; vertex pc; REAL detsum; #endif /* not ANSI_DECLARATORS */ { INEXACT REAL acx, acy, bcx, bcy; REAL acxtail, acytail, bcxtail, bcytail; INEXACT REAL detleft, detright; REAL detlefttail, detrighttail; REAL det, errbound; REAL B[4], C1[8], C2[12], D[16]; INEXACT REAL B3; int C1length, C2length, Dlength; REAL u[4]; INEXACT REAL u3; INEXACT REAL s1, t1; REAL s0, t0; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j; REAL _0; acx = (REAL) (pa[0] - pc[0]); bcx = (REAL) (pb[0] - pc[0]); acy = (REAL) (pa[1] - pc[1]); bcy = (REAL) (pb[1] - pc[1]); Two_Product(acx, bcy, detleft, detlefttail); Two_Product(acy, bcx, detright, detrighttail); Two_Two_Diff(detleft, detlefttail, detright, detrighttail, B3, B[2], B[1], B[0]); B[3] = B3; det = estimate(4, B); errbound = ccwerrboundB * detsum; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pc[0], acx, acxtail); Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); Two_Diff_Tail(pa[1], pc[1], acy, acytail); Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); if ((acxtail == 0.0) && (acytail == 0.0) && (bcxtail == 0.0) && (bcytail == 0.0)) { return det; } errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail); if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Product(acxtail, bcy, s1, s0); Two_Product(acytail, bcx, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); Two_Product(acx, bcytail, s1, s0); Two_Product(acy, bcxtail, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); Two_Product(acxtail, bcytail, s1, s0); Two_Product(acytail, bcxtail, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); return(D[Dlength - 1]); } #ifdef ANSI_DECLARATORS REAL counterclockwise(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc) #else /* not ANSI_DECLARATORS */ REAL counterclockwise(m, b, pa, pb, pc) struct mesh *m; struct behavior *b; vertex pa; vertex pb; vertex pc; #endif /* not ANSI_DECLARATORS */ { REAL detleft, detright, det; REAL detsum, errbound; m->counterclockcount++; detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); det = detleft - detright; if (b->noexact) { return det; } if (detleft > 0.0) { if (detright <= 0.0) { return det; } else { detsum = detleft + detright; } } else if (detleft < 0.0) { if (detright >= 0.0) { return det; } else { detsum = -detleft - detright; } } else { return det; } errbound = ccwerrboundA * detsum; if ((det >= errbound) || (-det >= errbound)) { return det; } return counterclockwiseadapt(pa, pb, pc, detsum); } /*****************************************************************************/ /* */ /* incircle() Return a positive value if the point pd lies inside the */ /* circle passing through pa, pb, and pc; a negative value if */ /* it lies outside; and zero if the four points are cocircular.*/ /* The points pa, pb, and pc must be in counterclockwise */ /* order, or the sign of the result will be reversed. */ /* */ /* Uses exact arithmetic if necessary to ensure a correct answer. The */ /* result returned is the determinant of a matrix. This determinant is */ /* computed adaptively, in the sense that exact arithmetic is used only to */ /* the degree it is needed to ensure that the returned value has the */ /* correct sign. Hence, this function is usually quite fast, but will run */ /* more slowly when the input points are cocircular or nearly so. */ /* */ /* See my Robust Predicates paper for details. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent) #else /* not ANSI_DECLARATORS */ REAL incircleadapt(pa, pb, pc, pd, permanent) vertex pa; vertex pb; vertex pc; vertex pd; REAL permanent; #endif /* not ANSI_DECLARATORS */ { INEXACT REAL adx, bdx, cdx, ady, bdy, cdy; REAL det, errbound; INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; REAL bc[4], ca[4], ab[4]; INEXACT REAL bc3, ca3, ab3; REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; int axbclen, axxbclen, aybclen, ayybclen, alen; REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32]; int bxcalen, bxxcalen, bycalen, byycalen, blen; REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32]; int cxablen, cxxablen, cyablen, cyyablen, clen; REAL abdet[64]; int ablen; REAL fin1[1152], fin2[1152]; REAL *finnow, *finother, *finswap; int finlength; REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; REAL aa[4], bb[4], cc[4]; INEXACT REAL aa3, bb3, cc3; INEXACT REAL ti1, tj1; REAL ti0, tj0; REAL u[4], v[4]; INEXACT REAL u3, v3; REAL temp8[8], temp16a[16], temp16b[16], temp16c[16]; REAL temp32a[32], temp32b[32], temp48[48], temp64[64]; int temp8len, temp16alen, temp16blen, temp16clen; int temp32alen, temp32blen, temp48len, temp64len; REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; int axtbblen, axtcclen, aytbblen, aytcclen; REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; int bxtaalen, bxtcclen, bytaalen, bytcclen; REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; int cxtaalen, cxtbblen, cytaalen, cytbblen; REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen; REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; REAL axtbctt[8], aytbctt[8], bxtcatt[8]; REAL bytcatt[8], cxtabtt[8], cytabtt[8]; int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; REAL abt[8], bct[8], cat[8]; int abtlen, bctlen, catlen; REAL abtt[4], bctt[4], catt[4]; int abttlen, bcttlen, cattlen; INEXACT REAL abtt3, bctt3, catt3; REAL negate; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j; REAL _0; adx = (REAL) (pa[0] - pd[0]); bdx = (REAL) (pb[0] - pd[0]); cdx = (REAL) (pc[0] - pd[0]); ady = (REAL) (pa[1] - pd[1]); bdy = (REAL) (pb[1] - pd[1]); cdy = (REAL) (pc[1] - pd[1]); Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); bc[3] = bc3; axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); Two_Product(cdx, ady, cdxady1, cdxady0); Two_Product(adx, cdy, adxcdy1, adxcdy0); Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); ca[3] = ca3; bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); Two_Product(adx, bdy, adxbdy1, adxbdy0); Two_Product(bdx, ady, bdxady1, bdxady0); Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); ab[3] = ab3; cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); det = estimate(finlength, fin1); errbound = iccerrboundB * permanent; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pd[0], adx, adxtail); Two_Diff_Tail(pa[1], pd[1], ady, adytail); Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) { return det; } errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); if ((det >= errbound) || (-det >= errbound)) { return det; } finnow = fin1; finother = fin2; if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) { Square(adx, adxadx1, adxadx0); Square(ady, adyady1, adyady0); Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); aa[3] = aa3; } if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) { Square(bdx, bdxbdx1, bdxbdx0); Square(bdy, bdybdy1, bdybdy0); Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); bb[3] = bb3; } if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) { Square(cdx, cdxcdx1, cdxcdx0); Square(cdy, cdycdy1, cdycdy0); Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); cc[3] = cc3; } if (adxtail != 0.0) { axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, temp16a); axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, temp16a); aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdxtail != 0.0) { bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, temp16a); bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, temp16a); bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdxtail != 0.0) { cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, temp16a); cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, temp16a); cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if ((adxtail != 0.0) || (adytail != 0.0)) { if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) { Two_Product(bdxtail, cdy, ti1, ti0); Two_Product(bdx, cdytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -bdy; Two_Product(cdxtail, negate, ti1, ti0); negate = -bdytail; Two_Product(cdx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); Two_Product(bdxtail, cdytail, ti1, ti0); Two_Product(cdxtail, bdytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); bctt[3] = bctt3; bcttlen = 4; } else { bct[0] = 0.0; bctlen = 1; bctt[0] = 0.0; bcttlen = 1; } if (adxtail != 0.0) { temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, temp32a); axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, temp16a); temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, temp32a); aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, temp16a); temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } if ((bdxtail != 0.0) || (bdytail != 0.0)) { if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) { Two_Product(cdxtail, ady, ti1, ti0); Two_Product(cdx, adytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -cdy; Two_Product(adxtail, negate, ti1, ti0); negate = -cdytail; Two_Product(adx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); Two_Product(cdxtail, adytail, ti1, ti0); Two_Product(adxtail, cdytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); catt[3] = catt3; cattlen = 4; } else { cat[0] = 0.0; catlen = 1; catt[0] = 0.0; cattlen = 1; } if (bdxtail != 0.0) { temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, temp32a); bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, temp16a); temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, temp32a); bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, temp16a); temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } if ((cdxtail != 0.0) || (cdytail != 0.0)) { if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) { Two_Product(adxtail, bdy, ti1, ti0); Two_Product(adx, bdytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -ady; Two_Product(bdxtail, negate, ti1, ti0); negate = -adytail; Two_Product(bdx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); Two_Product(adxtail, bdytail, ti1, ti0); Two_Product(bdxtail, adytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); abtt[3] = abtt3; abttlen = 4; } else { abt[0] = 0.0; abtlen = 1; abtt[0] = 0.0; abttlen = 1; } if (cdxtail != 0.0) { temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (adytail != 0.0) { temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, temp32a); cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, temp16a); temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, temp32a); cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, temp16a); temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } return finnow[finlength - 1]; } #ifdef ANSI_DECLARATORS REAL incircle(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd) #else /* not ANSI_DECLARATORS */ REAL incircle(m, b, pa, pb, pc, pd) struct mesh *m; struct behavior *b; vertex pa; vertex pb; vertex pc; vertex pd; #endif /* not ANSI_DECLARATORS */ { REAL adx, bdx, cdx, ady, bdy, cdy; REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; REAL alift, blift, clift; REAL det; REAL permanent, errbound; m->incirclecount++; adx = pa[0] - pd[0]; bdx = pb[0] - pd[0]; cdx = pc[0] - pd[0]; ady = pa[1] - pd[1]; bdy = pb[1] - pd[1]; cdy = pc[1] - pd[1]; bdxcdy = bdx * cdy; cdxbdy = cdx * bdy; alift = adx * adx + ady * ady; cdxady = cdx * ady; adxcdy = adx * cdy; blift = bdx * bdx + bdy * bdy; adxbdy = adx * bdy; bdxady = bdx * ady; clift = cdx * cdx + cdy * cdy; det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) + clift * (adxbdy - bdxady); if (b->noexact) { return det; } permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift + (Absolute(cdxady) + Absolute(adxcdy)) * blift + (Absolute(adxbdy) + Absolute(bdxady)) * clift; errbound = iccerrboundA * permanent; if ((det > errbound) || (-det > errbound)) { return det; } return incircleadapt(pa, pb, pc, pd, permanent); } /*****************************************************************************/ /* */ /* orient3d() Return a positive value if the point pd lies below the */ /* plane passing through pa, pb, and pc; "below" is defined so */ /* that pa, pb, and pc appear in counterclockwise order when */ /* viewed from above the plane. Returns a negative value if */ /* pd lies above the plane. Returns zero if the points are */ /* coplanar. The result is also a rough approximation of six */ /* times the signed volume of the tetrahedron defined by the */ /* four points. */ /* */ /* Uses exact arithmetic if necessary to ensure a correct answer. The */ /* result returned is the determinant of a matrix. This determinant is */ /* computed adaptively, in the sense that exact arithmetic is used only to */ /* the degree it is needed to ensure that the returned value has the */ /* correct sign. Hence, this function is usually quite fast, but will run */ /* more slowly when the input points are coplanar or nearly so. */ /* */ /* See my Robust Predicates paper for details. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight, REAL permanent) #else /* not ANSI_DECLARATORS */ REAL orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, permanent) vertex pa; vertex pb; vertex pc; vertex pd; REAL aheight; REAL bheight; REAL cheight; REAL dheight; REAL permanent; #endif /* not ANSI_DECLARATORS */ { INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; REAL det, errbound; INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; REAL bc[4], ca[4], ab[4]; INEXACT REAL bc3, ca3, ab3; REAL adet[8], bdet[8], cdet[8]; int alen, blen, clen; REAL abdet[16]; int ablen; REAL *finnow, *finother, *finswap; REAL fin1[192], fin2[192]; int finlength; REAL adxtail, bdxtail, cdxtail; REAL adytail, bdytail, cdytail; REAL adheighttail, bdheighttail, cdheighttail; INEXACT REAL at_blarge, at_clarge; INEXACT REAL bt_clarge, bt_alarge; INEXACT REAL ct_alarge, ct_blarge; REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4]; int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen; INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1; INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1; REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0; REAL adxt_cdy0, adxt_bdy0, bdxt_ady0; INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1; INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1; REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0; REAL adyt_cdx0, adyt_bdx0, bdyt_adx0; REAL bct[8], cat[8], abt[8]; int bctlen, catlen, abtlen; INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1; INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1; REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0; REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0; REAL u[4], v[12], w[16]; INEXACT REAL u3; int vlength, wlength; REAL negate; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j, _k; REAL _0; adx = (REAL) (pa[0] - pd[0]); bdx = (REAL) (pb[0] - pd[0]); cdx = (REAL) (pc[0] - pd[0]); ady = (REAL) (pa[1] - pd[1]); bdy = (REAL) (pb[1] - pd[1]); cdy = (REAL) (pc[1] - pd[1]); adheight = (REAL) (aheight - dheight); bdheight = (REAL) (bheight - dheight); cdheight = (REAL) (cheight - dheight); Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); bc[3] = bc3; alen = scale_expansion_zeroelim(4, bc, adheight, adet); Two_Product(cdx, ady, cdxady1, cdxady0); Two_Product(adx, cdy, adxcdy1, adxcdy0); Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); ca[3] = ca3; blen = scale_expansion_zeroelim(4, ca, bdheight, bdet); Two_Product(adx, bdy, adxbdy1, adxbdy0); Two_Product(bdx, ady, bdxady1, bdxady0); Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); ab[3] = ab3; clen = scale_expansion_zeroelim(4, ab, cdheight, cdet); ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); det = estimate(finlength, fin1); errbound = o3derrboundB * permanent; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pd[0], adx, adxtail); Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); Two_Diff_Tail(pa[1], pd[1], ady, adytail); Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); Two_Diff_Tail(aheight, dheight, adheight, adheighttail); Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail); Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail); if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) && (adheighttail == 0.0) && (bdheighttail == 0.0) && (cdheighttail == 0.0)) { return det; } errbound = o3derrboundC * permanent + resulterrbound * Absolute(det); det += (adheight * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + adheighttail * (bdx * cdy - bdy * cdx)) + (bdheight * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + bdheighttail * (cdx * ady - cdy * adx)) + (cdheight * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + cdheighttail * (adx * bdy - ady * bdx)); if ((det >= errbound) || (-det >= errbound)) { return det; } finnow = fin1; finother = fin2; if (adxtail == 0.0) { if (adytail == 0.0) { at_b[0] = 0.0; at_blen = 1; at_c[0] = 0.0; at_clen = 1; } else { negate = -adytail; Two_Product(negate, bdx, at_blarge, at_b[0]); at_b[1] = at_blarge; at_blen = 2; Two_Product(adytail, cdx, at_clarge, at_c[0]); at_c[1] = at_clarge; at_clen = 2; } } else { if (adytail == 0.0) { Two_Product(adxtail, bdy, at_blarge, at_b[0]); at_b[1] = at_blarge; at_blen = 2; negate = -adxtail; Two_Product(negate, cdy, at_clarge, at_c[0]); at_c[1] = at_clarge; at_clen = 2; } else { Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0); Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0); Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, at_blarge, at_b[2], at_b[1], at_b[0]); at_b[3] = at_blarge; at_blen = 4; Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0); Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0); Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, at_clarge, at_c[2], at_c[1], at_c[0]); at_c[3] = at_clarge; at_clen = 4; } } if (bdxtail == 0.0) { if (bdytail == 0.0) { bt_c[0] = 0.0; bt_clen = 1; bt_a[0] = 0.0; bt_alen = 1; } else { negate = -bdytail; Two_Product(negate, cdx, bt_clarge, bt_c[0]); bt_c[1] = bt_clarge; bt_clen = 2; Two_Product(bdytail, adx, bt_alarge, bt_a[0]); bt_a[1] = bt_alarge; bt_alen = 2; } } else { if (bdytail == 0.0) { Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]); bt_c[1] = bt_clarge; bt_clen = 2; negate = -bdxtail; Two_Product(negate, ady, bt_alarge, bt_a[0]); bt_a[1] = bt_alarge; bt_alen = 2; } else { Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0); Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0); Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, bt_clarge, bt_c[2], bt_c[1], bt_c[0]); bt_c[3] = bt_clarge; bt_clen = 4; Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0); Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0); Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, bt_alarge, bt_a[2], bt_a[1], bt_a[0]); bt_a[3] = bt_alarge; bt_alen = 4; } } if (cdxtail == 0.0) { if (cdytail == 0.0) { ct_a[0] = 0.0; ct_alen = 1; ct_b[0] = 0.0; ct_blen = 1; } else { negate = -cdytail; Two_Product(negate, adx, ct_alarge, ct_a[0]); ct_a[1] = ct_alarge; ct_alen = 2; Two_Product(cdytail, bdx, ct_blarge, ct_b[0]); ct_b[1] = ct_blarge; ct_blen = 2; } } else { if (cdytail == 0.0) { Two_Product(cdxtail, ady, ct_alarge, ct_a[0]); ct_a[1] = ct_alarge; ct_alen = 2; negate = -cdxtail; Two_Product(negate, bdy, ct_blarge, ct_b[0]); ct_b[1] = ct_blarge; ct_blen = 2; } else { Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0); Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0); Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, ct_alarge, ct_a[2], ct_a[1], ct_a[0]); ct_a[3] = ct_alarge; ct_alen = 4; Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0); Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0); Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, ct_blarge, ct_b[2], ct_b[1], ct_b[0]); ct_b[3] = ct_blarge; ct_blen = 4; } } bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct); wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat); wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt); wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, bc, adheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adxtail != 0.0) { if (bdytail != 0.0) { Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0); Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdheighttail != 0.0) { Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (cdytail != 0.0) { negate = -adxtail; Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0); Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdheighttail != 0.0) { Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (bdxtail != 0.0) { if (cdytail != 0.0) { Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0); Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (adytail != 0.0) { negate = -bdxtail; Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0); Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdheighttail != 0.0) { Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (cdxtail != 0.0) { if (adytail != 0.0) { Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0); Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdheighttail != 0.0) { Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (bdytail != 0.0) { negate = -cdxtail; Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0); Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (adheighttail != 0.0) { wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdheighttail != 0.0) { wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdheighttail != 0.0) { wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } return finnow[finlength - 1]; } #ifdef ANSI_DECLARATORS REAL orient3d(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight) #else /* not ANSI_DECLARATORS */ REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight) struct mesh *m; struct behavior *b; vertex pa; vertex pb; vertex pc; vertex pd; REAL aheight; REAL bheight; REAL cheight; REAL dheight; #endif /* not ANSI_DECLARATORS */ { REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; REAL det; REAL permanent, errbound; m->orient3dcount++; adx = pa[0] - pd[0]; bdx = pb[0] - pd[0]; cdx = pc[0] - pd[0]; ady = pa[1] - pd[1]; bdy = pb[1] - pd[1]; cdy = pc[1] - pd[1]; adheight = aheight - dheight; bdheight = bheight - dheight; cdheight = cheight - dheight; bdxcdy = bdx * cdy; cdxbdy = cdx * bdy; cdxady = cdx * ady; adxcdy = adx * cdy; adxbdy = adx * bdy; bdxady = bdx * ady; det = adheight * (bdxcdy - cdxbdy) + bdheight * (cdxady - adxcdy) + cdheight * (adxbdy - bdxady); if (b->noexact) { return det; } permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight) + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight) + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight); errbound = o3derrboundA * permanent; if ((det > errbound) || (-det > errbound)) { return det; } return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, permanent); } /*****************************************************************************/ /* */ /* nonregular() Return a positive value if the point pd is incompatible */ /* with the circle or plane passing through pa, pb, and pc */ /* (meaning that pd is inside the circle or below the */ /* plane); a negative value if it is compatible; and zero if */ /* the four points are cocircular/coplanar. The points pa, */ /* pb, and pc must be in counterclockwise order, or the sign */ /* of the result will be reversed. */ /* */ /* If the -w switch is used, the points are lifted onto the parabolic */ /* lifting map, then they are dropped according to their weights, then the */ /* 3D orientation test is applied. If the -W switch is used, the points' */ /* heights are already provided, so the 3D orientation test is applied */ /* directly. If neither switch is used, the incircle test is applied. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS REAL nonregular(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd) #else /* not ANSI_DECLARATORS */ REAL nonregular(m, b, pa, pb, pc, pd) struct mesh *m; struct behavior *b; vertex pa; vertex pb; vertex pc; vertex pd; #endif /* not ANSI_DECLARATORS */ { if (b->weighted == 0) { return incircle(m, b, pa, pb, pc, pd); } else if (b->weighted == 1) { return orient3d(m, b, pa, pb, pc, pd, pa[0] * pa[0] + pa[1] * pa[1] - pa[2], pb[0] * pb[0] + pb[1] * pb[1] - pb[2], pc[0] * pc[0] + pc[1] * pc[1] - pc[2], pd[0] * pd[0] + pd[1] * pd[1] - pd[2]); } else { return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]); } } /*****************************************************************************/ /* */ /* findcircumcenter() Find the circumcenter of a triangle. */ /* */ /* The result is returned both in terms of x-y coordinates and xi-eta */ /* (barycentric) coordinates. The xi-eta coordinate system is defined in */ /* terms of the triangle: the origin of the triangle is the origin of the */ /* coordinate system; the destination of the triangle is one unit along the */ /* xi axis; and the apex of the triangle is one unit along the eta axis. */ /* This procedure also returns the square of the length of the triangle's */ /* shortest edge. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void findcircumcenter(struct mesh *m, struct behavior *b, vertex torg, vertex tdest, vertex tapex, vertex circumcenter, REAL *xi, REAL *eta, REAL *minedge) #else /* not ANSI_DECLARATORS */ void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta, minedge) struct mesh *m; struct behavior *b; vertex torg; vertex tdest; vertex tapex; vertex circumcenter; REAL *xi; REAL *eta; REAL *minedge; #endif /* not ANSI_DECLARATORS */ { REAL xdo, ydo, xao, yao; REAL dodist, aodist, dadist; REAL denominator; REAL dx, dy; m->circumcentercount++; /* Compute the circumcenter of the triangle. */ xdo = tdest[0] - torg[0]; ydo = tdest[1] - torg[1]; xao = tapex[0] - torg[0]; yao = tapex[1] - torg[1]; dodist = xdo * xdo + ydo * ydo; aodist = xao * xao + yao * yao; dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) + (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]); if (b->noexact) { denominator = 0.5 / (xdo * yao - xao * ydo); } else { /* Use the counterclockwise() routine to ensure a positive (and */ /* reasonably accurate) result, avoiding any possibility of */ /* division by zero. */ denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg); /* Don't count the above as an orientation test. */ m->counterclockcount--; } circumcenter[0] = torg[0] - (ydo * aodist - yao * dodist) * denominator; circumcenter[1] = torg[1] + (xdo * aodist - xao * dodist) * denominator; /* To interpolate vertex attributes for the new vertex inserted at */ /* the circumcenter, define a coordinate system with a xi-axis, */ /* directed from the triangle's origin to its destination, and */ /* an eta-axis, directed from its origin to its apex. */ /* Calculate the xi and eta coordinates of the circumcenter. */ dx = circumcenter[0] - torg[0]; dy = circumcenter[1] - torg[1]; *xi = (dx * yao - xao * dy) * (2.0 * denominator); *eta = (xdo * dy - dx * ydo) * (2.0 * denominator); /* Find the length of the triangle's shortest edge. This serves as */ /* a conservative estimate of the insertion radius of the */ /* circumcenter's parent. The estimate is used to ensure that */ /* the algorithm terminates even if very small angles appear in */ /* the input PSLG. */ *minedge = ((dodist < aodist) && (dodist < dadist)) ? dodist : (aodist < dadist) ? aodist : dadist; } /** **/ /** **/ /********* Geometric primitives end here *********/ /*****************************************************************************/ /* */ /* triangleinit() Initialize some variables. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void triangleinit(struct mesh *m) #else /* not ANSI_DECLARATORS */ void triangleinit(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { m->vertices.maxitems = m->triangles.maxitems = m->subsegs.maxitems = m->viri.maxitems = m->badsubsegs.maxitems = m->badtriangles.maxitems = m->flipstackers.maxitems = m->splaynodes.maxitems = 0l; m->vertices.itembytes = m->triangles.itembytes = m->subsegs.itembytes = m->viri.itembytes = m->badsubsegs.itembytes = m->badtriangles.itembytes = m->flipstackers.itembytes = m->splaynodes.itembytes = 0; m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ m->undeads = 0; /* No eliminated input vertices yet. */ m->samples = 1; /* Point location should take at least one sample. */ m->checksegments = 0; /* There are no segments in the triangulation yet. */ m->checkquality = 0; /* The quality triangulation stage has not begun. */ m->incirclecount = m->counterclockcount = m->orient3dcount = 0; m->hyperbolacount = m->circletopcount = m->circumcentercount = 0; randomseed = 1; exactinit(); /* Initialize exact arithmetic constants. */ } /*****************************************************************************/ /* */ /* randomnation() Generate a random number between 0 and `choices' - 1. */ /* */ /* This is a simple linear congruential random number generator. Hence, it */ /* is a bad random number generator, but good enough for most randomized */ /* geometric algorithms. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS unsigned long randomnation(unsigned int choices) #else /* not ANSI_DECLARATORS */ unsigned long randomnation(choices) unsigned int choices; #endif /* not ANSI_DECLARATORS */ { randomseed = (randomseed * 1366l + 150889l) % 714025l; return randomseed / (714025l / choices + 1); } /********* Mesh quality testing routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* checkmesh() Test the mesh for topological consistency. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifdef ANSI_DECLARATORS void checkmesh(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void checkmesh(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop; struct otri oppotri, oppooppotri; vertex triorg, tridest, triapex; vertex oppoorg, oppodest; int horrors; int saveexact; triangle ptr; /* Temporary variable used by sym(). */ /* Temporarily turn on exact arithmetic if it's off. */ saveexact = b->noexact; b->noexact = 0; if (!b->quiet) { printf(" Checking consistency of mesh...\n"); } horrors = 0; /* Run through the list of triangles, checking each one. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three edges of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); dest(triangleloop, tridest); if (triangleloop.orient == 0) { /* Only test for inversion once. */ /* Test if the triangle is flat or inverted. */ apex(triangleloop, triapex); if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) { printf(" !! !! Inverted "); printtriangle(m, b, &triangleloop); horrors++; } } /* Find the neighboring triangle on this edge. */ sym(triangleloop, oppotri); if (oppotri.tri != m->dummytri) { /* Check that the triangle's neighbor knows it's a neighbor. */ sym(oppotri, oppooppotri); if ((triangleloop.tri != oppooppotri.tri) || (triangleloop.orient != oppooppotri.orient)) { printf(" !! !! Asymmetric triangle-triangle bond:\n"); if (triangleloop.tri == oppooppotri.tri) { printf(" (Right triangle, wrong orientation)\n"); } printf(" First "); printtriangle(m, b, &triangleloop); printf(" Second (nonreciprocating) "); printtriangle(m, b, &oppotri); horrors++; } /* Check that both triangles agree on the identities */ /* of their shared vertices. */ org(oppotri, oppoorg); dest(oppotri, oppodest); if ((triorg != oppodest) || (tridest != oppoorg)) { printf(" !! !! Mismatched edge coordinates between two triangles:\n" ); printf(" First mismatched "); printtriangle(m, b, &triangleloop); printf(" Second mismatched "); printtriangle(m, b, &oppotri); horrors++; } } } triangleloop.tri = triangletraverse(m); } if (horrors == 0) { if (!b->quiet) { printf(" In my studied opinion, the mesh appears to be consistent.\n"); } } else if (horrors == 1) { printf(" !! !! !! !! Precisely one festering wound discovered.\n"); } else { printf(" !! !! !! !! %d abominations witnessed.\n", horrors); } /* Restore the status of exact arithmetic. */ b->noexact = saveexact; } #endif /* not REDUCED */ /*****************************************************************************/ /* */ /* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifdef ANSI_DECLARATORS void checkdelaunay(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void checkdelaunay(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop; struct otri oppotri; struct osub opposubseg; vertex triorg, tridest, triapex; vertex oppoapex; int shouldbedelaunay; int horrors; int saveexact; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Temporarily turn on exact arithmetic if it's off. */ saveexact = b->noexact; b->noexact = 0; if (!b->quiet) { printf(" Checking Delaunay property of mesh...\n"); } horrors = 0; /* Run through the list of triangles, checking each one. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three edges of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); dest(triangleloop, tridest); apex(triangleloop, triapex); sym(triangleloop, oppotri); apex(oppotri, oppoapex); /* Only test that the edge is locally Delaunay if there is an */ /* adjoining triangle whose pointer is larger (to ensure that */ /* each pair isn't tested twice). */ shouldbedelaunay = (oppotri.tri != m->dummytri) && !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) && (triorg != m->infvertex1) && (triorg != m->infvertex2) && (triorg != m->infvertex3) && (tridest != m->infvertex1) && (tridest != m->infvertex2) && (tridest != m->infvertex3) && (triapex != m->infvertex1) && (triapex != m->infvertex2) && (triapex != m->infvertex3) && (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) && (oppoapex != m->infvertex3); if (m->checksegments && shouldbedelaunay) { /* If a subsegment separates the triangles, then the edge is */ /* constrained, so no local Delaunay test should be done. */ tspivot(triangleloop, opposubseg); if (opposubseg.ss != m->dummysub){ shouldbedelaunay = 0; } } if (shouldbedelaunay) { if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) { if (!b->weighted) { printf(" !! !! Non-Delaunay pair of triangles:\n"); printf(" First non-Delaunay "); printtriangle(m, b, &triangleloop); printf(" Second non-Delaunay "); } else { printf(" !! !! Non-regular pair of triangles:\n"); printf(" First non-regular "); printtriangle(m, b, &triangleloop); printf(" Second non-regular "); } printtriangle(m, b, &oppotri); horrors++; } } } triangleloop.tri = triangletraverse(m); } if (horrors == 0) { if (!b->quiet) { printf( " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); } } else if (horrors == 1) { printf( " !! !! !! !! Precisely one terrifying transgression identified.\n"); } else { printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); } /* Restore the status of exact arithmetic. */ b->noexact = saveexact; } #endif /* not REDUCED */ /*****************************************************************************/ /* */ /* enqueuebadtriang() Add a bad triangle data structure to the end of a */ /* queue. */ /* */ /* The queue is actually a set of 64 queues. I use multiple queues to give */ /* priority to smaller angles. I originally implemented a heap, but the */ /* queues are faster by a larger margin than I'd suspected. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void enqueuebadtriang(struct mesh *m, struct behavior *b, struct badtriang *badtri) #else /* not ANSI_DECLARATORS */ void enqueuebadtriang(m, b, badtri) struct mesh *m; struct behavior *b; struct badtriang *badtri; #endif /* not ANSI_DECLARATORS */ { int queuenumber; int i; if (b->verbose > 2) { printf(" Queueing bad triangle:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", badtri->triangorg[0], badtri->triangorg[1], badtri->triangdest[0], badtri->triangdest[1], badtri->triangapex[0], badtri->triangapex[1]); } /* Determine the appropriate queue to put the bad triangle into. */ if (badtri->key > 0.6) { queuenumber = (int) (160.0 * (badtri->key - 0.6)); if (queuenumber > 63) { queuenumber = 63; } } else { /* It's not a bad angle; put the triangle in the lowest-priority queue. */ queuenumber = 0; } /* Are we inserting into an empty queue? */ if (m->queuefront[queuenumber] == (struct badtriang *) NULL) { /* Yes, we are inserting into an empty queue. */ /* Will this become the highest-priority queue? */ if (queuenumber > m->firstnonemptyq) { /* Yes, this is the highest-priority queue. */ m->nextnonemptyq[queuenumber] = m->firstnonemptyq; m->firstnonemptyq = queuenumber; } else { /* No, this is not the highest-priority queue. */ /* Find the queue with next higher priority. */ i = queuenumber + 1; while (m->queuefront[i] == (struct badtriang *) NULL) { i++; } /* Mark the newly nonempty queue as following a higher-priority queue. */ m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i]; m->nextnonemptyq[i] = queuenumber; } /* Put the bad triangle at the beginning of the (empty) queue. */ m->queuefront[queuenumber] = badtri; } else { /* Add the bad triangle to the end of an already nonempty queue. */ m->queuetail[queuenumber]->nexttriang = badtri; } /* Maintain a pointer to the last triangle of the queue. */ m->queuetail[queuenumber] = badtri; /* Newly enqueued bad triangle has no successor in the queue. */ badtri->nexttriang = (struct badtriang *) NULL; } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* enqueuebadtri() Add a bad triangle to the end of a queue. */ /* */ /* Allocates a badtriang data structure for the triangle, then passes it to */ /* enqueuebadtriang(). */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri, REAL angle, vertex enqapex, vertex enqorg, vertex enqdest) #else /* not ANSI_DECLARATORS */ void enqueuebadtri(m, b, enqtri, angle, enqapex, enqorg, enqdest) struct mesh *m; struct behavior *b; struct otri *enqtri; REAL angle; vertex enqapex; vertex enqorg; vertex enqdest; #endif /* not ANSI_DECLARATORS */ { struct badtriang *newbad; /* Allocate space for the bad triangle. */ newbad = (struct badtriang *) poolalloc(&m->badtriangles); newbad->poortri = encode(*enqtri); newbad->key = angle; newbad->triangapex = enqapex; newbad->triangorg = enqorg; newbad->triangdest = enqdest; enqueuebadtriang(m, b, newbad); } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* dequeuebadtriang() Remove a triangle from the front of the queue. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS struct badtriang *dequeuebadtriang(struct mesh *m) #else /* not ANSI_DECLARATORS */ struct badtriang *dequeuebadtriang(m) struct mesh *m; #endif /* not ANSI_DECLARATORS */ { struct badtriang *result; /* If no queues are nonempty, return NULL. */ if (m->firstnonemptyq < 0) { return (struct badtriang *) NULL; } /* Find the first triangle of the highest-priority queue. */ result = m->queuefront[m->firstnonemptyq]; /* Remove the triangle from the queue. */ m->queuefront[m->firstnonemptyq] = result->nexttriang; /* If this queue is now empty, note the new highest-priority */ /* nonempty queue. */ if (result == m->queuetail[m->firstnonemptyq]) { m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq]; } return result; } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* under60degrees() Return 1 if the two incident input segments are */ /* separated by an angle less than 60 degrees; */ /* 0 otherwise. */ /* */ /* The two input segments MUST have the same origin. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY int under60degrees(struct osub *sub1, struct osub *sub2) { vertex segmentapex, v1, v2; REAL dotprod; sorg(*sub1, segmentapex); sdest(*sub1, v1); sdest(*sub2, v2); dotprod = (v2[0] - segmentapex[0]) * (v1[0] - segmentapex[0]) + (v2[1] - segmentapex[1]) * (v1[1] - segmentapex[1]); return (dotprod > 0.0) && (4.0 * dotprod * dotprod > ((v1[0] - segmentapex[0]) * (v1[0] - segmentapex[0]) + (v1[1] - segmentapex[1]) * (v1[1] - segmentapex[1])) * ((v2[0] - segmentapex[0]) * (v2[0] - segmentapex[0]) + (v2[1] - segmentapex[1]) * (v2[1] - segmentapex[1]))); } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* clockwiseseg() Find the next segment clockwise from `thissub' having */ /* the same origin and return it as `nextsub' if the */ /* intervening region is inside the domain. */ /* */ /* Returns 1 if the next segment is separated from `thissub' by less than */ /* 60 degrees, and the intervening region is inside the domain. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY int clockwiseseg(struct mesh *m, struct osub *thissub, struct osub *nextsub) { struct otri neighbortri; triangle ptr; /* Temporary variable used by sym() and stpivot(). */ subseg sptr; /* Temporary variable used by tspivot(). */ stpivot(*thissub, neighbortri); if (neighbortri.tri == m->dummytri) { return 0; } else { lnextself(neighbortri); tspivot(neighbortri, *nextsub); while (nextsub->ss == m->dummysub) { symself(neighbortri); lnextself(neighbortri); tspivot(neighbortri, *nextsub); } ssymself(*nextsub); return under60degrees(thissub, nextsub); } } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* counterclockwiseseg() Find the next segment counterclockwise from */ /* `thissub' having the same origin and return it */ /* as `nextsub' if the intervening region is inside */ /* the domain. */ /* */ /* Returns 1 if the next segment is separated from `thissub' by less than */ /* 60 degrees, and the intervening region is inside the domain. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY int counterclockwiseseg(struct mesh *m, struct osub *thissub, struct osub *nextsub) { struct otri neighbortri; struct osub subsym; triangle ptr; /* Temporary variable used by sym() and stpivot(). */ subseg sptr; /* Temporary variable used by tspivot(). */ ssym(*thissub, subsym); stpivot(subsym, neighbortri); if (neighbortri.tri == m->dummytri) { return 0; } else { lprevself(neighbortri); tspivot(neighbortri, *nextsub); while (nextsub->ss == m->dummysub) { symself(neighbortri); lprevself(neighbortri); tspivot(neighbortri, *nextsub); } return under60degrees(thissub, nextsub); } } #endif /* not CDT_ONLY */ #ifndef CDT_ONLY /*****************************************************************************/ /* */ /* splitpermitted() Return 1 if `testsubseg' is part of a subsegment */ /* cluster that is eligible for splitting. */ /* */ /* The term "subsegment cluster" is formally defined in my paper "Mesh */ /* Generation for Domains with Small Angles." The algorithm that uses this */ /* procedure is also described there. */ /* */ /* A subsegment cluster is eligible for splitting if (1) it includes a */ /* subsegment whose length is not a power of two, (2) its subsegments are */ /* not all the same length, or (3) no new edge that will be created by */ /* splitting all the subsegments in the cluster has a length shorter than */ /* the insertion radius of the encroaching vertex, whose square is given */ /* as the parameter `iradius'. Note that the shortest edges created by */ /* splitting a cluster are those whose endpoints are both subsegment */ /* midpoints introduced when the cluster is split. */ /* */ /* `testsubseg' is also eligible for splitting (and a 1 will be returned) */ /* if it is part of two subsegment clusters; one at its origin and one at */ /* its destination. */ /* */ /*****************************************************************************/ int splitpermitted(struct mesh *m, struct osub *testsubseg, REAL iradius) { struct osub cwsubseg, ccwsubseg, cwsubseg2, ccwsubseg2; struct osub testsym; struct osub startsubseg, nowsubseg; vertex suborg, dest1, dest2; REAL nearestpoweroffour, seglength, prevseglength, edgelength; int cwsmall, ccwsmall, cwsmall2, ccwsmall2; int orgcluster, destcluster; int toosmall; /* Find the square of the subsegment's length, and the nearest power of */ /* four (which is the square of the nearest power of two to the */ /* subsegment's length). */ sorg(*testsubseg, suborg); sdest(*testsubseg, dest1); seglength = (dest1[0] - suborg[0]) * (dest1[0] - suborg[0]) + (dest1[1] - suborg[1]) * (dest1[1] - suborg[1]); nearestpoweroffour = 1.0; while (seglength > 2.0 * nearestpoweroffour) { nearestpoweroffour *= 4.0; } while (seglength < 0.5 * nearestpoweroffour) { nearestpoweroffour *= 0.25; } /* If the segment's length is not a power of two, the segment */ /* is eligible for splitting. */ if ((nearestpoweroffour > 1.001 * seglength) || (nearestpoweroffour < 0.999 * seglength)) { return 1; } /* Is `testsubseg' part of a subsegment cluster at its origin? */ cwsmall = clockwiseseg(m, testsubseg, &cwsubseg); ccwsmall = cwsmall ? 0 : counterclockwiseseg(m, testsubseg, &ccwsubseg); orgcluster = cwsmall || ccwsmall; /* Is `testsubseg' part of a subsegment cluster at its destination? */ ssym(*testsubseg, testsym); cwsmall2 = clockwiseseg(m, &testsym, &cwsubseg2); ccwsmall2 = cwsmall2 ? 0 : counterclockwiseseg(m, &testsym, &ccwsubseg2); destcluster = cwsmall2 || ccwsmall2; if (orgcluster == destcluster) { /* `testsubseg' is part of two clusters or none, */ /* and thus should be split. */ return 1; } else if (orgcluster) { /* `testsubseg' is part of a cluster at its origin. */ subsegcopy(*testsubseg, startsubseg); } else { /* `testsubseg' is part of a cluster at its destination; switch to */ /* the symmetric case, so we can use the same code to handle it. */ subsegcopy(testsym, startsubseg); subsegcopy(cwsubseg2, cwsubseg); subsegcopy(ccwsubseg2, ccwsubseg); cwsmall = cwsmall2; ccwsmall = ccwsmall2; } toosmall = 0; if (cwsmall) { /* Check the subsegment(s) clockwise from `testsubseg'. */ subsegcopy(startsubseg, nowsubseg); sorg(nowsubseg, suborg); sdest(nowsubseg, dest1); prevseglength = nearestpoweroffour; do { /* Is the next subsegment shorter than `startsubseg'? */ sdest(cwsubseg, dest2); seglength = (dest2[0] - suborg[0]) * (dest2[0] - suborg[0]) + (dest2[1] - suborg[1]) * (dest2[1] - suborg[1]); if (nearestpoweroffour > 1.001 * seglength) { /* It's shorter; it's safe to split `startsubseg'. */ return 1; } /* If the current and previous subsegments are split to a length */ /* half that of `startsubseg' (which is a likely consequence if */ /* `startsubseg' is split), what will be (the square of) the */ /* length of the free edge between the splitting vertices? */ edgelength = 0.5 * nearestpoweroffour * (1 - (((dest1[0] - suborg[0]) * (dest2[0] - suborg[0]) + (dest1[1] - suborg[1]) * (dest2[1] - suborg[1])) / sqrt(prevseglength * seglength))); if (edgelength < iradius) { /* If this cluster is split, the new edge dest1-dest2 will be */ /* smaller than the insertion radius of the encroaching vertex. */ /* Hence, we'd prefer to avoid splitting it if possible. */ toosmall = 1; } if (cwsubseg.ss == startsubseg.ss) { /* We've gone all the way around the vertex. Split the cluster */ /* if no edges will be too short. */ return !toosmall; } /* Find the next subsegment clockwise around the vertex. */ subsegcopy(cwsubseg, nowsubseg); dest1 = dest2; prevseglength = seglength; cwsmall = clockwiseseg(m, &nowsubseg, &cwsubseg); } while (cwsmall); /* Prepare to start searching counterclockwise from */ /* the starting subsegment. */ ccwsmall = counterclockwiseseg(m, &startsubseg, &ccwsubseg); } if (ccwsmall) { /* Check the subsegment(s) counterclockwise from `testsubseg'. */ subsegcopy(startsubseg, nowsubseg); sorg(nowsubseg, suborg); sdest(nowsubseg, dest1); prevseglength = nearestpoweroffour; do { /* Is the next subsegment shorter than `startsubseg'? */ sdest(ccwsubseg, dest2); seglength = (dest2[0] - suborg[0]) * (dest2[0] - suborg[0]) + (dest2[1] - suborg[1]) * (dest2[1] - suborg[1]); if (nearestpoweroffour > 1.001 * seglength) { /* It's shorter; it's safe to split `startsubseg'. */ return 1; } /* half that of `startsubseg' (which is a likely consequence if */ /* `startsubseg' is split), what will be (the square of) the */ /* length of the free edge between the splitting vertices? */ edgelength = 0.5 * nearestpoweroffour * (1 - (((dest1[0] - suborg[0]) * (dest2[0] - suborg[0]) + (dest1[1] - suborg[1]) * (dest2[1] - suborg[1])) / sqrt(prevseglength * seglength))); if (edgelength < iradius) { /* If this cluster is split, the new edge dest1-dest2 will be */ /* smaller than the insertion radius of the encroaching vertex. */ /* Hence, we'd prefer to avoid splitting it if possible. */ toosmall = 1; } if (ccwsubseg.ss == startsubseg.ss) { /* We've gone all the way around the vertex. Split the cluster */ /* if no edges will be too short. */ return !toosmall; } /* Find the next subsegment counterclockwise around the vertex. */ subsegcopy(ccwsubseg, nowsubseg); dest1 = dest2; prevseglength = seglength; ccwsmall = counterclockwiseseg(m, &nowsubseg, &ccwsubseg); } while (ccwsmall); } /* We've found every subsegment in the cluster. Split the cluster */ /* if no edges will be too short. */ return !toosmall; } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* checkseg4encroach() Check a subsegment to see if it is encroached; add */ /* it to the list if it is. */ /* */ /* A subsegment is encroached if there is a vertex in its diametral circle */ /* (that is, the subsegment faces an angle greater than 90 degrees). This */ /* definition is due to Ruppert. */ /* */ /* Returns a nonzero value if the subsegment is encroached. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS int checkseg4encroach(struct mesh *m, struct behavior *b, struct osub *testsubseg, REAL iradius) #else /* not ANSI_DECLARATORS */ int checkseg4encroach(m, b, testsubseg, iradius) struct mesh *m; struct behavior *b; struct osub *testsubseg; REAL iradius; #endif /* not ANSI_DECLARATORS */ { struct otri neighbortri; struct osub testsym; struct badsubseg *encroachedseg; REAL dotproduct; int encroached; int sides; int enq; vertex eorg, edest, eapex; triangle ptr; /* Temporary variable used by stpivot(). */ encroached = 0; sides = 0; sorg(*testsubseg, eorg); sdest(*testsubseg, edest); /* Check one neighbor of the subsegment. */ stpivot(*testsubseg, neighbortri); /* Does the neighbor exist, or is this a boundary edge? */ if (neighbortri.tri != m->dummytri) { sides++; /* Find a vertex opposite this subsegment. */ apex(neighbortri, eapex); /* Check whether the apex is in the diametral lens of the subsegment */ /* (or the diametral circle, if `nolenses' is set). A dot product */ /* of two sides of the triangle is used to check whether the angle */ /* at the apex is greater than 120 degrees (for lenses; 90 degrees */ /* for diametral circles). */ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); if (dotproduct < 0.0) { if (b->nolenses || (dotproduct * dotproduct >= 0.25 * ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { encroached = 1; } } } /* Check the other neighbor of the subsegment. */ ssym(*testsubseg, testsym); stpivot(testsym, neighbortri); /* Does the neighbor exist, or is this a boundary edge? */ if (neighbortri.tri != m->dummytri) { sides++; /* Find the other vertex opposite this subsegment. */ apex(neighbortri, eapex); /* Check whether the apex is in the diametral lens of the subsegment */ /* (or the diametral circle, if `nolenses' is set). */ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); if (dotproduct < 0.0) { if (b->nolenses || (dotproduct * dotproduct >= 0.25 * ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { encroached += 2; } } } if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) { /* Decide whether `testsubseg' should be split. */ if (iradius > 0.0) { /* The encroaching vertex is a triangle circumcenter, which will be */ /* rejected. Hence, `testsubseg' probably should be split, unless */ /* it is part of a subsegment cluster which, according to the rules */ /* described in my paper "Mesh Generation for Domains with Small */ /* Angles," should not be split. */ enq = splitpermitted(m, testsubseg, iradius); } else { /* The encroaching vertex is an input vertex or was inserted in a */ /* subsegment, so the encroached subsegment must be split. */ enq = 1; } if (enq) { if (b->verbose > 2) { printf( " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", eorg[0], eorg[1], edest[0], edest[1]); } /* Add the subsegment to the list of encroached subsegments. */ /* Be sure to get the orientation right. */ encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs); if (encroached == 1) { encroachedseg->encsubseg = sencode(*testsubseg); encroachedseg->subsegorg = eorg; encroachedseg->subsegdest = edest; } else { encroachedseg->encsubseg = sencode(testsym); encroachedseg->subsegorg = edest; encroachedseg->subsegdest = eorg; } } } return encroached; } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* testtriangle() Test a face for quality measures. */ /* */ /* Tests a triangle to see if it satisfies the minimum angle condition and */ /* the maximum area condition. Triangles that aren't up to spec are added */ /* to the bad triangle queue. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri) #else /* not ANSI_DECLARATORS */ void testtriangle(m, b, testtri) struct mesh *m; struct behavior *b; struct otri *testtri; #endif /* not ANSI_DECLARATORS */ { struct otri sametesttri; struct osub subseg1, subseg2; vertex torg, tdest, tapex; vertex anglevertex; REAL dxod, dyod, dxda, dyda, dxao, dyao; REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; REAL apexlen, orglen, destlen; REAL angle; REAL area; subseg sptr; /* Temporary variable used by tspivot(). */ org(*testtri, torg); dest(*testtri, tdest); apex(*testtri, tapex); dxod = torg[0] - tdest[0]; dyod = torg[1] - tdest[1]; dxda = tdest[0] - tapex[0]; dyda = tdest[1] - tapex[1]; dxao = tapex[0] - torg[0]; dyao = tapex[1] - torg[1]; dxod2 = dxod * dxod; dyod2 = dyod * dyod; dxda2 = dxda * dxda; dyda2 = dyda * dyda; dxao2 = dxao * dxao; dyao2 = dyao * dyao; /* Find the lengths of the triangle's three edges. */ apexlen = dxod2 + dyod2; orglen = dxda2 + dyda2; destlen = dxao2 + dyao2; if ((apexlen < orglen) && (apexlen < destlen)) { /* The edge opposite the apex is shortest. */ /* Find the square of the cosine of the angle at the apex. */ angle = dxda * dxao + dyda * dyao; angle = angle * angle / (orglen * destlen); anglevertex = tapex; lnext(*testtri, sametesttri); tspivot(sametesttri, subseg1); lnextself(sametesttri); tspivot(sametesttri, subseg2); } else if (orglen < destlen) { /* The edge opposite the origin is shortest. */ /* Find the square of the cosine of the angle at the origin. */ angle = dxod * dxao + dyod * dyao; angle = angle * angle / (apexlen * destlen); anglevertex = torg; tspivot(*testtri, subseg1); lprev(*testtri, sametesttri); tspivot(sametesttri, subseg2); } else { /* The edge opposite the destination is shortest. */ /* Find the square of the cosine of the angle at the destination. */ angle = dxod * dxda + dyod * dyda; angle = angle * angle / (apexlen * orglen); anglevertex = tdest; tspivot(*testtri, subseg1); lnext(*testtri, sametesttri); tspivot(sametesttri, subseg2); } /* Check if both edges that form the angle are segments. */ if ((subseg1.ss != m->dummysub) && (subseg2.ss != m->dummysub)) { /* The angle is a segment intersection. Don't add this bad triangle to */ /* the list; there's nothing that can be done about a small angle */ /* between two segments. */ angle = 0.0; } /* Check whether the angle is smaller than permitted. */ if (angle > b->goodangle) { /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, angle, tapex, torg, tdest); return; } if (b->vararea || b->fixedarea || b->usertest) { /* Check whether the area is larger than permitted. */ area = 0.5 * (dxod * dyda - dyod * dxda); if (b->fixedarea && (area > b->maxarea)) { /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, angle, tapex, torg, tdest); return; } /* Nonpositive area constraints are treated as unconstrained. */ if ((b->vararea) && (area > areabound(*testtri)) && (areabound(*testtri) > 0.0)) { /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, angle, tapex, torg, tdest); return; } if (b->usertest) { /* Check whether the user thinks this triangle is too large. */ if (triunsuitable(torg, tdest, tapex, area)) { enqueuebadtri(m, b, testtri, angle, tapex, torg, tdest); return; } } } } #endif /* not CDT_ONLY */ /** **/ /** **/ /********* Mesh quality testing routines end here *********/ /********* Point location routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* makevertexmap() Construct a mapping from vertices to triangles to */ /* improve the speed of point location for segment */ /* insertion. */ /* */ /* Traverses all the triangles, and provides each corner of each triangle */ /* with a pointer to that triangle. Of course, pointers will be */ /* overwritten by other pointers because (almost) each vertex is a corner */ /* of several triangles, but in the end every vertex will point to some */ /* triangle that contains it. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void makevertexmap(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void makevertexmap(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop; vertex triorg; if (b->verbose) { printf(" Constructing mapping from vertices to triangles.\n"); } traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three vertices of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); setvertex2tri(triorg, encode(triangleloop)); } triangleloop.tri = triangletraverse(m); } } /*****************************************************************************/ /* */ /* preciselocate() Find a triangle or edge containing a given point. */ /* */ /* Begins its search from `searchtri'. It is important that `searchtri' */ /* be a handle with the property that `searchpoint' is strictly to the left */ /* of the edge denoted by `searchtri', or is collinear with that edge and */ /* does not intersect that edge. (In particular, `searchpoint' should not */ /* be the origin or destination of that edge.) */ /* */ /* These conditions are imposed because preciselocate() is normally used in */ /* one of two situations: */ /* */ /* (1) To try to find the location to insert a new point. Normally, we */ /* know an edge that the point is strictly to the left of. In the */ /* incremental Delaunay algorithm, that edge is a bounding box edge. */ /* In Ruppert's Delaunay refinement algorithm for quality meshing, */ /* that edge is the shortest edge of the triangle whose circumcenter */ /* is being inserted. */ /* */ /* (2) To try to find an existing point. In this case, any edge on the */ /* convex hull is a good starting edge. You must screen out the */ /* possibility that the vertex sought is an endpoint of the starting */ /* edge before you call preciselocate(). */ /* */ /* On completion, `searchtri' is a triangle that contains `searchpoint'. */ /* */ /* This implementation differs from that given by Guibas and Stolfi. It */ /* walks from triangle to triangle, crossing an edge only if `searchpoint' */ /* is on the other side of the line containing that edge. After entering */ /* a triangle, there are two edges by which one can leave that triangle. */ /* If both edges are valid (`searchpoint' is on the other side of both */ /* edges), one of the two is chosen by drawing a line perpendicular to */ /* the entry edge (whose endpoints are `forg' and `fdest') passing through */ /* `fapex'. Depending on which side of this perpendicular `searchpoint' */ /* falls on, an exit edge is chosen. */ /* */ /* This implementation is empirically faster than the Guibas and Stolfi */ /* point location routine (which I originally used), which tends to spiral */ /* in toward its target. */ /* */ /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ /* is a handle whose origin is the existing vertex. */ /* */ /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ /* handle whose primary edge is the edge on which the point lies. */ /* */ /* Returns INTRIANGLE if the point lies strictly within a triangle. */ /* `searchtri' is a handle on the triangle that contains the point. */ /* */ /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ /* handle whose primary edge the point is to the right of. This might */ /* occur when the circumcenter of a triangle falls just slightly outside */ /* the mesh due to floating-point roundoff error. It also occurs when */ /* seeking a hole or region point that a foolish user has placed outside */ /* the mesh. */ /* */ /* If `stopatsubsegment' is nonzero, the search will stop if it tries to */ /* walk through a subsegment, and will return OUTSIDE. */ /* */ /* WARNING: This routine is designed for convex triangulations, and will */ /* not generally work after the holes and concavities have been carved. */ /* However, it can still be used to find the circumcenter of a triangle, as */ /* long as the search is begun from the triangle in question. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS enum locateresult preciselocate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri, int stopatsubsegment) #else /* not ANSI_DECLARATORS */ enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment) struct mesh *m; struct behavior *b; vertex searchpoint; struct otri *searchtri; int stopatsubsegment; #endif /* not ANSI_DECLARATORS */ { struct otri backtracktri; struct osub checkedge; vertex forg, fdest, fapex; REAL orgorient, destorient; int moveleft; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 2) { printf(" Searching for point (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); } /* Where are we? */ org(*searchtri, forg); dest(*searchtri, fdest); apex(*searchtri, fapex); while (1) { if (b->verbose > 2) { printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); } /* Check whether the apex is the point we seek. */ if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { lprevself(*searchtri); return ONVERTEX; } /* Does the point lie on the other side of the line defined by the */ /* triangle edge opposite the triangle's destination? */ destorient = counterclockwise(m, b, forg, fapex, searchpoint); /* Does the point lie on the other side of the line defined by the */ /* triangle edge opposite the triangle's origin? */ orgorient = counterclockwise(m, b, fapex, fdest, searchpoint); if (destorient > 0.0) { if (orgorient > 0.0) { /* Move left if the inner product of (fapex - searchpoint) and */ /* (fdest - forg) is positive. This is equivalent to drawing */ /* a line perpendicular to the line (forg, fdest) and passing */ /* through `fapex', and determining which side of this line */ /* `searchpoint' falls on. */ moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0; } else { moveleft = 1; } } else { if (orgorient > 0.0) { moveleft = 0; } else { /* The point we seek must be on the boundary of or inside this */ /* triangle. */ if (destorient == 0.0) { lprevself(*searchtri); return ONEDGE; } if (orgorient == 0.0) { lnextself(*searchtri); return ONEDGE; } return INTRIANGLE; } } /* Move to another triangle. Leave a trace `backtracktri' in case */ /* floating-point roundoff or some such bogey causes us to walk */ /* off a boundary of the triangulation. */ if (moveleft) { lprev(*searchtri, backtracktri); fdest = fapex; } else { lnext(*searchtri, backtracktri); forg = fapex; } sym(backtracktri, *searchtri); if (m->checksegments && stopatsubsegment) { /* Check for walking through a subsegment. */ tspivot(backtracktri, checkedge); if (checkedge.ss != m->dummysub) { /* Go back to the last triangle. */ otricopy(backtracktri, *searchtri); return OUTSIDE; } } /* Check for walking right out of the triangulation. */ if (searchtri->tri == m->dummytri) { /* Go back to the last triangle. */ otricopy(backtracktri, *searchtri); return OUTSIDE; } apex(*searchtri, fapex); } } /*****************************************************************************/ /* */ /* locate() Find a triangle or edge containing a given point. */ /* */ /* Searching begins from one of: the input `searchtri', a recently */ /* encountered triangle `recenttri', or from a triangle chosen from a */ /* random sample. The choice is made by determining which triangle's */ /* origin is closest to the point we are searching for. Normally, */ /* `searchtri' should be a handle on the convex hull of the triangulation. */ /* */ /* Details on the random sampling method can be found in the Mucke, Saias, */ /* and Zhu paper cited in the header of this code. */ /* */ /* On completion, `searchtri' is a triangle that contains `searchpoint'. */ /* */ /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ /* is a handle whose origin is the existing vertex. */ /* */ /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ /* handle whose primary edge is the edge on which the point lies. */ /* */ /* Returns INTRIANGLE if the point lies strictly within a triangle. */ /* `searchtri' is a handle on the triangle that contains the point. */ /* */ /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ /* handle whose primary edge the point is to the right of. This might */ /* occur when the circumcenter of a triangle falls just slightly outside */ /* the mesh due to floating-point roundoff error. It also occurs when */ /* seeking a hole or region point that a foolish user has placed outside */ /* the mesh. */ /* */ /* WARNING: This routine is designed for convex triangulations, and will */ /* not generally work after the holes and concavities have been carved. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS enum locateresult locate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri) #else /* not ANSI_DECLARATORS */ enum locateresult locate(m, b, searchpoint, searchtri) struct mesh *m; struct behavior *b; vertex searchpoint; struct otri *searchtri; #endif /* not ANSI_DECLARATORS */ { VOID **sampleblock; triangle *firsttri; struct otri sampletri; vertex torg, tdest; unsigned long alignptr; REAL searchdist, dist; REAL ahead; long sampleblocks, samplesperblock, samplenum; long triblocks; long i, j; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose > 2) { printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); } /* Record the distance from the suggested starting triangle to the */ /* point we seek. */ org(*searchtri, torg); searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (b->verbose > 2) { printf(" Boundary triangle has origin (%.12g, %.12g).\n", torg[0], torg[1]); } /* If a recently encountered triangle has been recorded and has not been */ /* deallocated, test it as a good starting point. */ if (m->recenttri.tri != (triangle *) NULL) { if (!deadtri(m->recenttri.tri)) { org(m->recenttri, torg); if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { otricopy(m->recenttri, *searchtri); return ONVERTEX; } dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (dist < searchdist) { otricopy(m->recenttri, *searchtri); searchdist = dist; if (b->verbose > 2) { printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", torg[0], torg[1]); } } } } /* The number of random samples taken is proportional to the cube root of */ /* the number of triangles in the mesh. The next bit of code assumes */ /* that the number of triangles increases monotonically. */ while (SAMPLEFACTOR * m->samples * m->samples * m->samples < m->triangles.items) { m->samples++; } triblocks = (m->triangles.maxitems + TRIPERBLOCK - 1) / TRIPERBLOCK; samplesperblock = (m->samples + triblocks - 1) / triblocks; sampleblocks = m->samples / samplesperblock; sampleblock = m->triangles.firstblock; sampletri.orient = 0; for (i = 0; i < sampleblocks; i++) { alignptr = (unsigned long) (sampleblock + 1); firsttri = (triangle *) (alignptr + (unsigned long) m->triangles.alignbytes - (alignptr % (unsigned long) m->triangles.alignbytes)); for (j = 0; j < samplesperblock; j++) { if (i == triblocks - 1) { samplenum = randomnation((int) (m->triangles.maxitems - (i * TRIPERBLOCK))); } else { samplenum = randomnation(TRIPERBLOCK); } sampletri.tri = (triangle *) (firsttri + (samplenum * m->triangles.itemwords)); if (!deadtri(sampletri.tri)) { org(sampletri, torg); dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (dist < searchdist) { otricopy(sampletri, *searchtri); searchdist = dist; if (b->verbose > 2) { printf(" Choosing triangle with origin (%.12g, %.12g).\n", torg[0], torg[1]); } } } } sampleblock = (VOID **) *sampleblock; } /* Where are we? */ org(*searchtri, torg); dest(*searchtri, tdest); /* Check the starting triangle's vertices. */ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { return ONVERTEX; } if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { lnextself(*searchtri); return ONVERTEX; } /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ ahead = counterclockwise(m, b, torg, tdest, searchpoint); if (ahead < 0.0) { /* Turn around so that `searchpoint' is to the left of the */ /* edge specified by `searchtri'. */ symself(*searchtri); } else if (ahead == 0.0) { /* Check if `searchpoint' is between `torg' and `tdest'. */ if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) && ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { return ONEDGE; } } return preciselocate(m, b, searchpoint, searchtri, 0); } /** **/ /** **/ /********* Point location routines end here *********/ /********* Mesh transformation routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* insertsubseg() Create a new subsegment and insert it between two */ /* triangles. */ /* */ /* The new subsegment is inserted at the edge described by the handle */ /* `tri'. Its vertices are properly initialized. The marker `subsegmark' */ /* is applied to the subsegment and, if appropriate, its vertices. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, int subsegmark) #else /* not ANSI_DECLARATORS */ void insertsubseg(m, b, tri, subsegmark) struct mesh *m; struct behavior *b; struct otri *tri; /* Edge at which to insert the new subsegment. */ int subsegmark; /* Marker for the new subsegment. */ #endif /* not ANSI_DECLARATORS */ { struct otri oppotri; struct osub newsubseg; vertex triorg, tridest; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*tri, triorg); dest(*tri, tridest); /* Mark vertices if possible. */ if (vertexmark(triorg) == 0) { setvertexmark(triorg, subsegmark); } if (vertexmark(tridest) == 0) { setvertexmark(tridest, subsegmark); } /* Check if there's already a subsegment here. */ tspivot(*tri, newsubseg); if (newsubseg.ss == m->dummysub) { /* Make new subsegment and initialize its vertices. */ makesubseg(m, &newsubseg); setsorg(newsubseg, tridest); setsdest(newsubseg, triorg); /* Bond new subsegment to the two triangles it is sandwiched between. */ /* Note that the facing triangle `oppotri' might be equal to */ /* `dummytri' (outer space), but the new subsegment is bonded to it */ /* all the same. */ tsbond(*tri, newsubseg); sym(*tri, oppotri); ssymself(newsubseg); tsbond(oppotri, newsubseg); setmark(newsubseg, subsegmark); if (b->verbose > 2) { printf(" Inserting new "); printsubseg(m, b, &newsubseg); } } else { if (mark(newsubseg) == 0) { setmark(newsubseg, subsegmark); } } } /*****************************************************************************/ /* */ /* Terminology */ /* */ /* A "local transformation" replaces a small set of triangles with another */ /* set of triangles. This may or may not involve inserting or deleting a */ /* vertex. */ /* */ /* The term "casing" is used to describe the set of triangles that are */ /* attached to the triangles being transformed, but are not transformed */ /* themselves. Think of the casing as a fixed hollow structure inside */ /* which all the action happens. A "casing" is only defined relative to */ /* a single transformation; each occurrence of a transformation will */ /* involve a different casing. */ /* */ /*****************************************************************************/ /*****************************************************************************/ /* */ /* flip() Transform two triangles to two different triangles by flipping */ /* an edge counterclockwise within a quadrilateral. */ /* */ /* Imagine the original triangles, abc and bad, oriented so that the */ /* shared edge ab lies in a horizontal plane, with the vertex b on the left */ /* and the vertex a on the right. The vertex c lies below the edge, and */ /* the vertex d lies above the edge. The `flipedge' handle holds the edge */ /* ab of triangle abc, and is directed left, from vertex a to vertex b. */ /* */ /* The triangles abc and bad are deleted and replaced by the triangles cdb */ /* and dca. The triangles that represent abc and bad are NOT deallocated; */ /* they are reused for dca and cdb, respectively. Hence, any handles that */ /* may have held the original triangles are still valid, although not */ /* directed as they were before. */ /* */ /* Upon completion of this routine, the `flipedge' handle holds the edge */ /* dc of triangle dca, and is directed down, from vertex d to vertex c. */ /* (Hence, the two triangles have rotated counterclockwise.) */ /* */ /* WARNING: This transformation is geometrically valid only if the */ /* quadrilateral adbc is convex. Furthermore, this transformation is */ /* valid only if there is not a subsegment between the triangles abc and */ /* bad. This routine does not check either of these preconditions, and */ /* it is the responsibility of the calling routine to ensure that they are */ /* met. If they are not, the streets shall be filled with wailing and */ /* gnashing of teeth. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void flip(struct mesh *m, struct behavior *b, struct otri *flipedge) #else /* not ANSI_DECLARATORS */ void flip(m, b, flipedge) struct mesh *m; struct behavior *b; struct otri *flipedge; /* Handle for the triangle abc. */ #endif /* not ANSI_DECLARATORS */ { struct otri botleft, botright; struct otri topleft, topright; struct otri top; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; vertex leftvertex, rightvertex, botvertex; vertex farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Identify the vertices of the quadrilateral. */ org(*flipedge, rightvertex); dest(*flipedge, leftvertex); apex(*flipedge, botvertex); sym(*flipedge, top); #ifdef SELF_CHECK if (top.tri == m->dummytri) { printf("Internal error in flip(): Attempt to flip on boundary.\n"); lnextself(*flipedge); return; } if (m->checksegments) { tspivot(*flipedge, toplsubseg); if (toplsubseg.ss != m->dummysub) { printf("Internal error in flip(): Attempt to flip a segment.\n"); lnextself(*flipedge); return; } } #endif /* SELF_CHECK */ apex(top, farvertex); /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(*flipedge, botleft); sym(botleft, botlcasing); lprev(*flipedge, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn counterclockwise. */ bond(topleft, botlcasing); bond(botleft, botrcasing); bond(botright, toprcasing); bond(topright, toplcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(*flipedge, farvertex); setdest(*flipedge, botvertex); setapex(*flipedge, rightvertex); setorg(top, botvertex); setdest(top, farvertex); setapex(top, leftvertex); if (b->verbose > 2) { printf(" Edge flip results in left "); printtriangle(m, b, &top); printf(" and right "); printtriangle(m, b, flipedge); } } /*****************************************************************************/ /* */ /* unflip() Transform two triangles to two different triangles by */ /* flipping an edge clockwise within a quadrilateral. Reverses */ /* the flip() operation so that the data structures representing */ /* the triangles are back where they were before the flip(). */ /* */ /* Imagine the original triangles, abc and bad, oriented so that the */ /* shared edge ab lies in a horizontal plane, with the vertex b on the left */ /* and the vertex a on the right. The vertex c lies below the edge, and */ /* the vertex d lies above the edge. The `flipedge' handle holds the edge */ /* ab of triangle abc, and is directed left, from vertex a to vertex b. */ /* */ /* The triangles abc and bad are deleted and replaced by the triangles cdb */ /* and dca. The triangles that represent abc and bad are NOT deallocated; */ /* they are reused for cdb and dca, respectively. Hence, any handles that */ /* may have held the original triangles are still valid, although not */ /* directed as they were before. */ /* */ /* Upon completion of this routine, the `flipedge' handle holds the edge */ /* cd of triangle cdb, and is directed up, from vertex c to vertex d. */ /* (Hence, the two triangles have rotated clockwise.) */ /* */ /* WARNING: This transformation is geometrically valid only if the */ /* quadrilateral adbc is convex. Furthermore, this transformation is */ /* valid only if there is not a subsegment between the triangles abc and */ /* bad. This routine does not check either of these preconditions, and */ /* it is the responsibility of the calling routine to ensure that they are */ /* met. If they are not, the streets shall be filled with wailing and */ /* gnashing of teeth. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge) #else /* not ANSI_DECLARATORS */ void unflip(m, b, flipedge) struct mesh *m; struct behavior *b; struct otri *flipedge; /* Handle for the triangle abc. */ #endif /* not ANSI_DECLARATORS */ { struct otri botleft, botright; struct otri topleft, topright; struct otri top; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; vertex leftvertex, rightvertex, botvertex; vertex farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Identify the vertices of the quadrilateral. */ org(*flipedge, rightvertex); dest(*flipedge, leftvertex); apex(*flipedge, botvertex); sym(*flipedge, top); #ifdef SELF_CHECK if (top.tri == m->dummytri) { printf("Internal error in unflip(): Attempt to flip on boundary.\n"); lnextself(*flipedge); return; } if (m->checksegments) { tspivot(*flipedge, toplsubseg); if (toplsubseg.ss != m->dummysub) { printf("Internal error in unflip(): Attempt to flip a subsegment.\n"); lnextself(*flipedge); return; } } #endif /* SELF_CHECK */ apex(top, farvertex); /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(*flipedge, botleft); sym(botleft, botlcasing); lprev(*flipedge, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn clockwise. */ bond(topleft, toprcasing); bond(botleft, toplcasing); bond(botright, botlcasing); bond(topright, botrcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(*flipedge, botvertex); setdest(*flipedge, farvertex); setapex(*flipedge, leftvertex); setorg(top, farvertex); setdest(top, botvertex); setapex(top, rightvertex); if (b->verbose > 2) { printf(" Edge unflip results in left "); printtriangle(m, b, flipedge); printf(" and right "); printtriangle(m, b, &top); } } /*****************************************************************************/ /* */ /* insertvertex() Insert a vertex into a Delaunay triangulation, */ /* performing flips as necessary to maintain the Delaunay */ /* property. */ /* */ /* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */ /* the search for the containing triangle begins from `searchtri'. If */ /* `searchtri.tri' is NULL, a full point location procedure is called. */ /* If `insertvertex' is found inside a triangle, the triangle is split into */ /* three; if `insertvertex' lies on an edge, the edge is split in two, */ /* thereby splitting the two adjacent triangles into four. Edge flips are */ /* used to restore the Delaunay property. If `insertvertex' lies on an */ /* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */ /* returned. On return, `searchtri' is set to a handle whose origin is the */ /* existing vertex. */ /* */ /* Normally, the parameter `splitseg' is set to NULL, implying that no */ /* subsegment should be split. In this case, if `insertvertex' is found to */ /* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */ /* returned. On return, `searchtri' is set to a handle whose primary edge */ /* is the violated subsegment. */ /* */ /* If the calling routine wishes to split a subsegment by inserting a */ /* vertex in it, the parameter `splitseg' should be that subsegment. In */ /* this case, `searchtri' MUST be the triangle handle reached by pivoting */ /* from that subsegment; no point location is done. */ /* */ /* `segmentflaws' and `triflaws' are flags that indicate whether or not */ /* there should be checks for the creation of encroached subsegments or bad */ /* quality triangles. If a newly inserted vertex encroaches upon */ /* subsegments, these subsegments are added to the list of subsegments to */ /* be split if `segmentflaws' is set. If bad triangles are created, these */ /* are added to the queue if `triflaws' is set. */ /* */ /* If a duplicate vertex or violated segment does not prevent the vertex */ /* from being inserted, the return value will be ENCROACHINGVERTEX if the */ /* vertex encroaches upon a subsegment (and checking is enabled), or */ /* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */ /* handle whose origin is the newly inserted vertex. */ /* */ /* insertvertex() does not use flip() for reasons of speed; some */ /* information can be reused from edge flip to edge flip, like the */ /* locations of subsegments. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, vertex newvertex, struct otri *searchtri, struct osub *splitseg, int segmentflaws, int triflaws, REAL iradius) #else /* not ANSI_DECLARATORS */ enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg, segmentflaws, triflaws, iradius) struct mesh *m; struct behavior *b; vertex newvertex; struct otri *searchtri; struct osub *splitseg; int segmentflaws; int triflaws; REAL iradius; #endif /* not ANSI_DECLARATORS */ { struct otri horiz; struct otri top; struct otri botleft, botright; struct otri topleft, topright; struct otri newbotleft, newbotright; struct otri newtopright; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct otri testtri; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; struct osub brokensubseg; struct osub checksubseg; struct osub rightsubseg; struct osub newsubseg; struct badsubseg *encroached; struct flipstacker *newflip; vertex first; vertex leftvertex, rightvertex, botvertex, topvertex, farvertex; REAL attrib; REAL area; enum insertvertexresult success; enum locateresult intersect; int doflip; int mirrorflag; int enq; int i; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by spivot() and tspivot(). */ if (b->verbose > 1) { printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } if (splitseg == (struct osub *) NULL) { /* Find the location of the vertex to be inserted. Check if a good */ /* starting triangle has already been provided by the caller. */ if (searchtri->tri == m->dummytri) { /* Find a boundary triangle. */ horiz.tri = m->dummytri; horiz.orient = 0; symself(horiz); /* Search for a triangle containing `newvertex'. */ intersect = locate(m, b, newvertex, &horiz); } else { /* Start searching from the triangle provided by the caller. */ otricopy(*searchtri, horiz); intersect = preciselocate(m, b, newvertex, &horiz, 1); } } else { /* The calling routine provides the subsegment in which */ /* the vertex is inserted. */ otricopy(*searchtri, horiz); intersect = ONEDGE; } if (intersect == ONVERTEX) { /* There's already a vertex there. Return in `searchtri' a triangle */ /* whose origin is the existing vertex. */ otricopy(horiz, *searchtri); otricopy(horiz, m->recenttri); return DUPLICATEVERTEX; } if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { /* The vertex falls on an edge or boundary. */ if (m->checksegments && (splitseg == (struct osub *) NULL)) { /* Check whether the vertex falls on a subsegment. */ tspivot(horiz, brokensubseg); if (brokensubseg.ss != m->dummysub) { /* The vertex falls on a subsegment, and hence will not be inserted. */ if (segmentflaws) { if (b->nobisect == 2) { enq = 0; #ifndef CDT_ONLY } else if (iradius > 0.0) { enq = splitpermitted(m, &brokensubseg, iradius); #endif /* not CDT_ONLY */ } else { enq = 1; } if (enq && (b->nobisect == 1)) { /* This subsegment may be split only if it is an */ /* internal boundary. */ sym(horiz, testtri); enq = testtri.tri != m->dummytri; } if (enq) { /* Add the subsegment to the list of encroached subsegments. */ encroached = (struct badsubseg *) poolalloc(&m->badsubsegs); encroached->encsubseg = sencode(brokensubseg); sorg(brokensubseg, encroached->subsegorg); sdest(brokensubseg, encroached->subsegdest); if (b->verbose > 2) { printf( " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", encroached->subsegorg[0], encroached->subsegorg[1], encroached->subsegdest[0], encroached->subsegdest[1]); } } } /* Return a handle whose primary edge contains the vertex, */ /* which has not been inserted. */ otricopy(horiz, *searchtri); otricopy(horiz, m->recenttri); return VIOLATINGVERTEX; } } /* Insert the vertex on an edge, dividing one triangle into two (if */ /* the edge lies on a boundary) or two triangles into four. */ lprev(horiz, botright); sym(botright, botrcasing); sym(horiz, topright); /* Is there a second triangle? (Or does this edge lie on a boundary?) */ mirrorflag = topright.tri != m->dummytri; if (mirrorflag) { lnextself(topright); sym(topright, toprcasing); maketriangle(m, b, &newtopright); } else { /* Splitting a boundary edge increases the number of boundary edges. */ m->hullsize++; } maketriangle(m, b, &newbotright); /* Set the vertices of changed and new triangles. */ org(horiz, rightvertex); dest(horiz, leftvertex); apex(horiz, botvertex); setorg(newbotright, botvertex); setdest(newbotright, rightvertex); setapex(newbotright, newvertex); setorg(horiz, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of a new triangle. */ setelemattribute(newbotright, i, elemattribute(botright, i)); } if (b->vararea) { /* Set the area constraint of a new triangle. */ setareabound(newbotright, areabound(botright)); } if (mirrorflag) { dest(topright, topvertex); setorg(newtopright, rightvertex); setdest(newtopright, topvertex); setapex(newtopright, newvertex); setorg(topright, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of another new triangle. */ setelemattribute(newtopright, i, elemattribute(topright, i)); } if (b->vararea) { /* Set the area constraint of another new triangle. */ setareabound(newtopright, areabound(topright)); } } /* There may be subsegments that need to be bonded */ /* to the new triangle(s). */ if (m->checksegments) { tspivot(botright, botrsubseg); if (botrsubseg.ss != m->dummysub) { tsdissolve(botright); tsbond(newbotright, botrsubseg); } if (mirrorflag) { tspivot(topright, toprsubseg); if (toprsubseg.ss != m->dummysub) { tsdissolve(topright); tsbond(newtopright, toprsubseg); } } } /* Bond the new triangle(s) to the surrounding triangles. */ bond(newbotright, botrcasing); lprevself(newbotright); bond(newbotright, botright); lprevself(newbotright); if (mirrorflag) { bond(newtopright, toprcasing); lnextself(newtopright); bond(newtopright, topright); lnextself(newtopright); bond(newtopright, newbotright); } if (splitseg != (struct osub *) NULL) { /* Split the subsegment into two. */ setsdest(*splitseg, newvertex); ssymself(*splitseg); spivot(*splitseg, rightsubseg); insertsubseg(m, b, &newbotright, mark(*splitseg)); tspivot(newbotright, newsubseg); sbond(*splitseg, newsubseg); ssymself(newsubseg); sbond(newsubseg, rightsubseg); ssymself(*splitseg); /* Transfer the subsegment's boundary marker to the vertex */ /* if required. */ if (vertexmark(newvertex) == 0) { setvertexmark(newvertex, mark(*splitseg)); } } if (m->checkquality) { poolrestart(&m->flipstackers); m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); m->lastflip->flippedtri = encode(horiz); m->lastflip->prevflip = (struct flipstacker *) &insertvertex; } #ifdef SELF_CHECK if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle prior to edge vertex insertion (bottom).\n"); } if (mirrorflag) { if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge vertex insertion (top).\n"); } if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (top right).\n"); } if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (top left).\n"); } } if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (bottom left).\n"); } if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (bottom right).\n"); } #endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Updating bottom left "); printtriangle(m, b, &botright); if (mirrorflag) { printf(" Updating top left "); printtriangle(m, b, &topright); printf(" Creating top right "); printtriangle(m, b, &newtopright); } printf(" Creating bottom right "); printtriangle(m, b, &newbotright); } /* Position `horiz' on the first edge to check for */ /* the Delaunay property. */ lnextself(horiz); } else { /* Insert the vertex in a triangle, splitting it into three. */ lnext(horiz, botleft); lprev(horiz, botright); sym(botleft, botlcasing); sym(botright, botrcasing); maketriangle(m, b, &newbotleft); maketriangle(m, b, &newbotright); /* Set the vertices of changed and new triangles. */ org(horiz, rightvertex); dest(horiz, leftvertex); apex(horiz, botvertex); setorg(newbotleft, leftvertex); setdest(newbotleft, botvertex); setapex(newbotleft, newvertex); setorg(newbotright, botvertex); setdest(newbotright, rightvertex); setapex(newbotright, newvertex); setapex(horiz, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of the new triangles. */ attrib = elemattribute(horiz, i); setelemattribute(newbotleft, i, attrib); setelemattribute(newbotright, i, attrib); } if (b->vararea) { /* Set the area constraint of the new triangles. */ area = areabound(horiz); setareabound(newbotleft, area); setareabound(newbotright, area); } /* There may be subsegments that need to be bonded */ /* to the new triangles. */ if (m->checksegments) { tspivot(botleft, botlsubseg); if (botlsubseg.ss != m->dummysub) { tsdissolve(botleft); tsbond(newbotleft, botlsubseg); } tspivot(botright, botrsubseg); if (botrsubseg.ss != m->dummysub) { tsdissolve(botright); tsbond(newbotright, botrsubseg); } } /* Bond the new triangles to the surrounding triangles. */ bond(newbotleft, botlcasing); bond(newbotright, botrcasing); lnextself(newbotleft); lprevself(newbotright); bond(newbotleft, newbotright); lnextself(newbotleft); bond(botleft, newbotleft); lprevself(newbotright); bond(botright, newbotright); if (m->checkquality) { poolrestart(&m->flipstackers); m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); m->lastflip->flippedtri = encode(horiz); m->lastflip->prevflip = (struct flipstacker *) NULL; } #ifdef SELF_CHECK if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to vertex insertion.\n"); } if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (top).\n"); } if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (left).\n"); } if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (right).\n"); } #endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Updating top "); printtriangle(m, b, &horiz); printf(" Creating left "); printtriangle(m, b, &newbotleft); printf(" Creating right "); printtriangle(m, b, &newbotright); } } /* The insertion is successful by default, unless an encroached */ /* subsegment is found. */ success = SUCCESSFULVERTEX; /* Circle around the newly inserted vertex, checking each edge opposite */ /* it for the Delaunay property. Non-Delaunay edges are flipped. */ /* `horiz' is always the edge being checked. `first' marks where to */ /* stop circling. */ org(horiz, first); rightvertex = first; dest(horiz, leftvertex); /* Circle until finished. */ while (1) { /* By default, the edge will be flipped. */ doflip = 1; if (m->checksegments) { /* Check for a subsegment, which cannot be flipped. */ tspivot(horiz, checksubseg); if (checksubseg.ss != m->dummysub) { /* The edge is a subsegment and cannot be flipped. */ doflip = 0; #ifndef CDT_ONLY if (segmentflaws) { /* Does the new vertex encroach upon this subsegment? */ if (checkseg4encroach(m, b, &checksubseg, iradius)) { success = ENCROACHINGVERTEX; } } #endif /* not CDT_ONLY */ } } if (doflip) { /* Check if the edge is a boundary edge. */ sym(horiz, top); if (top.tri == m->dummytri) { /* The edge is a boundary edge and cannot be flipped. */ doflip = 0; } else { /* Find the vertex on the other side of the edge. */ apex(top, farvertex); /* In the incremental Delaunay triangulation algorithm, any of */ /* `leftvertex', `rightvertex', and `farvertex' could be vertices */ /* of the triangular bounding box. These vertices must be */ /* treated as if they are infinitely distant, even though their */ /* "coordinates" are not. */ if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) || (leftvertex == m->infvertex3)) { /* `leftvertex' is infinitely distant. Check the convexity of */ /* the boundary of the triangulation. 'farvertex' might be */ /* infinite as well, but trust me, this same condition should */ /* be applied. */ doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex) > 0.0; } else if ((rightvertex == m->infvertex1) || (rightvertex == m->infvertex2) || (rightvertex == m->infvertex3)) { /* `rightvertex' is infinitely distant. Check the convexity of */ /* the boundary of the triangulation. 'farvertex' might be */ /* infinite as well, but trust me, this same condition should */ /* be applied. */ doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex) > 0.0; } else if ((farvertex == m->infvertex1) || (farvertex == m->infvertex2) || (farvertex == m->infvertex3)) { /* `farvertex' is infinitely distant and cannot be inside */ /* the circumcircle of the triangle `horiz'. */ doflip = 0; } else { /* Test whether the edge is locally Delaunay. */ doflip = incircle(m, b, leftvertex, newvertex, rightvertex, farvertex) > 0.0; } if (doflip) { /* We made it! Flip the edge `horiz' by rotating its containing */ /* quadrilateral (the two triangles adjacent to `horiz'). */ /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(horiz, botleft); sym(botleft, botlcasing); lprev(horiz, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn counterclockwise. */ bond(topleft, botlcasing); bond(botleft, botrcasing); bond(botright, toprcasing); bond(topright, toplcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(horiz, farvertex); setdest(horiz, newvertex); setapex(horiz, rightvertex); setorg(top, newvertex); setdest(top, farvertex); setapex(top, leftvertex); for (i = 0; i < m->eextras; i++) { /* Take the average of the two triangles' attributes. */ attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); setelemattribute(top, i, attrib); setelemattribute(horiz, i, attrib); } if (b->vararea) { if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) { area = -1.0; } else { /* Take the average of the two triangles' area constraints. */ /* This prevents small area constraints from migrating a */ /* long, long way from their original location due to flips. */ area = 0.5 * (areabound(top) + areabound(horiz)); } setareabound(top, area); setareabound(horiz, area); } if (m->checkquality) { newflip = (struct flipstacker *) poolalloc(&m->flipstackers); newflip->flippedtri = encode(horiz); newflip->prevflip = m->lastflip; m->lastflip = newflip; } #ifdef SELF_CHECK if (newvertex != (vertex) NULL) { if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge flip (bottom).\n"); } /* The following test has been removed because constrainededge() */ /* sometimes generates inverted triangles that insertvertex() */ /* removes. */ /* if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge flip (top).\n"); } */ if (counterclockwise(m, b, farvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after edge flip (left).\n"); } if (counterclockwise(m, b, newvertex, rightvertex, farvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after edge flip (right).\n"); } } #endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Edge flip results in left "); lnextself(topleft); printtriangle(m, b, &topleft); printf(" and right "); printtriangle(m, b, &horiz); } /* On the next iterations, consider the two edges that were */ /* exposed (this is, are now visible to the newly inserted */ /* vertex) by the edge flip. */ lprevself(horiz); leftvertex = farvertex; } } } if (!doflip) { /* The handle `horiz' is accepted as locally Delaunay. */ #ifndef CDT_ONLY if (triflaws) { /* Check the triangle `horiz' for quality. */ testtriangle(m, b, &horiz); } #endif /* not CDT_ONLY */ /* Look for the next edge around the newly inserted vertex. */ lnextself(horiz); sym(horiz, testtri); /* Check for finishing a complete revolution about the new vertex, or */ /* falling outside of the triangulation. The latter will happen */ /* when a vertex is inserted at a boundary. */ if ((leftvertex == first) || (testtri.tri == m->dummytri)) { /* We're done. Return a triangle whose origin is the new vertex. */ lnext(horiz, *searchtri); lnext(horiz, m->recenttri); return success; } /* Finish finding the next edge around the newly inserted vertex. */ lnext(testtri, horiz); rightvertex = leftvertex; dest(horiz, leftvertex); } } } /*****************************************************************************/ /* */ /* triangulatepolygon() Find the Delaunay triangulation of a polygon that */ /* has a certain "nice" shape. This includes the */ /* polygons that result from deletion of a vertex or */ /* insertion of a segment. */ /* */ /* This is a conceptually difficult routine. The starting assumption is */ /* that we have a polygon with n sides. n - 1 of these sides are currently */ /* represented as edges in the mesh. One side, called the "base", need not */ /* be. */ /* */ /* Inside the polygon is a structure I call a "fan", consisting of n - 1 */ /* triangles that share a common origin. For each of these triangles, the */ /* edge opposite the origin is one of the sides of the polygon. The */ /* primary edge of each triangle is the edge directed from the origin to */ /* the destination; note that this is not the same edge that is a side of */ /* the polygon. `firstedge' is the primary edge of the first triangle. */ /* From there, the triangles follow in counterclockwise order about the */ /* polygon, until `lastedge', the primary edge of the last triangle. */ /* `firstedge' and `lastedge' are probably connected to other triangles */ /* beyond the extremes of the fan, but their identity is not important, as */ /* long as the fan remains connected to them. */ /* */ /* Imagine the polygon oriented so that its base is at the bottom. This */ /* puts `firstedge' on the far right, and `lastedge' on the far left. */ /* The right vertex of the base is the destination of `firstedge', and the */ /* left vertex of the base is the apex of `lastedge'. */ /* */ /* The challenge now is to find the right sequence of edge flips to */ /* transform the fan into a Delaunay triangulation of the polygon. Each */ /* edge flip effectively removes one triangle from the fan, committing it */ /* to the polygon. The resulting polygon has one fewer edge. If `doflip' */ /* is set, the final flip will be performed, resulting in a fan of one */ /* (useless?) triangle. If `doflip' is not set, the final flip is not */ /* performed, resulting in a fan of two triangles, and an unfinished */ /* triangular polygon that is not yet filled out with a single triangle. */ /* On completion of the routine, `lastedge' is the last remaining triangle, */ /* or the leftmost of the last two. */ /* */ /* Although the flips are performed in the order described above, the */ /* decisions about what flips to perform are made in precisely the reverse */ /* order. The recursive triangulatepolygon() procedure makes a decision, */ /* uses up to two recursive calls to triangulate the "subproblems" */ /* (polygons with fewer edges), and then performs an edge flip. */ /* */ /* The "decision" it makes is which vertex of the polygon should be */ /* connected to the base. This decision is made by testing every possible */ /* vertex. Once the best vertex is found, the two edges that connect this */ /* vertex to the base become the bases for two smaller polygons. These */ /* are triangulated recursively. Unfortunately, this approach can take */ /* O(n^2) time not only in the worst case, but in many common cases. It's */ /* rarely a big deal for vertex deletion, where n is rarely larger than */ /* ten, but it could be a big deal for segment insertion, especially if */ /* there's a lot of long segments that each cut many triangles. I ought to */ /* code a faster algorithm some day. */ /* */ /* The `edgecount' parameter is the number of sides of the polygon, */ /* including its base. `triflaws' is a flag that determines whether the */ /* new triangles should be tested for quality, and enqueued if they are */ /* bad. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void triangulatepolygon(struct mesh *m, struct behavior *b, struct otri *firstedge, struct otri *lastedge, int edgecount, int doflip, int triflaws) #else /* not ANSI_DECLARATORS */ void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws) struct mesh *m; struct behavior *b; struct otri *firstedge; struct otri *lastedge; int edgecount; int doflip; int triflaws; #endif /* not ANSI_DECLARATORS */ { struct otri testtri; struct otri besttri; struct otri tempedge; vertex leftbasevertex, rightbasevertex; vertex testvertex; vertex bestvertex; int bestnumber; int i; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ /* Identify the base vertices. */ apex(*lastedge, leftbasevertex); dest(*firstedge, rightbasevertex); if (b->verbose > 2) { printf(" Triangulating interior polygon at edge\n"); printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0], leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]); } /* Find the best vertex to connect the base to. */ onext(*firstedge, besttri); dest(besttri, bestvertex); otricopy(besttri, testtri); bestnumber = 1; for (i = 2; i <= edgecount - 2; i++) { onextself(testtri); dest(testtri, testvertex); /* Is this a better vertex? */ if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex, testvertex) > 0.0) { otricopy(testtri, besttri); bestvertex = testvertex; bestnumber = i; } } if (b->verbose > 2) { printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0], bestvertex[1]); } if (bestnumber > 1) { /* Recursively triangulate the smaller polygon on the right. */ oprev(besttri, tempedge); triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1, triflaws); } if (bestnumber < edgecount - 2) { /* Recursively triangulate the smaller polygon on the left. */ sym(besttri, tempedge); triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1, triflaws); /* Find `besttri' again; it may have been lost to edge flips. */ sym(tempedge, besttri); } if (doflip) { /* Do one final edge flip. */ flip(m, b, &besttri); #ifndef CDT_ONLY if (triflaws) { /* Check the quality of the newly committed triangle. */ sym(besttri, testtri); testtriangle(m, b, &testtri); } #endif /* not CDT_ONLY */ } /* Return the base triangle. */ otricopy(besttri, *lastedge); } /*****************************************************************************/ /* */ /* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */ /* that the triangulation remains Delaunay. */ /* */ /* The origin of `deltri' is deleted. The union of the triangles adjacent */ /* to this vertex is a polygon, for which the Delaunay triangulation is */ /* found. Two triangles are removed from the mesh. */ /* */ /* Only interior vertices that do not lie on segments or boundaries may be */ /* deleted. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri) #else /* not ANSI_DECLARATORS */ void deletevertex(m, b, deltri) struct mesh *m; struct behavior *b; struct otri *deltri; #endif /* not ANSI_DECLARATORS */ { struct otri countingtri; struct otri firstedge, lastedge; struct otri deltriright; struct otri lefttri, righttri; struct otri leftcasing, rightcasing; struct osub leftsubseg, rightsubseg; vertex delvertex; vertex neworg; int edgecount; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*deltri, delvertex); if (b->verbose > 1) { printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]); } vertexdealloc(m, delvertex); /* Count the degree of the vertex being deleted. */ onext(*deltri, countingtri); edgecount = 1; while (!otriequal(*deltri, countingtri)) { #ifdef SELF_CHECK if (countingtri.tri == m->dummytri) { printf("Internal error in deletevertex():\n"); printf(" Attempt to delete boundary vertex.\n"); internalerror(); } #endif /* SELF_CHECK */ edgecount++; onextself(countingtri); } #ifdef SELF_CHECK if (edgecount < 3) { printf("Internal error in deletevertex():\n Vertex has degree %d.\n", edgecount); internalerror(); } #endif /* SELF_CHECK */ if (edgecount > 3) { /* Triangulate the polygon defined by the union of all triangles */ /* adjacent to the vertex being deleted. Check the quality of */ /* the resulting triangles. */ onext(*deltri, firstedge); oprev(*deltri, lastedge); triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0, !b->nobisect); } /* Splice out two triangles. */ lprev(*deltri, deltriright); dnext(*deltri, lefttri); sym(lefttri, leftcasing); oprev(deltriright, righttri); sym(righttri, rightcasing); bond(*deltri, leftcasing); bond(deltriright, rightcasing); tspivot(lefttri, leftsubseg); if (leftsubseg.ss != m->dummysub) { tsbond(*deltri, leftsubseg); } tspivot(righttri, rightsubseg); if (rightsubseg.ss != m->dummysub) { tsbond(deltriright, rightsubseg); } /* Set the new origin of `deltri' and check its quality. */ org(lefttri, neworg); setorg(*deltri, neworg); if (!b->nobisect) { testtriangle(m, b, deltri); } /* Delete the two spliced-out triangles. */ triangledealloc(m, lefttri.tri); triangledealloc(m, righttri.tri); } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* undovertex() Undo the most recent vertex insertion. */ /* */ /* Walks through the list of transformations (flips and a vertex insertion) */ /* in the reverse of the order in which they were done, and undoes them. */ /* The inserted vertex is removed from the triangulation and deallocated. */ /* Two triangles (possibly just one) are also deallocated. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void undovertex(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void undovertex(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri fliptri; struct otri botleft, botright, topright; struct otri botlcasing, botrcasing, toprcasing; struct otri gluetri; struct osub botlsubseg, botrsubseg, toprsubseg; vertex botvertex, rightvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Walk through the list of transformations (flips and a vertex insertion) */ /* in the reverse of the order in which they were done, and undo them. */ while (m->lastflip != (struct flipstacker *) NULL) { /* Find a triangle involved in the last unreversed transformation. */ decode(m->lastflip->flippedtri, fliptri); /* We are reversing one of three transformations: a trisection of one */ /* triangle into three (by inserting a vertex in the triangle), a */ /* bisection of two triangles into four (by inserting a vertex in an */ /* edge), or an edge flip. */ if (m->lastflip->prevflip == (struct flipstacker *) NULL) { /* Restore a triangle that was split into three triangles, */ /* so it is again one triangle. */ dprev(fliptri, botleft); lnextself(botleft); onext(fliptri, botright); lprevself(botright); sym(botleft, botlcasing); sym(botright, botrcasing); dest(botleft, botvertex); setapex(fliptri, botvertex); lnextself(fliptri); bond(fliptri, botlcasing); tspivot(botleft, botlsubseg); tsbond(fliptri, botlsubseg); lnextself(fliptri); bond(fliptri, botrcasing); tspivot(botright, botrsubseg); tsbond(fliptri, botrsubseg); /* Delete the two spliced-out triangles. */ triangledealloc(m, botleft.tri); triangledealloc(m, botright.tri); } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) { /* Restore two triangles that were split into four triangles, */ /* so they are again two triangles. */ lprev(fliptri, gluetri); sym(gluetri, botright); lnextself(botright); sym(botright, botrcasing); dest(botright, rightvertex); setorg(fliptri, rightvertex); bond(gluetri, botrcasing); tspivot(botright, botrsubseg); tsbond(gluetri, botrsubseg); /* Delete the spliced-out triangle. */ triangledealloc(m, botright.tri); sym(fliptri, gluetri); if (gluetri.tri != m->dummytri) { lnextself(gluetri); dnext(gluetri, topright); sym(topright, toprcasing); setorg(gluetri, rightvertex); bond(gluetri, toprcasing); tspivot(topright, toprsubseg); tsbond(gluetri, toprsubseg); /* Delete the spliced-out triangle. */ triangledealloc(m, topright.tri); } /* This is the end of the list, sneakily encoded. */ m->lastflip->prevflip = (struct flipstacker *) NULL; } else { /* Undo an edge flip. */ unflip(m, b, &fliptri); } /* Go on and process the next transformation. */ m->lastflip = m->lastflip->prevflip; } } #endif /* not CDT_ONLY */ /** **/ /** **/ /********* Mesh transformation routines end here *********/ /********* Divide-and-conquer Delaunay triangulation begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* The divide-and-conquer bounding box */ /* */ /* I originally implemented the divide-and-conquer and incremental Delaunay */ /* triangulations using the edge-based data structure presented by Guibas */ /* and Stolfi. Switching to a triangle-based data structure doubled the */ /* speed. However, I had to think of a few extra tricks to maintain the */ /* elegance of the original algorithms. */ /* */ /* The "bounding box" used by my variant of the divide-and-conquer */ /* algorithm uses one triangle for each edge of the convex hull of the */ /* triangulation. These bounding triangles all share a common apical */ /* vertex, which is represented by NULL and which represents nothing. */ /* The bounding triangles are linked in a circular fan about this NULL */ /* vertex, and the edges on the convex hull of the triangulation appear */ /* opposite the NULL vertex. You might find it easiest to imagine that */ /* the NULL vertex is a point in 3D space behind the center of the */ /* triangulation, and that the bounding triangles form a sort of cone. */ /* */ /* This bounding box makes it easy to represent degenerate cases. For */ /* instance, the triangulation of two vertices is a single edge. This edge */ /* is represented by two bounding box triangles, one on each "side" of the */ /* edge. These triangles are also linked together in a fan about the NULL */ /* vertex. */ /* */ /* The bounding box also makes it easy to traverse the convex hull, as the */ /* divide-and-conquer algorithm needs to do. */ /* */ /*****************************************************************************/ /*****************************************************************************/ /* */ /* vertexsort() Sort an array of vertices by x-coordinate, using the */ /* y-coordinate as a secondary key. */ /* */ /* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */ /* the usual quicksort mistakes. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void vertexsort(vertex *sortarray, int arraysize) #else /* not ANSI_DECLARATORS */ void vertexsort(sortarray, arraysize) vertex *sortarray; int arraysize; #endif /* not ANSI_DECLARATORS */ { int left, right; int pivot; REAL pivotx, pivoty; vertex temp; if (arraysize == 2) { /* Recursive base case. */ if ((sortarray[0][0] > sortarray[1][0]) || ((sortarray[0][0] == sortarray[1][0]) && (sortarray[0][1] > sortarray[1][1]))) { temp = sortarray[1]; sortarray[1] = sortarray[0]; sortarray[0] = temp; } return; } /* Choose a random pivot to split the array. */ pivot = (int) randomnation(arraysize); pivotx = sortarray[pivot][0]; pivoty = sortarray[pivot][1]; /* Split the array. */ left = -1; right = arraysize; while (left < right) { /* Search for a vertex whose x-coordinate is too large for the left. */ do { left++; } while ((left <= right) && ((sortarray[left][0] < pivotx) || ((sortarray[left][0] == pivotx) && (sortarray[left][1] < pivoty)))); /* Search for a vertex whose x-coordinate is too small for the right. */ do { right--; } while ((left <= right) && ((sortarray[right][0] > pivotx) || ((sortarray[right][0] == pivotx) && (sortarray[right][1] > pivoty)))); if (left < right) { /* Swap the left and right vertices. */ temp = sortarray[left]; sortarray[left] = sortarray[right]; sortarray[right] = temp; } } if (left > 1) { /* Recursively sort the left subset. */ vertexsort(sortarray, left); } if (right < arraysize - 2) { /* Recursively sort the right subset. */ vertexsort(&sortarray[right + 1], arraysize - right - 1); } } /*****************************************************************************/ /* */ /* vertexmedian() An order statistic algorithm, almost. Shuffles an */ /* array of vertices so that the first `median' vertices */ /* occur lexicographically before the remaining vertices. */ /* */ /* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */ /* if axis == 1. Very similar to the vertexsort() procedure, but runs in */ /* randomized linear time. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void vertexmedian(vertex *sortarray, int arraysize, int median, int axis) #else /* not ANSI_DECLARATORS */ void vertexmedian(sortarray, arraysize, median, axis) vertex *sortarray; int arraysize; int median; int axis; #endif /* not ANSI_DECLARATORS */ { int left, right; int pivot; REAL pivot1, pivot2; vertex temp; if (arraysize == 2) { /* Recursive base case. */ if ((sortarray[0][axis] > sortarray[1][axis]) || ((sortarray[0][axis] == sortarray[1][axis]) && (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { temp = sortarray[1]; sortarray[1] = sortarray[0]; sortarray[0] = temp; } return; } /* Choose a random pivot to split the array. */ pivot = (int) randomnation(arraysize); pivot1 = sortarray[pivot][axis]; pivot2 = sortarray[pivot][1 - axis]; /* Split the array. */ left = -1; right = arraysize; while (left < right) { /* Search for a vertex whose x-coordinate is too large for the left. */ do { left++; } while ((left <= right) && ((sortarray[left][axis] < pivot1) || ((sortarray[left][axis] == pivot1) && (sortarray[left][1 - axis] < pivot2)))); /* Search for a vertex whose x-coordinate is too small for the right. */ do { right--; } while ((left <= right) && ((sortarray[right][axis] > pivot1) || ((sortarray[right][axis] == pivot1) && (sortarray[right][1 - axis] > pivot2)))); if (left < right) { /* Swap the left and right vertices. */ temp = sortarray[left]; sortarray[left] = sortarray[right]; sortarray[right] = temp; } } /* Unlike in vertexsort(), at most one of the following */ /* conditionals is true. */ if (left > median) { /* Recursively shuffle the left subset. */ vertexmedian(sortarray, left, median, axis); } if (right < median - 1) { /* Recursively shuffle the right subset. */ vertexmedian(&sortarray[right + 1], arraysize - right - 1, median - right - 1, axis); } } /*****************************************************************************/ /* */ /* alternateaxes() Sorts the vertices as appropriate for the divide-and- */ /* conquer algorithm with alternating cuts. */ /* */ /* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */ /* For the base case, subsets containing only two or three vertices are */ /* always sorted by x-coordinate. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void alternateaxes(vertex *sortarray, int arraysize, int axis) #else /* not ANSI_DECLARATORS */ void alternateaxes(sortarray, arraysize, axis) vertex *sortarray; int arraysize; int axis; #endif /* not ANSI_DECLARATORS */ { int divider; divider = arraysize >> 1; if (arraysize <= 3) { /* Recursive base case: subsets of two or three vertices will be */ /* handled specially, and should always be sorted by x-coordinate. */ axis = 0; } /* Partition with a horizontal or vertical cut. */ vertexmedian(sortarray, arraysize, divider, axis); /* Recursively partition the subsets with a cross cut. */ if (arraysize - divider >= 2) { if (divider >= 2) { alternateaxes(sortarray, divider, 1 - axis); } alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); } } /*****************************************************************************/ /* */ /* mergehulls() Merge two adjacent Delaunay triangulations into a */ /* single Delaunay triangulation. */ /* */ /* This is similar to the algorithm given by Guibas and Stolfi, but uses */ /* a triangle-based, rather than edge-based, data structure. */ /* */ /* The algorithm walks up the gap between the two triangulations, knitting */ /* them together. As they are merged, some of their bounding triangles */ /* are converted into real triangles of the triangulation. The procedure */ /* pulls each hull's bounding triangles apart, then knits them together */ /* like the teeth of two gears. The Delaunay property determines, at each */ /* step, whether the next "tooth" is a bounding triangle of the left hull */ /* or the right. When a bounding triangle becomes real, its apex is */ /* changed from NULL to a real vertex. */ /* */ /* Only two new triangles need to be allocated. These become new bounding */ /* triangles at the top and bottom of the seam. They are used to connect */ /* the remaining bounding triangles (those that have not been converted */ /* into real triangles) into a single fan. */ /* */ /* On entry, `farleft' and `innerleft' are bounding triangles of the left */ /* triangulation. The origin of `farleft' is the leftmost vertex, and */ /* the destination of `innerleft' is the rightmost vertex of the */ /* triangulation. Similarly, `innerright' and `farright' are bounding */ /* triangles of the right triangulation. The origin of `innerright' and */ /* destination of `farright' are the leftmost and rightmost vertices. */ /* */ /* On completion, the origin of `farleft' is the leftmost vertex of the */ /* merged triangulation, and the destination of `farright' is the rightmost */ /* vertex. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, struct otri *innerleft, struct otri *innerright, struct otri *farright, int axis) #else /* not ANSI_DECLARATORS */ void mergehulls(m, b, farleft, innerleft, innerright, farright, axis) struct mesh *m; struct behavior *b; struct otri *farleft; struct otri *innerleft; struct otri *innerright; struct otri *farright; int axis; #endif /* not ANSI_DECLARATORS */ { struct otri leftcand, rightcand; struct otri baseedge; struct otri nextedge; struct otri sidecasing, topcasing, outercasing; struct otri checkedge; vertex innerleftdest; vertex innerrightorg; vertex innerleftapex, innerrightapex; vertex farleftpt, farrightpt; vertex farleftapex, farrightapex; vertex lowerleft, lowerright; vertex upperleft, upperright; vertex nextapex; vertex checkvertex; int changemade; int badedge; int leftfinished, rightfinished; triangle ptr; /* Temporary variable used by sym(). */ dest(*innerleft, innerleftdest); apex(*innerleft, innerleftapex); org(*innerright, innerrightorg); apex(*innerright, innerrightapex); /* Special treatment for horizontal cuts. */ if (b->dwyer && (axis == 1)) { org(*farleft, farleftpt); apex(*farleft, farleftapex); dest(*farright, farrightpt); apex(*farright, farrightapex); /* The pointers to the extremal vertices are shifted to point to the */ /* topmost and bottommost vertex of each hull, rather than the */ /* leftmost and rightmost vertices. */ while (farleftapex[1] < farleftpt[1]) { lnextself(*farleft); symself(*farleft); farleftpt = farleftapex; apex(*farleft, farleftapex); } sym(*innerleft, checkedge); apex(checkedge, checkvertex); while (checkvertex[1] > innerleftdest[1]) { lnext(checkedge, *innerleft); innerleftapex = innerleftdest; innerleftdest = checkvertex; sym(*innerleft, checkedge); apex(checkedge, checkvertex); } while (innerrightapex[1] < innerrightorg[1]) { lnextself(*innerright); symself(*innerright); innerrightorg = innerrightapex; apex(*innerright, innerrightapex); } sym(*farright, checkedge); apex(checkedge, checkvertex); while (checkvertex[1] > farrightpt[1]) { lnext(checkedge, *farright); farrightapex = farrightpt; farrightpt = checkvertex; sym(*farright, checkedge); apex(checkedge, checkvertex); } } /* Find a line tangent to and below both hulls. */ do { changemade = 0; /* Make innerleftdest the "bottommost" vertex of the left hull. */ if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) > 0.0) { lprevself(*innerleft); symself(*innerleft); innerleftdest = innerleftapex; apex(*innerleft, innerleftapex); changemade = 1; } /* Make innerrightorg the "bottommost" vertex of the right hull. */ if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) > 0.0) { lnextself(*innerright); symself(*innerright); innerrightorg = innerrightapex; apex(*innerright, innerrightapex); changemade = 1; } } while (changemade); /* Find the two candidates to be the next "gear tooth." */ sym(*innerleft, leftcand); sym(*innerright, rightcand); /* Create the bottom new bounding triangle. */ maketriangle(m, b, &baseedge); /* Connect it to the bounding boxes of the left and right triangulations. */ bond(baseedge, *innerleft); lnextself(baseedge); bond(baseedge, *innerright); lnextself(baseedge); setorg(baseedge, innerrightorg); setdest(baseedge, innerleftdest); /* Apex is intentionally left NULL. */ if (b->verbose > 2) { printf(" Creating base bounding "); printtriangle(m, b, &baseedge); } /* Fix the extreme triangles if necessary. */ org(*farleft, farleftpt); if (innerleftdest == farleftpt) { lnext(baseedge, *farleft); } dest(*farright, farrightpt); if (innerrightorg == farrightpt) { lprev(baseedge, *farright); } /* The vertices of the current knitting edge. */ lowerleft = innerleftdest; lowerright = innerrightorg; /* The candidate vertices for knitting. */ apex(leftcand, upperleft); apex(rightcand, upperright); /* Walk up the gap between the two triangulations, knitting them together. */ while (1) { /* Have we reached the top? (This isn't quite the right question, */ /* because even though the left triangulation might seem finished now, */ /* moving up on the right triangulation might reveal a new vertex of */ /* the left triangulation. And vice-versa.) */ leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <= 0.0; rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright) <= 0.0; if (leftfinished && rightfinished) { /* Create the top new bounding triangle. */ maketriangle(m, b, &nextedge); setorg(nextedge, lowerleft); setdest(nextedge, lowerright); /* Apex is intentionally left NULL. */ /* Connect it to the bounding boxes of the two triangulations. */ bond(nextedge, baseedge); lnextself(nextedge); bond(nextedge, rightcand); lnextself(nextedge); bond(nextedge, leftcand); if (b->verbose > 2) { printf(" Creating top bounding "); printtriangle(m, b, &nextedge); } /* Special treatment for horizontal cuts. */ if (b->dwyer && (axis == 1)) { org(*farleft, farleftpt); apex(*farleft, farleftapex); dest(*farright, farrightpt); apex(*farright, farrightapex); sym(*farleft, checkedge); apex(checkedge, checkvertex); /* The pointers to the extremal vertices are restored to the */ /* leftmost and rightmost vertices (rather than topmost and */ /* bottommost). */ while (checkvertex[0] < farleftpt[0]) { lprev(checkedge, *farleft); farleftapex = farleftpt; farleftpt = checkvertex; sym(*farleft, checkedge); apex(checkedge, checkvertex); } while (farrightapex[0] > farrightpt[0]) { lprevself(*farright); symself(*farright); farrightpt = farrightapex; apex(*farright, farrightapex); } } return; } /* Consider eliminating edges from the left triangulation. */ if (!leftfinished) { /* What vertex would be exposed if an edge were deleted? */ lprev(leftcand, nextedge); symself(nextedge); apex(nextedge, nextapex); /* If nextapex is NULL, then no vertex would be exposed; the */ /* triangulation would have been eaten right through. */ if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > 0.0; while (badedge) { /* Eliminate the edge with an edge flip. As a result, the */ /* left triangulation will have one more boundary triangle. */ lnextself(nextedge); sym(nextedge, topcasing); lnextself(nextedge); sym(nextedge, sidecasing); bond(nextedge, topcasing); bond(leftcand, sidecasing); lnextself(leftcand); sym(leftcand, outercasing); lprevself(nextedge); bond(nextedge, outercasing); /* Correct the vertices to reflect the edge flip. */ setorg(leftcand, lowerleft); setdest(leftcand, NULL); setapex(leftcand, nextapex); setorg(nextedge, NULL); setdest(nextedge, upperleft); setapex(nextedge, nextapex); /* Consider the newly exposed vertex. */ upperleft = nextapex; /* What vertex would be exposed if another edge were deleted? */ otricopy(sidecasing, nextedge); apex(nextedge, nextapex); if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > 0.0; } else { /* Avoid eating right through the triangulation. */ badedge = 0; } } } } /* Consider eliminating edges from the right triangulation. */ if (!rightfinished) { /* What vertex would be exposed if an edge were deleted? */ lnext(rightcand, nextedge); symself(nextedge); apex(nextedge, nextapex); /* If nextapex is NULL, then no vertex would be exposed; the */ /* triangulation would have been eaten right through. */ if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > 0.0; while (badedge) { /* Eliminate the edge with an edge flip. As a result, the */ /* right triangulation will have one more boundary triangle. */ lprevself(nextedge); sym(nextedge, topcasing); lprevself(nextedge); sym(nextedge, sidecasing); bond(nextedge, topcasing); bond(rightcand, sidecasing); lprevself(rightcand); sym(rightcand, outercasing); lnextself(nextedge); bond(nextedge, outercasing); /* Correct the vertices to reflect the edge flip. */ setorg(rightcand, NULL); setdest(rightcand, lowerright); setapex(rightcand, nextapex); setorg(nextedge, upperright); setdest(nextedge, NULL); setapex(nextedge, nextapex); /* Consider the newly exposed vertex. */ upperright = nextapex; /* What vertex would be exposed if another edge were deleted? */ otricopy(sidecasing, nextedge); apex(nextedge, nextapex); if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > 0.0; } else { /* Avoid eating right through the triangulation. */ badedge = 0; } } } } if (leftfinished || (!rightfinished && (incircle(m, b, upperleft, lowerleft, lowerright, upperright) > 0.0))) { /* Knit the triangulations, adding an edge from `lowerleft' */ /* to `upperright'. */ bond(baseedge, rightcand); lprev(rightcand, baseedge); setdest(baseedge, lowerleft); lowerright = upperright; sym(baseedge, rightcand); apex(rightcand, upperright); } else { /* Knit the triangulations, adding an edge from `upperleft' */ /* to `lowerright'. */ bond(baseedge, leftcand); lnext(leftcand, baseedge); setorg(baseedge, lowerright); lowerleft = upperleft; sym(baseedge, leftcand); apex(leftcand, upperleft); } if (b->verbose > 2) { printf(" Connecting "); printtriangle(m, b, &baseedge); } } } /*****************************************************************************/ /* */ /* divconqrecurse() Recursively form a Delaunay triangulation by the */ /* divide-and-conquer method. */ /* */ /* Recursively breaks down the problem into smaller pieces, which are */ /* knitted together by mergehulls(). The base cases (problems of two or */ /* three vertices) are handled specially here. */ /* */ /* On completion, `farleft' and `farright' are bounding triangles such that */ /* the origin of `farleft' is the leftmost vertex (breaking ties by */ /* choosing the highest leftmost vertex), and the destination of */ /* `farright' is the rightmost vertex (breaking ties by choosing the */ /* lowest rightmost vertex). */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, int vertices, int axis, struct otri *farleft, struct otri *farright) #else /* not ANSI_DECLARATORS */ void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright) struct mesh *m; struct behavior *b; vertex *sortarray; int vertices; int axis; struct otri *farleft; struct otri *farright; #endif /* not ANSI_DECLARATORS */ { struct otri midtri, tri1, tri2, tri3; struct otri innerleft, innerright; REAL area; int divider; if (b->verbose > 2) { printf(" Triangulating %d vertices.\n", vertices); } if (vertices == 2) { /* The triangulation of two vertices is an edge. An edge is */ /* represented by two bounding triangles. */ maketriangle(m, b, farleft); setorg(*farleft, sortarray[0]); setdest(*farleft, sortarray[1]); /* The apex is intentionally left NULL. */ maketriangle(m, b, farright); setorg(*farright, sortarray[1]); setdest(*farright, sortarray[0]); /* The apex is intentionally left NULL. */ bond(*farleft, *farright); lprevself(*farleft); lnextself(*farright); bond(*farleft, *farright); lprevself(*farleft); lnextself(*farright); bond(*farleft, *farright); if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, farleft); printf(" Creating "); printtriangle(m, b, farright); } /* Ensure that the origin of `farleft' is sortarray[0]. */ lprev(*farright, *farleft); return; } else if (vertices == 3) { /* The triangulation of three vertices is either a triangle (with */ /* three bounding triangles) or two edges (with four bounding */ /* triangles). In either case, four triangles are created. */ maketriangle(m, b, &midtri); maketriangle(m, b, &tri1); maketriangle(m, b, &tri2); maketriangle(m, b, &tri3); area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]); if (area == 0.0) { /* Three collinear vertices; the triangulation is two edges. */ setorg(midtri, sortarray[0]); setdest(midtri, sortarray[1]); setorg(tri1, sortarray[1]); setdest(tri1, sortarray[0]); setorg(tri2, sortarray[2]); setdest(tri2, sortarray[1]); setorg(tri3, sortarray[1]); setdest(tri3, sortarray[2]); /* All apices are intentionally left NULL. */ bond(midtri, tri1); bond(tri2, tri3); lnextself(midtri); lprevself(tri1); lnextself(tri2); lprevself(tri3); bond(midtri, tri3); bond(tri1, tri2); lnextself(midtri); lprevself(tri1); lnextself(tri2); lprevself(tri3); bond(midtri, tri1); bond(tri2, tri3); /* Ensure that the origin of `farleft' is sortarray[0]. */ otricopy(tri1, *farleft); /* Ensure that the destination of `farright' is sortarray[2]. */ otricopy(tri2, *farright); } else { /* The three vertices are not collinear; the triangulation is one */ /* triangle, namely `midtri'. */ setorg(midtri, sortarray[0]); setdest(tri1, sortarray[0]); setorg(tri3, sortarray[0]); /* Apices of tri1, tri2, and tri3 are left NULL. */ if (area > 0.0) { /* The vertices are in counterclockwise order. */ setdest(midtri, sortarray[1]); setorg(tri1, sortarray[1]); setdest(tri2, sortarray[1]); setapex(midtri, sortarray[2]); setorg(tri2, sortarray[2]); setdest(tri3, sortarray[2]); } else { /* The vertices are in clockwise order. */ setdest(midtri, sortarray[2]); setorg(tri1, sortarray[2]); setdest(tri2, sortarray[2]); setapex(midtri, sortarray[1]); setorg(tri2, sortarray[1]); setdest(tri3, sortarray[1]); } /* The topology does not depend on how the vertices are ordered. */ bond(midtri, tri1); lnextself(midtri); bond(midtri, tri2); lnextself(midtri); bond(midtri, tri3); lprevself(tri1); lnextself(tri2); bond(tri1, tri2); lprevself(tri1); lprevself(tri3); bond(tri1, tri3); lnextself(tri2); lprevself(tri3); bond(tri2, tri3); /* Ensure that the origin of `farleft' is sortarray[0]. */ otricopy(tri1, *farleft); /* Ensure that the destination of `farright' is sortarray[2]. */ if (area > 0.0) { otricopy(tri2, *farright); } else { lnext(*farleft, *farright); } } if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, &midtri); printf(" Creating "); printtriangle(m, b, &tri1); printf(" Creating "); printtriangle(m, b, &tri2); printf(" Creating "); printtriangle(m, b, &tri3); } return; } else { /* Split the vertices in half. */ divider = vertices >> 1; /* Recursively triangulate each half. */ divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft); divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis, &innerright, farright); if (b->verbose > 1) { printf(" Joining triangulations with %d and %d vertices.\n", divider, vertices - divider); } /* Merge the two triangulations into one. */ mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis); } } #ifdef ANSI_DECLARATORS long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost) #else /* not ANSI_DECLARATORS */ long removeghosts(m, b, startghost) struct mesh *m; struct behavior *b; struct otri *startghost; #endif /* not ANSI_DECLARATORS */ { struct otri searchedge; struct otri dissolveedge; struct otri deadtriangle; vertex markorg; long hullsize; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose) { printf(" Removing ghost triangles.\n"); } /* Find an edge on the convex hull to start point location from. */ lprev(*startghost, searchedge); symself(searchedge); m->dummytri[0] = encode(searchedge); /* Remove the bounding box and count the convex hull edges. */ otricopy(*startghost, dissolveedge); hullsize = 0; do { hullsize++; lnext(dissolveedge, deadtriangle); lprevself(dissolveedge); symself(dissolveedge); /* If no PSLG is involved, set the boundary markers of all the vertices */ /* on the convex hull. If a PSLG is used, this step is done later. */ if (!b->poly) { /* Watch out for the case where all the input vertices are collinear. */ if (dissolveedge.tri != m->dummytri) { org(dissolveedge, markorg); if (vertexmark(markorg) == 0) { setvertexmark(markorg, 1); } } } /* Remove a bounding triangle from a convex hull triangle. */ dissolve(dissolveedge); /* Find the next bounding triangle. */ sym(deadtriangle, dissolveedge); /* Delete the bounding triangle. */ triangledealloc(m, deadtriangle.tri); } while (!otriequal(dissolveedge, *startghost)); return hullsize; } /*****************************************************************************/ /* */ /* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */ /* conquer method. */ /* */ /* Sorts the vertices, calls a recursive procedure to triangulate them, and */ /* removes the bounding box, setting boundary markers as appropriate. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS long divconqdelaunay(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ long divconqdelaunay(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { vertex *sortarray; struct otri hullleft, hullright; int divider; int i, j; if (b->verbose) { printf(" Sorting vertices.\n"); } /* Allocate an array of pointers to vertices for sorting. */ sortarray = (vertex *) trimalloc(m->invertices * sizeof(vertex)); traversalinit(&m->vertices); for (i = 0; i < m->invertices; i++) { sortarray[i] = vertextraverse(m); } /* Sort the vertices. */ vertexsort(sortarray, m->invertices); /* Discard duplicate vertices, which can really mess up the algorithm. */ i = 0; for (j = 1; j < m->invertices; j++) { if ((sortarray[i][0] == sortarray[j][0]) && (sortarray[i][1] == sortarray[j][1])) { if (!b->quiet) { printf( "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", sortarray[j][0], sortarray[j][1]); } setvertextype(sortarray[j], UNDEADVERTEX); m->undeads++; } else { i++; sortarray[i] = sortarray[j]; } } i++; if (b->dwyer) { /* Re-sort the array of vertices to accommodate alternating cuts. */ divider = i >> 1; if (i - divider >= 2) { if (divider >= 2) { alternateaxes(sortarray, divider, 1); } alternateaxes(&sortarray[divider], i - divider, 1); } } if (b->verbose) { printf(" Forming triangulation.\n"); } /* Form the Delaunay triangulation. */ divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright); trifree((VOID *) sortarray); return removeghosts(m, b, &hullleft); } /** **/ /** **/ /********* Divide-and-conquer Delaunay triangulation ends here *********/ /********* Incremental Delaunay triangulation begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* boundingbox() Form an "infinite" bounding triangle to insert vertices */ /* into. */ /* */ /* The vertices at "infinity" are assigned finite coordinates, which are */ /* used by the point location routines, but (mostly) ignored by the */ /* Delaunay edge flip routines. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifdef ANSI_DECLARATORS void boundingbox(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void boundingbox(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri inftri; /* Handle for the triangular bounding box. */ REAL width; if (b->verbose) { printf(" Creating triangular bounding box.\n"); } /* Find the width (or height, whichever is larger) of the triangulation. */ width = m->xmax - m->xmin; if (m->ymax - m->ymin > width) { width = m->ymax - m->ymin; } if (width == 0.0) { width = 1.0; } /* Create the vertices of the bounding box. */ m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex1[0] = m->xmin - 50.0 * width; m->infvertex1[1] = m->ymin - 40.0 * width; m->infvertex2[0] = m->xmax + 50.0 * width; m->infvertex2[1] = m->ymin - 40.0 * width; m->infvertex3[0] = 0.5 * (m->xmin + m->xmax); m->infvertex3[1] = m->ymax + 60.0 * width; /* Create the bounding box. */ maketriangle(m, b, &inftri); setorg(inftri, m->infvertex1); setdest(inftri, m->infvertex2); setapex(inftri, m->infvertex3); /* Link dummytri to the bounding box so we can always find an */ /* edge to begin searching (point location) from. */ m->dummytri[0] = (triangle) inftri.tri; if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, &inftri); } } #endif /* not REDUCED */ /*****************************************************************************/ /* */ /* removebox() Remove the "infinite" bounding triangle, setting boundary */ /* markers as appropriate. */ /* */ /* The triangular bounding box has three boundary triangles (one for each */ /* side of the bounding box), and a bunch of triangles fanning out from */ /* the three bounding box vertices (one triangle for each edge of the */ /* convex hull of the inner mesh). This routine removes these triangles. */ /* */ /* Returns the number of edges on the convex hull of the triangulation. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifdef ANSI_DECLARATORS long removebox(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ long removebox(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri deadtriangle; struct otri searchedge; struct otri checkedge; struct otri nextedge, finaledge, dissolveedge; vertex markorg; long hullsize; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose) { printf(" Removing triangular bounding box.\n"); } /* Find a boundary triangle. */ nextedge.tri = m->dummytri; nextedge.orient = 0; symself(nextedge); /* Mark a place to stop. */ lprev(nextedge, finaledge); lnextself(nextedge); symself(nextedge); /* Find a triangle (on the boundary of the vertex set) that isn't */ /* a bounding box triangle. */ lprev(nextedge, searchedge); symself(searchedge); /* Check whether nextedge is another boundary triangle */ /* adjacent to the first one. */ lnext(nextedge, checkedge); symself(checkedge); if (checkedge.tri == m->dummytri) { /* Go on to the next triangle. There are only three boundary */ /* triangles, and this next triangle cannot be the third one, */ /* so it's safe to stop here. */ lprevself(searchedge); symself(searchedge); } /* Find a new boundary edge to search from, as the current search */ /* edge lies on a bounding box triangle and will be deleted. */ m->dummytri[0] = encode(searchedge); hullsize = -2l; while (!otriequal(nextedge, finaledge)) { hullsize++; lprev(nextedge, dissolveedge); symself(dissolveedge); /* If not using a PSLG, the vertices should be marked now. */ /* (If using a PSLG, markhull() will do the job.) */ if (!b->poly) { /* Be careful! One must check for the case where all the input */ /* vertices are collinear, and thus all the triangles are part of */ /* the bounding box. Otherwise, the setvertexmark() call below */ /* will cause a bad pointer reference. */ if (dissolveedge.tri != m->dummytri) { org(dissolveedge, markorg); if (vertexmark(markorg) == 0) { setvertexmark(markorg, 1); } } } /* Disconnect the bounding box triangle from the mesh triangle. */ dissolve(dissolveedge); lnext(nextedge, deadtriangle); sym(deadtriangle, nextedge); /* Get rid of the bounding box triangle. */ triangledealloc(m, deadtriangle.tri); /* Do we need to turn the corner? */ if (nextedge.tri == m->dummytri) { /* Turn the corner. */ otricopy(dissolveedge, nextedge); } } triangledealloc(m, finaledge.tri); trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */ trifree((VOID *) m->infvertex2); trifree((VOID *) m->infvertex3); return hullsize; } #endif /* not REDUCED */ /*****************************************************************************/ /* */ /* incrementaldelaunay() Form a Delaunay triangulation by incrementally */ /* inserting vertices. */ /* */ /* Returns the number of edges on the convex hull of the triangulation. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifdef ANSI_DECLARATORS long incrementaldelaunay(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ long incrementaldelaunay(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri starttri; vertex vertexloop; /* Create a triangular bounding box. */ boundingbox(m, b); if (b->verbose) { printf(" Incrementally inserting vertices.\n"); } traversalinit(&m->vertices); vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { starttri.tri = m->dummytri; if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0, 0.0) == DUPLICATEVERTEX) { if (!b->quiet) { printf( "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", vertexloop[0], vertexloop[1]); } setvertextype(vertexloop, UNDEADVERTEX); m->undeads++; } vertexloop = vertextraverse(m); } /* Remove the bounding box. */ return removebox(m, b); } #endif /* not REDUCED */ /** **/ /** **/ /********* Incremental Delaunay triangulation ends here *********/ /********* Sweepline Delaunay triangulation begins here *********/ /** **/ /** **/ #ifndef REDUCED #ifdef ANSI_DECLARATORS void eventheapinsert(struct event **heap, int heapsize, struct event *newevent) #else /* not ANSI_DECLARATORS */ void eventheapinsert(heap, heapsize, newevent) struct event **heap; int heapsize; struct event *newevent; #endif /* not ANSI_DECLARATORS */ { REAL eventx, eventy; int eventnum; int parent; int notdone; eventx = newevent->xkey; eventy = newevent->ykey; eventnum = heapsize; notdone = eventnum > 0; while (notdone) { parent = (eventnum - 1) >> 1; if ((heap[parent]->ykey < eventy) || ((heap[parent]->ykey == eventy) && (heap[parent]->xkey <= eventx))) { notdone = 0; } else { heap[eventnum] = heap[parent]; heap[eventnum]->heapposition = eventnum; eventnum = parent; notdone = eventnum > 0; } } heap[eventnum] = newevent; newevent->heapposition = eventnum; } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS void eventheapify(struct event **heap, int heapsize, int eventnum) #else /* not ANSI_DECLARATORS */ void eventheapify(heap, heapsize, eventnum) struct event **heap; int heapsize; int eventnum; #endif /* not ANSI_DECLARATORS */ { struct event *thisevent; REAL eventx, eventy; int leftchild, rightchild; int smallest; int notdone; thisevent = heap[eventnum]; eventx = thisevent->xkey; eventy = thisevent->ykey; leftchild = 2 * eventnum + 1; notdone = leftchild < heapsize; while (notdone) { if ((heap[leftchild]->ykey < eventy) || ((heap[leftchild]->ykey == eventy) && (heap[leftchild]->xkey < eventx))) { smallest = leftchild; } else { smallest = eventnum; } rightchild = leftchild + 1; if (rightchild < heapsize) { if ((heap[rightchild]->ykey < heap[smallest]->ykey) || ((heap[rightchild]->ykey == heap[smallest]->ykey) && (heap[rightchild]->xkey < heap[smallest]->xkey))) { smallest = rightchild; } } if (smallest == eventnum) { notdone = 0; } else { heap[eventnum] = heap[smallest]; heap[eventnum]->heapposition = eventnum; heap[smallest] = thisevent; thisevent->heapposition = smallest; eventnum = smallest; leftchild = 2 * eventnum + 1; notdone = leftchild < heapsize; } } } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS void eventheapdelete(struct event **heap, int heapsize, int eventnum) #else /* not ANSI_DECLARATORS */ void eventheapdelete(heap, heapsize, eventnum) struct event **heap; int heapsize; int eventnum; #endif /* not ANSI_DECLARATORS */ { struct event *moveevent; REAL eventx, eventy; int parent; int notdone; moveevent = heap[heapsize - 1]; if (eventnum > 0) { eventx = moveevent->xkey; eventy = moveevent->ykey; do { parent = (eventnum - 1) >> 1; if ((heap[parent]->ykey < eventy) || ((heap[parent]->ykey == eventy) && (heap[parent]->xkey <= eventx))) { notdone = 0; } else { heap[eventnum] = heap[parent]; heap[eventnum]->heapposition = eventnum; eventnum = parent; notdone = eventnum > 0; } } while (notdone); } heap[eventnum] = moveevent; moveevent->heapposition = eventnum; eventheapify(heap, heapsize - 1, eventnum); } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS void createeventheap(struct mesh *m, struct event ***eventheap, struct event **events, struct event **freeevents) #else /* not ANSI_DECLARATORS */ void createeventheap(m, eventheap, events, freeevents) struct mesh *m; struct event ***eventheap; struct event **events; struct event **freeevents; #endif /* not ANSI_DECLARATORS */ { vertex thisvertex; int maxevents; int i; maxevents = (3 * m->invertices) / 2; *eventheap = (struct event **) trimalloc(maxevents * sizeof(struct event *)); *events = (struct event *) trimalloc(maxevents * sizeof(struct event)); traversalinit(&m->vertices); for (i = 0; i < m->invertices; i++) { thisvertex = vertextraverse(m); (*events)[i].eventptr = (VOID *) thisvertex; (*events)[i].xkey = thisvertex[0]; (*events)[i].ykey = thisvertex[1]; eventheapinsert(*eventheap, i, *events + i); } *freeevents = (struct event *) NULL; for (i = maxevents - 1; i >= m->invertices; i--) { (*events)[i].eventptr = (VOID *) *freeevents; *freeevents = *events + i; } } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite) #else /* not ANSI_DECLARATORS */ int rightofhyperbola(m, fronttri, newsite) struct mesh *m; struct otri *fronttri; vertex newsite; #endif /* not ANSI_DECLARATORS */ { vertex leftvertex, rightvertex; REAL dxa, dya, dxb, dyb; m->hyperbolacount++; dest(*fronttri, leftvertex); apex(*fronttri, rightvertex); if ((leftvertex[1] < rightvertex[1]) || ((leftvertex[1] == rightvertex[1]) && (leftvertex[0] < rightvertex[0]))) { if (newsite[0] >= rightvertex[0]) { return 1; } } else { if (newsite[0] <= leftvertex[0]) { return 0; } } dxa = leftvertex[0] - newsite[0]; dya = leftvertex[1] - newsite[1]; dxb = rightvertex[0] - newsite[0]; dyb = rightvertex[1] - newsite[1]; return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya); } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc) #else /* not ANSI_DECLARATORS */ REAL circletop(m, pa, pb, pc, ccwabc) struct mesh *m; vertex pa; vertex pb; vertex pc; REAL ccwabc; #endif /* not ANSI_DECLARATORS */ { REAL xac, yac, xbc, ybc, xab, yab; REAL aclen2, bclen2, ablen2; m->circletopcount++; xac = pa[0] - pc[0]; yac = pa[1] - pc[1]; xbc = pb[0] - pc[0]; ybc = pb[1] - pc[1]; xab = pa[0] - pb[0]; yab = pa[1] - pb[1]; aclen2 = xac * xac + yac * yac; bclen2 = xbc * xbc + ybc * ybc; ablen2 = xab * xab + yab * yab; return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) / (2.0 * ccwabc); } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS void check4deadevent(struct otri *checktri, struct event **freeevents, struct event **eventheap, int *heapsize) #else /* not ANSI_DECLARATORS */ void check4deadevent(checktri, freeevents, eventheap, heapsize) struct otri *checktri; struct event **freeevents; struct event **eventheap; int *heapsize; #endif /* not ANSI_DECLARATORS */ { struct event *deadevent; vertex eventvertex; int eventnum; org(*checktri, eventvertex); if (eventvertex != (vertex) NULL) { deadevent = (struct event *) eventvertex; eventnum = deadevent->heapposition; deadevent->eventptr = (VOID *) *freeevents; *freeevents = deadevent; eventheapdelete(eventheap, *heapsize, eventnum); (*heapsize)--; setorg(*checktri, NULL); } } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS struct splaynode *splay(struct mesh *m, struct splaynode *splaytree, vertex searchpoint, struct otri *searchtri) #else /* not ANSI_DECLARATORS */ struct splaynode *splay(m, splaytree, searchpoint, searchtri) struct mesh *m; struct splaynode *splaytree; vertex searchpoint; struct otri *searchtri; #endif /* not ANSI_DECLARATORS */ { struct splaynode *child, *grandchild; struct splaynode *lefttree, *righttree; struct splaynode *leftright; vertex checkvertex; int rightofroot, rightofchild; if (splaytree == (struct splaynode *) NULL) { return (struct splaynode *) NULL; } dest(splaytree->keyedge, checkvertex); if (checkvertex == splaytree->keydest) { rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint); if (rightofroot) { otricopy(splaytree->keyedge, *searchtri); child = splaytree->rchild; } else { child = splaytree->lchild; } if (child == (struct splaynode *) NULL) { return splaytree; } dest(child->keyedge, checkvertex); if (checkvertex != child->keydest) { child = splay(m, child, searchpoint, searchtri); if (child == (struct splaynode *) NULL) { if (rightofroot) { splaytree->rchild = (struct splaynode *) NULL; } else { splaytree->lchild = (struct splaynode *) NULL; } return splaytree; } } rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint); if (rightofchild) { otricopy(child->keyedge, *searchtri); grandchild = splay(m, child->rchild, searchpoint, searchtri); child->rchild = grandchild; } else { grandchild = splay(m, child->lchild, searchpoint, searchtri); child->lchild = grandchild; } if (grandchild == (struct splaynode *) NULL) { if (rightofroot) { splaytree->rchild = child->lchild; child->lchild = splaytree; } else { splaytree->lchild = child->rchild; child->rchild = splaytree; } return child; } if (rightofchild) { if (rightofroot) { splaytree->rchild = child->lchild; child->lchild = splaytree; } else { splaytree->lchild = grandchild->rchild; grandchild->rchild = splaytree; } child->rchild = grandchild->lchild; grandchild->lchild = child; } else { if (rightofroot) { splaytree->rchild = grandchild->lchild; grandchild->lchild = splaytree; } else { splaytree->lchild = child->rchild; child->rchild = splaytree; } child->lchild = grandchild->rchild; grandchild->rchild = child; } return grandchild; } else { lefttree = splay(m, splaytree->lchild, searchpoint, searchtri); righttree = splay(m, splaytree->rchild, searchpoint, searchtri); pooldealloc(&m->splaynodes, (VOID *) splaytree); if (lefttree == (struct splaynode *) NULL) { return righttree; } else if (righttree == (struct splaynode *) NULL) { return lefttree; } else if (lefttree->rchild == (struct splaynode *) NULL) { lefttree->rchild = righttree->lchild; righttree->lchild = lefttree; return righttree; } else if (righttree->lchild == (struct splaynode *) NULL) { righttree->lchild = lefttree->rchild; lefttree->rchild = righttree; return lefttree; } else { /* printf("Holy Toledo!!!\n"); */ leftright = lefttree->rchild; while (leftright->rchild != (struct splaynode *) NULL) { leftright = leftright->rchild; } leftright->rchild = righttree; return lefttree; } } } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot, struct otri *newkey, vertex searchpoint) #else /* not ANSI_DECLARATORS */ struct splaynode *splayinsert(m, splayroot, newkey, searchpoint) struct mesh *m; struct splaynode *splayroot; struct otri *newkey; vertex searchpoint; #endif /* not ANSI_DECLARATORS */ { struct splaynode *newsplaynode; newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes); otricopy(*newkey, newsplaynode->keyedge); dest(*newkey, newsplaynode->keydest); if (splayroot == (struct splaynode *) NULL) { newsplaynode->lchild = (struct splaynode *) NULL; newsplaynode->rchild = (struct splaynode *) NULL; } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) { newsplaynode->lchild = splayroot; newsplaynode->rchild = splayroot->rchild; splayroot->rchild = (struct splaynode *) NULL; } else { newsplaynode->lchild = splayroot->lchild; newsplaynode->rchild = splayroot; splayroot->lchild = (struct splaynode *) NULL; } return newsplaynode; } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS struct splaynode *circletopinsert(struct mesh *m, struct behavior *b, struct splaynode *splayroot, struct otri *newkey, vertex pa, vertex pb, vertex pc, REAL topy) #else /* not ANSI_DECLARATORS */ struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy) struct mesh *m; struct behavior *b; struct splaynode *splayroot; struct otri *newkey; vertex pa; vertex pb; vertex pc; REAL topy; #endif /* not ANSI_DECLARATORS */ { REAL ccwabc; REAL xac, yac, xbc, ybc; REAL aclen2, bclen2; REAL searchpoint[2]; struct otri dummytri; ccwabc = counterclockwise(m, b, pa, pb, pc); xac = pa[0] - pc[0]; yac = pa[1] - pc[1]; xbc = pb[0] - pc[0]; ybc = pb[1] - pc[1]; aclen2 = xac * xac + yac * yac; bclen2 = xbc * xbc + ybc * ybc; searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); searchpoint[1] = topy; return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri), newkey, (vertex) searchpoint); } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot, struct otri *bottommost, vertex searchvertex, struct otri *searchtri, int *farright) #else /* not ANSI_DECLARATORS */ struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex, searchtri, farright) struct mesh *m; struct splaynode *splayroot; struct otri *bottommost; vertex searchvertex; struct otri *searchtri; int *farright; #endif /* not ANSI_DECLARATORS */ { int farrightflag; triangle ptr; /* Temporary variable used by onext(). */ otricopy(*bottommost, *searchtri); splayroot = splay(m, splayroot, searchvertex, searchtri); farrightflag = 0; while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) { onextself(*searchtri); farrightflag = otriequal(*searchtri, *bottommost); } *farright = farrightflag; return splayroot; } #endif /* not REDUCED */ #ifndef REDUCED #ifdef ANSI_DECLARATORS long sweeplinedelaunay(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ long sweeplinedelaunay(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct event **eventheap; struct event *events; struct event *freeevents; struct event *nextevent; struct event *newevent; struct splaynode *splayroot; struct otri bottommost; struct otri searchtri; struct otri fliptri; struct otri lefttri, righttri, farlefttri, farrighttri; struct otri inserttri; vertex firstvertex, secondvertex; vertex nextvertex, lastvertex; vertex connectvertex; vertex leftvertex, midvertex, rightvertex; REAL lefttest, righttest; int heapsize; int check4events, farrightflag; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, POINTER, 0); splayroot = (struct splaynode *) NULL; if (b->verbose) { printf(" Placing vertices in event heap.\n"); } createeventheap(m, &eventheap, &events, &freeevents); heapsize = m->invertices; if (b->verbose) { printf(" Forming triangulation.\n"); } maketriangle(m, b, &lefttri); maketriangle(m, b, &righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); firstvertex = (vertex) eventheap[0]->eventptr; eventheap[0]->eventptr = (VOID *) freeevents; freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; do { if (heapsize == 0) { printf("Error: Input vertices are all identical.\n"); exit(1); } secondvertex = (vertex) eventheap[0]->eventptr; eventheap[0]->eventptr = (VOID *) freeevents; freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; if ((firstvertex[0] == secondvertex[0]) && (firstvertex[1] == secondvertex[1])) { if (!b->quiet) { printf( "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", secondvertex[0], secondvertex[1]); } setvertextype(secondvertex, UNDEADVERTEX); m->undeads++; } } while ((firstvertex[0] == secondvertex[0]) && (firstvertex[1] == secondvertex[1])); setorg(lefttri, firstvertex); setdest(lefttri, secondvertex); setorg(righttri, secondvertex); setdest(righttri, firstvertex); lprev(lefttri, bottommost); lastvertex = secondvertex; while (heapsize > 0) { nextevent = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; check4events = 1; if (nextevent->xkey < m->xmin) { decode(nextevent->eventptr, fliptri); oprev(fliptri, farlefttri); check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); onext(fliptri, farrighttri); check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); if (otriequal(farlefttri, bottommost)) { lprev(fliptri, bottommost); } flip(m, b, &fliptri); setapex(fliptri, NULL); lprev(fliptri, lefttri); lnext(fliptri, righttri); sym(lefttri, farlefttri); if (randomnation(SAMPLERATE) == 0) { symself(fliptri); dest(fliptri, leftvertex); apex(fliptri, midvertex); org(fliptri, rightvertex); splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex, midvertex, rightvertex, nextevent->ykey); } } else { nextvertex = (vertex) nextevent->eventptr; if ((nextvertex[0] == lastvertex[0]) && (nextvertex[1] == lastvertex[1])) { if (!b->quiet) { printf( "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", nextvertex[0], nextvertex[1]); } setvertextype(nextvertex, UNDEADVERTEX); m->undeads++; check4events = 0; } else { lastvertex = nextvertex; splayroot = frontlocate(m, splayroot, &bottommost, nextvertex, &searchtri, &farrightflag); /* otricopy(bottommost, searchtri); farrightflag = 0; while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { onextself(searchtri); farrightflag = otriequal(searchtri, bottommost); } */ check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); otricopy(searchtri, farrighttri); sym(searchtri, farlefttri); maketriangle(m, b, &lefttri); maketriangle(m, b, &righttri); dest(farrighttri, connectvertex); setorg(lefttri, connectvertex); setdest(lefttri, nextvertex); setorg(righttri, nextvertex); setdest(righttri, connectvertex); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, farlefttri); bond(righttri, farrighttri); if (!farrightflag && otriequal(farrighttri, bottommost)) { otricopy(lefttri, bottommost); } if (randomnation(SAMPLERATE) == 0) { splayroot = splayinsert(m, splayroot, &lefttri, nextvertex); } else if (randomnation(SAMPLERATE) == 0) { lnext(righttri, inserttri); splayroot = splayinsert(m, splayroot, &inserttri, nextvertex); } } } nextevent->eventptr = (VOID *) freeevents; freeevents = nextevent; if (check4events) { apex(farlefttri, leftvertex); dest(lefttri, midvertex); apex(lefttri, rightvertex); lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); if (lefttest > 0.0) { newevent = freeevents; freeevents = (struct event *) freeevents->eventptr; newevent->xkey = m->xminextreme; newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, lefttest); newevent->eventptr = (VOID *) encode(lefttri); eventheapinsert(eventheap, heapsize, newevent); heapsize++; setorg(lefttri, newevent); } apex(righttri, leftvertex); org(righttri, midvertex); apex(farrighttri, rightvertex); righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); if (righttest > 0.0) { newevent = freeevents; freeevents = (struct event *) freeevents->eventptr; newevent->xkey = m->xminextreme; newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, righttest); newevent->eventptr = (VOID *) encode(farrighttri); eventheapinsert(eventheap, heapsize, newevent); heapsize++; setorg(farrighttri, newevent); } } } pooldeinit(&m->splaynodes); lprevself(bottommost); return removeghosts(m, b, &bottommost); } #endif /* not REDUCED */ /** **/ /** **/ /********* Sweepline Delaunay triangulation ends here *********/ /********* General mesh construction routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* delaunay() Form a Delaunay triangulation. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS long delaunay(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ long delaunay(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { long hulledges; m->eextras = 0; initializetrisubpools(m, b); #ifdef REDUCED if (!b->quiet) { printf( "Constructing Delaunay triangulation by divide-and-conquer method.\n"); } hulledges = divconqdelaunay(m, b); #else /* not REDUCED */ if (!b->quiet) { printf("Constructing Delaunay triangulation "); if (b->incremental) { printf("by incremental method.\n"); } else if (b->sweepline) { printf("by sweepline method.\n"); } else { printf("by divide-and-conquer method.\n"); } } if (b->incremental) { hulledges = incrementaldelaunay(m, b); } else if (b->sweepline) { hulledges = sweeplinedelaunay(m, b); } else { hulledges = divconqdelaunay(m, b); } #endif /* not REDUCED */ if (m->triangles.items == 0) { /* The input vertices were all collinear, so there are no triangles. */ return 0l; } else { return hulledges; } } /*****************************************************************************/ /* */ /* reconstruct() Reconstruct a triangulation from its .ele (and possibly */ /* .poly) file. Used when the -r switch is used. */ /* */ /* Reads an .ele file and reconstructs the original mesh. If the -p switch */ /* is used, this procedure will also read a .poly file and reconstruct the */ /* subsegments of the original mesh. If the -a switch is used, this */ /* procedure will also read an .area file and set a maximum area constraint */ /* on each triangle. */ /* */ /* Vertices that are not corners of triangles, such as nodes on edges of */ /* subparametric elements, are discarded. */ /* */ /* This routine finds the adjacencies between triangles (and subsegments) */ /* by forming one stack of triangles for each vertex. Each triangle is on */ /* three different stacks simultaneously. Each triangle's subsegment */ /* pointers are used to link the items in each stack. This memory-saving */ /* feature makes the code harder to read. The most important thing to keep */ /* in mind is that each triangle is removed from a stack precisely when */ /* the corresponding pointer is adjusted to refer to a subsegment rather */ /* than the next triangle of the stack. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist, REAL *triangleattriblist, REAL *trianglearealist, int elements, int corners, int attribs, int *segmentlist,int *segmentmarkerlist, int numberofsegments) #else /* not ANSI_DECLARATORS */ int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist, elements, corners, attribs, segmentlist, segmentmarkerlist, numberofsegments) struct mesh *m; struct behavior *b; int *trianglelist; REAL *triangleattriblist; REAL *trianglearealist; int elements; int corners; int attribs; int *segmentlist; int *segmentmarkerlist; int numberofsegments; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS long reconstruct(struct mesh *m, struct behavior *b, char *elefilename, char *areafilename, char *polyfilename, FILE *polyfile) #else /* not ANSI_DECLARATORS */ long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile) struct mesh *m; struct behavior *b; char *elefilename; char *areafilename; char *polyfilename; FILE *polyfile; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY int vertexindex; int attribindex; #else /* not TRILIBRARY */ FILE *elefile; FILE *areafile; char inputline[INPUTLINESIZE]; char *stringptr; int areaelements; #endif /* not TRILIBRARY */ struct otri triangleloop; struct otri triangleleft; struct otri checktri; struct otri checkleft; struct otri checkneighbor; struct osub subsegloop; triangle *vertexarray; triangle *prevlink; triangle nexttri; vertex tdest, tapex; vertex checkdest, checkapex; vertex shorg; vertex killvertex; REAL area; int corner[3]; int end[2]; int killvertexindex; int incorners; int segmentmarkers; int boundmarker; int aroundvertex; long hullsize; int notfound; long elementnumber, segmentnumber; int i, j; triangle ptr; /* Temporary variable used by sym(). */ #ifdef TRILIBRARY m->inelements = elements; incorners = corners; if (incorners < 3) { printf("Error: Triangles must have at least 3 vertices.\n"); exit(1); } m->eextras = attribs; #else /* not TRILIBRARY */ /* Read the triangles from an .ele file. */ if (!b->quiet) { printf("Opening %s.\n", elefilename); } elefile = fopen(elefilename, "r"); if (elefile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", elefilename); exit(1); } /* Read number of triangles, number of vertices per triangle, and */ /* number of triangle attributes from .ele file. */ stringptr = readline(inputline, elefile, elefilename); m->inelements = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { incorners = 3; } else { incorners = (int) strtol(stringptr, &stringptr, 0); if (incorners < 3) { printf("Error: Triangles in %s must have at least 3 vertices.\n", elefilename); exit(1); } } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->eextras = 0; } else { m->eextras = (int) strtol(stringptr, &stringptr, 0); } #endif /* not TRILIBRARY */ initializetrisubpools(m, b); /* Create the triangles. */ for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) { maketriangle(m, b, &triangleloop); /* Mark the triangle as living. */ triangleloop.tri[3] = (triangle) triangleloop.tri; } if (b->poly) { #ifdef TRILIBRARY m->insegments = numberofsegments; segmentmarkers = segmentmarkerlist != (int *) NULL; #else /* not TRILIBRARY */ /* Read number of segments and number of segment */ /* boundary markers from .poly file. */ stringptr = readline(inputline, polyfile, b->inpolyfilename); m->insegments = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { segmentmarkers = 0; } else { segmentmarkers = (int) strtol(stringptr, &stringptr, 0); } #endif /* not TRILIBRARY */ /* Create the subsegments. */ for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) { makesubseg(m, &subsegloop); /* Mark the subsegment as living. */ subsegloop.ss[2] = (subseg) subsegloop.ss; } } #ifdef TRILIBRARY vertexindex = 0; attribindex = 0; #else /* not TRILIBRARY */ if (b->vararea) { /* Open an .area file, check for consistency with the .ele file. */ if (!b->quiet) { printf("Opening %s.\n", areafilename); } areafile = fopen(areafilename, "r"); if (areafile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", areafilename); exit(1); } stringptr = readline(inputline, areafile, areafilename); areaelements = (int) strtol(stringptr, &stringptr, 0); if (areaelements != m->inelements) { printf("Error: %s and %s disagree on number of triangles.\n", elefilename, areafilename); exit(1); } } #endif /* not TRILIBRARY */ if (!b->quiet) { printf("Reconstructing mesh.\n"); } /* Allocate a temporary array that maps each vertex to some adjacent */ /* triangle. I took care to allocate all the permanent memory for */ /* triangles and subsegments first. */ vertexarray = (triangle *) trimalloc(m->vertices.items * sizeof(triangle)); /* Each vertex is initially unrepresented. */ for (i = 0; i < m->vertices.items; i++) { vertexarray[i] = (triangle) m->dummytri; } if (b->verbose) { printf(" Assembling triangles.\n"); } /* Read the triangles from the .ele file, and link */ /* together those that share an edge. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { #ifdef TRILIBRARY /* Copy the triangle's three corners. */ for (j = 0; j < 3; j++) { corner[j] = trianglelist[vertexindex++]; if ((corner[j] < b->firstnumber) || (corner[j] >= b->firstnumber + m->invertices)) { printf("Error: Triangle %ld has an invalid vertex index.\n", elementnumber); exit(1); } } #else /* not TRILIBRARY */ /* Read triangle number and the triangle's three corners. */ stringptr = readline(inputline, elefile, elefilename); for (j = 0; j < 3; j++) { stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Triangle %ld is missing vertex %d in %s.\n", elementnumber, j + 1, elefilename); exit(1); } else { corner[j] = (int) strtol(stringptr, &stringptr, 0); if ((corner[j] < b->firstnumber) || (corner[j] >= b->firstnumber + m->invertices)) { printf("Error: Triangle %ld has an invalid vertex index.\n", elementnumber); exit(1); } } } #endif /* not TRILIBRARY */ /* Find out about (and throw away) extra nodes. */ for (j = 3; j < incorners; j++) { #ifdef TRILIBRARY killvertexindex = trianglelist[vertexindex++]; #else /* not TRILIBRARY */ stringptr = findfield(stringptr); if (*stringptr != '\0') { killvertexindex = (int) strtol(stringptr, &stringptr, 0); #endif /* not TRILIBRARY */ if ((killvertexindex >= b->firstnumber) && (killvertexindex < b->firstnumber + m->invertices)) { /* Delete the non-corner vertex if it's not already deleted. */ killvertex = getvertex(m, b, killvertexindex); if (vertextype(killvertex) != DEADVERTEX) { vertexdealloc(m, killvertex); } } #ifndef TRILIBRARY } #endif /* not TRILIBRARY */ } /* Read the triangle's attributes. */ for (j = 0; j < m->eextras; j++) { #ifdef TRILIBRARY setelemattribute(triangleloop, j, triangleattriblist[attribindex++]); #else /* not TRILIBRARY */ stringptr = findfield(stringptr); if (*stringptr == '\0') { setelemattribute(triangleloop, j, 0); } else { setelemattribute(triangleloop, j, (REAL) strtod(stringptr, &stringptr)); } #endif /* not TRILIBRARY */ } if (b->vararea) { #ifdef TRILIBRARY area = trianglearealist[elementnumber - b->firstnumber]; #else /* not TRILIBRARY */ /* Read an area constraint from the .area file. */ stringptr = readline(inputline, areafile, areafilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { area = -1.0; /* No constraint on this triangle. */ } else { area = (REAL) strtod(stringptr, &stringptr); } #endif /* not TRILIBRARY */ setareabound(triangleloop, area); } /* Set the triangle's vertices. */ triangleloop.orient = 0; setorg(triangleloop, getvertex(m, b, corner[0])); setdest(triangleloop, getvertex(m, b, corner[1])); setapex(triangleloop, getvertex(m, b, corner[2])); /* Try linking the triangle to others that share these vertices. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { /* Take the number for the origin of triangleloop. */ aroundvertex = corner[triangleloop.orient]; /* Look for other triangles having this vertex. */ nexttri = vertexarray[aroundvertex - b->firstnumber]; /* Link the current triangle to the next one in the stack. */ triangleloop.tri[6 + triangleloop.orient] = nexttri; /* Push the current triangle onto the stack. */ vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop); decode(nexttri, checktri); if (checktri.tri != m->dummytri) { dest(triangleloop, tdest); apex(triangleloop, tapex); /* Look for other triangles that share an edge. */ do { dest(checktri, checkdest); apex(checktri, checkapex); if (tapex == checkdest) { /* The two triangles share an edge; bond them together. */ lprev(triangleloop, triangleleft); bond(triangleleft, checktri); } if (tdest == checkapex) { /* The two triangles share an edge; bond them together. */ lprev(checktri, checkleft); bond(triangleloop, checkleft); } /* Find the next triangle in the stack. */ nexttri = checktri.tri[6 + checktri.orient]; decode(nexttri, checktri); } while (checktri.tri != m->dummytri); } } triangleloop.tri = triangletraverse(m); elementnumber++; } #ifdef TRILIBRARY vertexindex = 0; #else /* not TRILIBRARY */ fclose(elefile); if (b->vararea) { fclose(areafile); } #endif /* not TRILIBRARY */ hullsize = 0; /* Prepare to count the boundary edges. */ if (b->poly) { if (b->verbose) { printf(" Marking segments in triangulation.\n"); } /* Read the segments from the .poly file, and link them */ /* to their neighboring triangles. */ boundmarker = 0; traversalinit(&m->subsegs); subsegloop.ss = subsegtraverse(m); segmentnumber = b->firstnumber; while (subsegloop.ss != (subseg *) NULL) { #ifdef TRILIBRARY end[0] = segmentlist[vertexindex++]; end[1] = segmentlist[vertexindex++]; if (segmentmarkers) { boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber]; } #else /* not TRILIBRARY */ /* Read the endpoints of each segment, and possibly a boundary marker. */ stringptr = readline(inputline, polyfile, b->inpolyfilename); /* Skip the first (segment number) field. */ stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber, polyfilename); exit(1); } else { end[0] = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %ld is missing its second endpoint in %s.\n", segmentnumber, polyfilename); exit(1); } else { end[1] = (int) strtol(stringptr, &stringptr, 0); } if (segmentmarkers) { stringptr = findfield(stringptr); if (*stringptr == '\0') { boundmarker = 0; } else { boundmarker = (int) strtol(stringptr, &stringptr, 0); } } #endif /* not TRILIBRARY */ for (j = 0; j < 2; j++) { if ((end[j] < b->firstnumber) || (end[j] >= b->firstnumber + m->invertices)) { printf("Error: Segment %ld has an invalid vertex index.\n", segmentnumber); exit(1); } } /* set the subsegment's vertices. */ subsegloop.ssorient = 0; setsorg(subsegloop, getvertex(m, b, end[0])); setsdest(subsegloop, getvertex(m, b, end[1])); setmark(subsegloop, boundmarker); /* Try linking the subsegment to triangles that share these vertices. */ for (subsegloop.ssorient = 0; subsegloop.ssorient < 2; subsegloop.ssorient++) { /* Take the number for the destination of subsegloop. */ aroundvertex = end[1 - subsegloop.ssorient]; /* Look for triangles having this vertex. */ prevlink = &vertexarray[aroundvertex - b->firstnumber]; nexttri = vertexarray[aroundvertex - b->firstnumber]; decode(nexttri, checktri); sorg(subsegloop, shorg); notfound = 1; /* Look for triangles having this edge. Note that I'm only */ /* comparing each triangle's destination with the subsegment; */ /* each triangle's apex is handled through a different vertex. */ /* Because each triangle appears on three vertices' lists, each */ /* occurrence of a triangle on a list can (and does) represent */ /* an edge. In this way, most edges are represented twice, and */ /* every triangle-subsegment bond is represented once. */ while (notfound && (checktri.tri != m->dummytri)) { dest(checktri, checkdest); if (shorg == checkdest) { /* We have a match. Remove this triangle from the list. */ *prevlink = checktri.tri[6 + checktri.orient]; /* Bond the subsegment to the triangle. */ tsbond(checktri, subsegloop); /* Check if this is a boundary edge. */ sym(checktri, checkneighbor); if (checkneighbor.tri == m->dummytri) { /* The next line doesn't insert a subsegment (because there's */ /* already one there), but it sets the boundary markers of */ /* the existing subsegment and its vertices. */ insertsubseg(m, b, &checktri, 1); hullsize++; } notfound = 0; } /* Find the next triangle in the stack. */ prevlink = &checktri.tri[6 + checktri.orient]; nexttri = checktri.tri[6 + checktri.orient]; decode(nexttri, checktri); } } subsegloop.ss = subsegtraverse(m); segmentnumber++; } } /* Mark the remaining edges as not being attached to any subsegment. */ /* Also, count the (yet uncounted) boundary edges. */ for (i = 0; i < m->vertices.items; i++) { /* Search the stack of triangles adjacent to a vertex. */ nexttri = vertexarray[i]; decode(nexttri, checktri); while (checktri.tri != m->dummytri) { /* Find the next triangle in the stack before this */ /* information gets overwritten. */ nexttri = checktri.tri[6 + checktri.orient]; /* No adjacent subsegment. (This overwrites the stack info.) */ tsdissolve(checktri); sym(checktri, checkneighbor); if (checkneighbor.tri == m->dummytri) { insertsubseg(m, b, &checktri, 1); hullsize++; } decode(nexttri, checktri); } } trifree((VOID *) vertexarray); return hullsize; } #endif /* not CDT_ONLY */ /** **/ /** **/ /********* General mesh construction routines end here *********/ /********* Segment insertion begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* finddirection() Find the first triangle on the path from one point */ /* to another. */ /* */ /* Finds the triangle that intersects a line segment drawn from the */ /* origin of `searchtri' to the point `searchpoint', and returns the result */ /* in `searchtri'. The origin of `searchtri' does not change, even though */ /* the triangle returned may differ from the one passed in. This routine */ /* is used to find the direction to move in to get from one point to */ /* another. */ /* */ /* The return value notes whether the destination or apex of the found */ /* triangle is collinear with the two points in question. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS enum finddirectionresult finddirection(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex searchpoint) #else /* not ANSI_DECLARATORS */ enum finddirectionresult finddirection(m, b, searchtri, searchpoint) struct mesh *m; struct behavior *b; struct otri *searchtri; vertex searchpoint; #endif /* not ANSI_DECLARATORS */ { struct otri checktri; vertex startvertex; vertex leftvertex, rightvertex; REAL leftccw, rightccw; int leftflag, rightflag; triangle ptr; /* Temporary variable used by onext() and oprev(). */ org(*searchtri, startvertex); dest(*searchtri, rightvertex); apex(*searchtri, leftvertex); /* Is `searchpoint' to the left? */ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); leftflag = leftccw > 0.0; /* Is `searchpoint' to the right? */ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); rightflag = rightccw > 0.0; if (leftflag && rightflag) { /* `searchtri' faces directly away from `searchpoint'. We could go left */ /* or right. Ask whether it's a triangle or a boundary on the left. */ onext(*searchtri, checktri); if (checktri.tri == m->dummytri) { leftflag = 0; } else { rightflag = 0; } } while (leftflag) { /* Turn left until satisfied. */ onextself(*searchtri); if (searchtri->tri == m->dummytri) { printf("Internal error in finddirection(): Unable to find a\n"); printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], startvertex[1]); printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); internalerror(); } apex(*searchtri, leftvertex); rightccw = leftccw; leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); leftflag = leftccw > 0.0; } while (rightflag) { /* Turn right until satisfied. */ oprevself(*searchtri); if (searchtri->tri == m->dummytri) { printf("Internal error in finddirection(): Unable to find a\n"); printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], startvertex[1]); printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); internalerror(); } dest(*searchtri, rightvertex); leftccw = rightccw; rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); rightflag = rightccw > 0.0; } if (leftccw == 0.0) { return LEFTCOLLINEAR; } else if (rightccw == 0.0) { return RIGHTCOLLINEAR; } else { return WITHIN; } } /*****************************************************************************/ /* */ /* segmentintersection() Find the intersection of an existing segment */ /* and a segment that is being inserted. Insert */ /* a vertex at the intersection, splitting an */ /* existing subsegment. */ /* */ /* The segment being inserted connects the apex of splittri to endpoint2. */ /* splitsubseg is the subsegment being split, and MUST adjoin splittri. */ /* Hence, endpoints of the subsegment being split are the origin and */ /* destination of splittri. */ /* */ /* On completion, splittri is a handle having the newly inserted */ /* intersection point as its origin, and endpoint1 as its destination. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void segmentintersection(struct mesh *m, struct behavior *b, struct otri *splittri, struct osub *splitsubseg, vertex endpoint2) #else /* not ANSI_DECLARATORS */ void segmentintersection(m, b, splittri, splitsubseg, endpoint2) struct mesh *m; struct behavior *b; struct otri *splittri; struct osub *splitsubseg; vertex endpoint2; #endif /* not ANSI_DECLARATORS */ { vertex endpoint1; vertex torg, tdest; vertex leftvertex, rightvertex; vertex newvertex; enum insertvertexresult success; enum finddirectionresult collinear; REAL ex, ey; REAL tx, ty; REAL etx, ety; REAL split, denom; int i; triangle ptr; /* Temporary variable used by onext(). */ /* Find the other three segment endpoints. */ apex(*splittri, endpoint1); org(*splittri, torg); dest(*splittri, tdest); /* Segment intersection formulae; see the Antonio reference. */ tx = tdest[0] - torg[0]; ty = tdest[1] - torg[1]; ex = endpoint2[0] - endpoint1[0]; ey = endpoint2[1] - endpoint1[1]; etx = torg[0] - endpoint2[0]; ety = torg[1] - endpoint2[1]; denom = ty * ex - tx * ey; if (denom == 0.0) { printf("Internal error in segmentintersection():"); printf(" Attempt to find intersection of parallel segments.\n"); internalerror(); } split = (ey * etx - ex * ety) / denom; /* Create the new vertex. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate its coordinate and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = torg[i] + split * (tdest[i] - torg[i]); } setvertexmark(newvertex, mark(*splitsubseg)); setvertextype(newvertex, INPUTVERTEX); if (b->verbose > 1) { printf( " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]); } /* Insert the intersection vertex. This should always succeed. */ success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0, 0.0); if (success != SUCCESSFULVERTEX) { printf("Internal error in segmentintersection():\n"); printf(" Failure to split a segment.\n"); internalerror(); } if (m->steinerleft > 0) { m->steinerleft--; } /* Inserting the vertex may have caused edge flips. We wish to rediscover */ /* the edge connecting endpoint1 to the new intersection vertex. */ collinear = finddirection(m, b, splittri, endpoint1); dest(*splittri, rightvertex); apex(*splittri, leftvertex); if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) { onextself(*splittri); } else if ((rightvertex[0] != endpoint1[0]) || (rightvertex[1] != endpoint1[1])) { printf("Internal error in segmentintersection():\n"); printf(" Topological inconsistency after splitting a segment.\n"); internalerror(); } /* `splittri' should have destination endpoint1. */ } /*****************************************************************************/ /* */ /* scoutsegment() Scout the first triangle on the path from one endpoint */ /* to another, and check for completion (reaching the */ /* second endpoint), a collinear vertex, or the */ /* intersection of two segments. */ /* */ /* Returns one if the entire segment is successfully inserted, and zero if */ /* the job must be finished by conformingedge() or constrainededge(). */ /* */ /* If the first triangle on the path has the second endpoint as its */ /* destination or apex, a subsegment is inserted and the job is done. */ /* */ /* If the first triangle on the path has a destination or apex that lies on */ /* the segment, a subsegment is inserted connecting the first endpoint to */ /* the collinear vertex, and the search is continued from the collinear */ /* vertex. */ /* */ /* If the first triangle on the path has a subsegment opposite its origin, */ /* then there is a segment that intersects the segment being inserted. */ /* Their intersection vertex is inserted, splitting the subsegment. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex endpoint2, int newmark) #else /* not ANSI_DECLARATORS */ int scoutsegment(m, b, searchtri, endpoint2, newmark) struct mesh *m; struct behavior *b; struct otri *searchtri; vertex endpoint2; int newmark; #endif /* not ANSI_DECLARATORS */ { struct otri crosstri; struct osub crosssubseg; vertex leftvertex, rightvertex; enum finddirectionresult collinear; subseg sptr; /* Temporary variable used by tspivot(). */ collinear = finddirection(m, b, searchtri, endpoint2); dest(*searchtri, rightvertex); apex(*searchtri, leftvertex); if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) || ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) { /* The segment is already an edge in the mesh. */ if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) { lprevself(*searchtri); } /* Insert a subsegment, if there isn't already one there. */ insertsubseg(m, b, searchtri, newmark); return 1; } else if (collinear == LEFTCOLLINEAR) { /* We've collided with a vertex between the segment's endpoints. */ /* Make the collinear vertex be the triangle's origin. */ lprevself(*searchtri); insertsubseg(m, b, searchtri, newmark); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } else if (collinear == RIGHTCOLLINEAR) { /* We've collided with a vertex between the segment's endpoints. */ insertsubseg(m, b, searchtri, newmark); /* Make the collinear vertex be the triangle's origin. */ lnextself(*searchtri); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } else { lnext(*searchtri, crosstri); tspivot(crosstri, crosssubseg); /* Check for a crossing segment. */ if (crosssubseg.ss == m->dummysub) { return 0; } else { /* Insert a vertex at the intersection. */ segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2); otricopy(crosstri, *searchtri); insertsubseg(m, b, searchtri, newmark); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } } } /*****************************************************************************/ /* */ /* conformingedge() Force a segment into a conforming Delaunay */ /* triangulation by inserting a vertex at its midpoint, */ /* and recursively forcing in the two half-segments if */ /* necessary. */ /* */ /* Generates a sequence of subsegments connecting `endpoint1' to */ /* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */ /* to each new splitting vertex and subsegment. */ /* */ /* Note that conformingedge() does not always maintain the conforming */ /* Delaunay property. Once inserted, segments are locked into place; */ /* vertices inserted later (to force other segments in) may render these */ /* fixed segments non-Delaunay. The conforming Delaunay property will be */ /* restored by enforcequality() by splitting encroached subsegments. */ /* */ /*****************************************************************************/ #ifndef REDUCED #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void conformingedge(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark) #else /* not ANSI_DECLARATORS */ void conformingedge(m, b, endpoint1, endpoint2, newmark) struct mesh *m; struct behavior *b; vertex endpoint1; vertex endpoint2; int newmark; #endif /* not ANSI_DECLARATORS */ { struct otri searchtri1, searchtri2; struct osub brokensubseg; vertex newvertex; vertex midvertex1, midvertex2; enum insertvertexresult success; int i; subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 2) { printf("Forcing segment into triangulation by recursive splitting:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); } /* Create a new vertex to insert in the middle of the segment. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate coordinates and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]); } setvertexmark(newvertex, newmark); setvertextype(newvertex, SEGMENTVERTEX); /* No known triangle to search from. */ searchtri1.tri = m->dummytri; /* Attempt to insert the new vertex. */ success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL, 0, 0, 0.0); if (success == DUPLICATEVERTEX) { if (b->verbose > 2) { printf(" Segment intersects existing vertex (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* Use the vertex that's already there. */ vertexdealloc(m, newvertex); org(searchtri1, newvertex); } else { if (success == VIOLATINGVERTEX) { if (b->verbose > 2) { printf(" Two segments intersect at (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* By fluke, we've landed right on another segment. Split it. */ tspivot(searchtri1, brokensubseg); success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg, 0, 0, 0.0); if (success != SUCCESSFULVERTEX) { printf("Internal error in conformingedge():\n"); printf(" Failure to split a segment.\n"); internalerror(); } } /* The vertex has been inserted successfully. */ if (m->steinerleft > 0) { m->steinerleft--; } } otricopy(searchtri1, searchtri2); /* `searchtri1' and `searchtri2' are fastened at their origins to */ /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */ /* respectively. First, we must get `searchtri2' out of the way so it */ /* won't be invalidated during the insertion of the first half of the */ /* segment. */ finddirection(m, b, &searchtri2, endpoint2); if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) { /* The origin of searchtri1 may have changed if a collision with an */ /* intervening vertex on the segment occurred. */ org(searchtri1, midvertex1); conformingedge(m, b, midvertex1, endpoint1, newmark); } if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) { /* The origin of searchtri2 may have changed if a collision with an */ /* intervening vertex on the segment occurred. */ org(searchtri2, midvertex2); conformingedge(m, b, midvertex2, endpoint2, newmark); } } #endif /* not CDT_ONLY */ #endif /* not REDUCED */ /*****************************************************************************/ /* */ /* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */ /* recursively from an existing vertex. Pay special */ /* attention to stacking inverted triangles. */ /* */ /* This is a support routine for inserting segments into a constrained */ /* Delaunay triangulation. */ /* */ /* The origin of fixuptri is treated as if it has just been inserted, and */ /* the local Delaunay condition needs to be enforced. It is only enforced */ /* in one sector, however, that being the angular range defined by */ /* fixuptri. */ /* */ /* This routine also needs to make decisions regarding the "stacking" of */ /* triangles. (Read the description of constrainededge() below before */ /* reading on here, so you understand the algorithm.) If the position of */ /* the new vertex (the origin of fixuptri) indicates that the vertex before */ /* it on the polygon is a reflex vertex, then "stack" the triangle by */ /* doing nothing. (fixuptri is an inverted triangle, which is how stacked */ /* triangles are identified.) */ /* */ /* Otherwise, check whether the vertex before that was a reflex vertex. */ /* If so, perform an edge flip, thereby eliminating an inverted triangle */ /* (popping it off the stack). The edge flip may result in the creation */ /* of a new inverted triangle, depending on whether or not the new vertex */ /* is visible to the vertex three edges behind on the polygon. */ /* */ /* If neither of the two vertices behind the new vertex are reflex */ /* vertices, fixuptri and fartri, the triangle opposite it, are not */ /* inverted; hence, ensure that the edge between them is locally Delaunay. */ /* */ /* `leftside' indicates whether or not fixuptri is to the left of the */ /* segment being inserted. (Imagine that the segment is pointing up from */ /* endpoint1 to endpoint2.) */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void delaunayfixup(struct mesh *m, struct behavior *b, struct otri *fixuptri, int leftside) #else /* not ANSI_DECLARATORS */ void delaunayfixup(m, b, fixuptri, leftside) struct mesh *m; struct behavior *b; struct otri *fixuptri; int leftside; #endif /* not ANSI_DECLARATORS */ { struct otri neartri; struct otri fartri; struct osub faredge; vertex nearvertex, leftvertex, rightvertex, farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ lnext(*fixuptri, neartri); sym(neartri, fartri); /* Check if the edge opposite the origin of fixuptri can be flipped. */ if (fartri.tri == m->dummytri) { return; } tspivot(neartri, faredge); if (faredge.ss != m->dummysub) { return; } /* Find all the relevant vertices. */ apex(neartri, nearvertex); org(neartri, leftvertex); dest(neartri, rightvertex); apex(fartri, farvertex); /* Check whether the previous polygon vertex is a reflex vertex. */ if (leftside) { if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) { /* leftvertex is a reflex vertex too. Nothing can */ /* be done until a convex section is found. */ return; } } else { if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) { /* rightvertex is a reflex vertex too. Nothing can */ /* be done until a convex section is found. */ return; } } if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) { /* fartri is not an inverted triangle, and farvertex is not a reflex */ /* vertex. As there are no reflex vertices, fixuptri isn't an */ /* inverted triangle, either. Hence, test the edge between the */ /* triangles to ensure it is locally Delaunay. */ if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <= 0.0) { return; } /* Not locally Delaunay; go on to an edge flip. */ } /* else fartri is inverted; remove it from the stack by flipping. */ flip(m, b, &neartri); lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ /* Recursively process the two triangles that result from the flip. */ delaunayfixup(m, b, fixuptri, leftside); delaunayfixup(m, b, &fartri, leftside); } /*****************************************************************************/ /* */ /* constrainededge() Force a segment into a constrained Delaunay */ /* triangulation by deleting the triangles it */ /* intersects, and triangulating the polygons that */ /* form on each side of it. */ /* */ /* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */ /* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */ /* boundary marker of the segment. */ /* */ /* To insert a segment, every triangle whose interior intersects the */ /* segment is deleted. The union of these deleted triangles is a polygon */ /* (which is not necessarily monotone, but is close enough), which is */ /* divided into two polygons by the new segment. This routine's task is */ /* to generate the Delaunay triangulation of these two polygons. */ /* */ /* You might think of this routine's behavior as a two-step process. The */ /* first step is to walk from endpoint1 to endpoint2, flipping each edge */ /* encountered. This step creates a fan of edges connected to endpoint1, */ /* including the desired edge to endpoint2. The second step enforces the */ /* Delaunay condition on each side of the segment in an incremental manner: */ /* proceeding along the polygon from endpoint1 to endpoint2 (this is done */ /* independently on each side of the segment), each vertex is "enforced" */ /* as if it had just been inserted, but affecting only the previous */ /* vertices. The result is the same as if the vertices had been inserted */ /* in the order they appear on the polygon, so the result is Delaunay. */ /* */ /* In truth, constrainededge() interleaves these two steps. The procedure */ /* walks from endpoint1 to endpoint2, and each time an edge is encountered */ /* and flipped, the newly exposed vertex (at the far end of the flipped */ /* edge) is "enforced" upon the previously flipped edges, usually affecting */ /* only one side of the polygon (depending upon which side of the segment */ /* the vertex falls on). */ /* */ /* The algorithm is complicated by the need to handle polygons that are not */ /* convex. Although the polygon is not necessarily monotone, it can be */ /* triangulated in a manner similar to the stack-based algorithms for */ /* monotone polygons. For each reflex vertex (local concavity) of the */ /* polygon, there will be an inverted triangle formed by one of the edge */ /* flips. (An inverted triangle is one with negative area - that is, its */ /* vertices are arranged in clockwise order - and is best thought of as a */ /* wrinkle in the fabric of the mesh.) Each inverted triangle can be */ /* thought of as a reflex vertex pushed on the stack, waiting to be fixed */ /* later. */ /* */ /* A reflex vertex is popped from the stack when a vertex is inserted that */ /* is visible to the reflex vertex. (However, if the vertex behind the */ /* reflex vertex is not visible to the reflex vertex, a new inverted */ /* triangle will take its place on the stack.) These details are handled */ /* by the delaunayfixup() routine above. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void constrainededge(struct mesh *m, struct behavior *b, struct otri *starttri, vertex endpoint2, int newmark) #else /* not ANSI_DECLARATORS */ void constrainededge(m, b, starttri, endpoint2, newmark) struct mesh *m; struct behavior *b; struct otri *starttri; vertex endpoint2; int newmark; #endif /* not ANSI_DECLARATORS */ { struct otri fixuptri, fixuptri2; struct osub crosssubseg; vertex endpoint1; vertex farvertex; REAL area; int collision; int done; triangle ptr; /* Temporary variable used by sym() and oprev(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*starttri, endpoint1); lnext(*starttri, fixuptri); flip(m, b, &fixuptri); /* `collision' indicates whether we have found a vertex directly */ /* between endpoint1 and endpoint2. */ collision = 0; done = 0; do { org(fixuptri, farvertex); /* `farvertex' is the extreme point of the polygon we are "digging" */ /* to get from endpoint1 to endpoint2. */ if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) { oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around endpoint2. */ delaunayfixup(m, b, &fixuptri, 0); delaunayfixup(m, b, &fixuptri2, 1); done = 1; } else { /* Check whether farvertex is to the left or right of the segment */ /* being inserted, to decide which edge of fixuptri to dig */ /* through next. */ area = counterclockwise(m, b, endpoint1, endpoint2, farvertex); if (area == 0.0) { /* We've collided with a vertex between endpoint1 and endpoint2. */ collision = 1; oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around farvertex. */ delaunayfixup(m, b, &fixuptri, 0); delaunayfixup(m, b, &fixuptri2, 1); done = 1; } else { if (area > 0.0) { /* farvertex is to the left of the segment. */ oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around farvertex, on the */ /* left side of the segment only. */ delaunayfixup(m, b, &fixuptri2, 1); /* Flip the edge that crosses the segment. After the edge is */ /* flipped, one of its endpoints is the fan vertex, and the */ /* destination of fixuptri is the fan vertex. */ lprevself(fixuptri); } else { /* farvertex is to the right of the segment. */ delaunayfixup(m, b, &fixuptri, 0); /* Flip the edge that crosses the segment. After the edge is */ /* flipped, one of its endpoints is the fan vertex, and the */ /* destination of fixuptri is the fan vertex. */ oprevself(fixuptri); } /* Check for two intersecting segments. */ tspivot(fixuptri, crosssubseg); if (crosssubseg.ss == m->dummysub) { flip(m, b, &fixuptri); /* May create inverted triangle at left. */ } else { /* We've collided with a segment between endpoint1 and endpoint2. */ collision = 1; /* Insert a vertex at the intersection. */ segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2); done = 1; } } } } while (!done); /* Insert a subsegment to make the segment permanent. */ insertsubseg(m, b, &fixuptri, newmark); /* If there was a collision with an interceding vertex, install another */ /* segment connecting that vertex with endpoint2. */ if (collision) { /* Insert the remainder of the segment. */ if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) { constrainededge(m, b, &fixuptri, endpoint2, newmark); } } } /*****************************************************************************/ /* */ /* insertsegment() Insert a PSLG segment into a triangulation. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void insertsegment(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark) #else /* not ANSI_DECLARATORS */ void insertsegment(m, b, endpoint1, endpoint2, newmark) struct mesh *m; struct behavior *b; vertex endpoint1; vertex endpoint2; int newmark; #endif /* not ANSI_DECLARATORS */ { struct otri searchtri1, searchtri2; triangle encodedtri; vertex checkvertex; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose > 1) { printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); } /* Find a triangle whose origin is the segment's first endpoint. */ checkvertex = (vertex) NULL; encodedtri = vertex2tri(endpoint1); if (encodedtri != (triangle) NULL) { decode(encodedtri, searchtri1); org(searchtri1, checkvertex); } if (checkvertex != endpoint1) { /* Find a boundary triangle to search from. */ searchtri1.tri = m->dummytri; searchtri1.orient = 0; symself(searchtri1); /* Search for the segment's first endpoint by point location. */ if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) { printf( "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); printf(" (%.12g, %.12g) in triangulation.\n", endpoint1[0], endpoint1[1]); internalerror(); } } /* Remember this triangle to improve subsequent point location. */ otricopy(searchtri1, m->recenttri); /* Scout the beginnings of a path from the first endpoint */ /* toward the second. */ if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) { /* The segment was easily inserted. */ return; } /* The first endpoint may have changed if a collision with an intervening */ /* vertex on the segment occurred. */ org(searchtri1, endpoint1); /* Find a triangle whose origin is the segment's second endpoint. */ checkvertex = (vertex) NULL; encodedtri = vertex2tri(endpoint2); if (encodedtri != (triangle) NULL) { decode(encodedtri, searchtri2); org(searchtri2, checkvertex); } if (checkvertex != endpoint2) { /* Find a boundary triangle to search from. */ searchtri2.tri = m->dummytri; searchtri2.orient = 0; symself(searchtri2); /* Search for the segment's second endpoint by point location. */ if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) { printf( "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); printf(" (%.12g, %.12g) in triangulation.\n", endpoint2[0], endpoint2[1]); internalerror(); } } /* Remember this triangle to improve subsequent point location. */ otricopy(searchtri2, m->recenttri); /* Scout the beginnings of a path from the second endpoint */ /* toward the first. */ if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) { /* The segment was easily inserted. */ return; } /* The second endpoint may have changed if a collision with an intervening */ /* vertex on the segment occurred. */ org(searchtri2, endpoint2); #ifndef REDUCED #ifndef CDT_ONLY if (b->splitseg) { /* Insert vertices to force the segment into the triangulation. */ conformingedge(m, b, endpoint1, endpoint2, newmark); } else { #endif /* not CDT_ONLY */ #endif /* not REDUCED */ /* Insert the segment directly into the triangulation. */ constrainededge(m, b, &searchtri1, endpoint2, newmark); #ifndef REDUCED #ifndef CDT_ONLY } #endif /* not CDT_ONLY */ #endif /* not REDUCED */ } /*****************************************************************************/ /* */ /* markhull() Cover the convex hull of a triangulation with subsegments. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void markhull(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void markhull(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri hulltri; struct otri nexttri; struct otri starttri; triangle ptr; /* Temporary variable used by sym() and oprev(). */ /* Find a triangle handle on the hull. */ hulltri.tri = m->dummytri; hulltri.orient = 0; symself(hulltri); /* Remember where we started so we know when to stop. */ otricopy(hulltri, starttri); /* Go once counterclockwise around the convex hull. */ do { /* Create a subsegment if there isn't already one here. */ insertsubseg(m, b, &hulltri, 1); /* To find the next hull edge, go clockwise around the next vertex. */ lnextself(hulltri); oprev(hulltri, nexttri); while (nexttri.tri != m->dummytri) { otricopy(nexttri, hulltri); oprev(hulltri, nexttri); } } while (!otriequal(hulltri, starttri)); } /*****************************************************************************/ /* */ /* formskeleton() Create the segments of a triangulation, including PSLG */ /* segments and edges on the convex hull. */ /* */ /* The PSLG segments are read from a .poly file. The return value is the */ /* number of segments in the file. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, int *segmentmarkerlist, int numberofsegments) #else /* not ANSI_DECLARATORS */ void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments) struct mesh *m; struct behavior *b; int *segmentlist; int *segmentmarkerlist; int numberofsegments; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void formskeleton(struct mesh *m, struct behavior *b, FILE *polyfile, char *polyfilename) #else /* not ANSI_DECLARATORS */ void formskeleton(m, b, polyfile, polyfilename) struct mesh *m; struct behavior *b; FILE *polyfile; char *polyfilename; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY char polyfilename[6]; int index; #else /* not TRILIBRARY */ char inputline[INPUTLINESIZE]; char *stringptr; #endif /* not TRILIBRARY */ vertex endpoint1, endpoint2; int segmentmarkers; int end1, end2; int boundmarker; int i; if (b->poly) { if (!b->quiet) { printf("Recovering segments in Delaunay triangulation.\n"); } #ifdef TRILIBRARY strcpy(polyfilename, "input"); m->insegments = numberofsegments; segmentmarkers = segmentmarkerlist != (int *) NULL; index = 0; #else /* not TRILIBRARY */ /* Read the segments from a .poly file. */ /* Read number of segments and number of boundary markers. */ stringptr = readline(inputline, polyfile, polyfilename); m->insegments = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { segmentmarkers = 0; } else { segmentmarkers = (int) strtol(stringptr, &stringptr, 0); } #endif /* not TRILIBRARY */ /* If the input vertices are collinear, there is no triangulation, */ /* so don't try to insert segments. */ if (m->triangles.items == 0) { return; } /* If segments are to be inserted, compute a mapping */ /* from vertices to triangles. */ if (m->insegments > 0) { makevertexmap(m, b); if (b->verbose) { printf(" Recovering PSLG segments.\n"); } } boundmarker = 0; /* Read and insert the segments. */ for (i = 0; i < m->insegments; i++) { #ifdef TRILIBRARY end1 = segmentlist[index++]; end2 = segmentlist[index++]; if (segmentmarkers) { boundmarker = segmentmarkerlist[i]; } #else /* not TRILIBRARY */ stringptr = readline(inputline, polyfile, b->inpolyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %d has no endpoints in %s.\n", b->firstnumber + i, polyfilename); exit(1); } else { end1 = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %d is missing its second endpoint in %s.\n", b->firstnumber + i, polyfilename); exit(1); } else { end2 = (int) strtol(stringptr, &stringptr, 0); } if (segmentmarkers) { stringptr = findfield(stringptr); if (*stringptr == '\0') { boundmarker = 0; } else { boundmarker = (int) strtol(stringptr, &stringptr, 0); } } #endif /* not TRILIBRARY */ if ((end1 < b->firstnumber) || (end1 >= b->firstnumber + m->invertices)) { if (!b->quiet) { printf("Warning: Invalid first endpoint of segment %d in %s.\n", b->firstnumber + i, polyfilename); } } else if ((end2 < b->firstnumber) || (end2 >= b->firstnumber + m->invertices)) { if (!b->quiet) { printf("Warning: Invalid second endpoint of segment %d in %s.\n", b->firstnumber + i, polyfilename); } } else { endpoint1 = getvertex(m, b, end1); endpoint2 = getvertex(m, b, end2); if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { if (!b->quiet) { printf("Warning: Endpoints of segment %d are coincident in %s.\n", b->firstnumber + i, polyfilename); } } else { insertsegment(m, b, endpoint1, endpoint2, boundmarker); } } } } else { m->insegments = 0; } if (b->convex || !b->poly) { /* Enclose the convex hull with subsegments. */ if (b->verbose) { printf(" Enclosing convex hull with segments.\n"); } markhull(m, b); } } /** **/ /** **/ /********* Segment insertion ends here *********/ /********* Carving out holes and concavities begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* infecthull() Virally infect all of the triangles of the convex hull */ /* that are not protected by subsegments. Where there are */ /* subsegments, set boundary markers as appropriate. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void infecthull(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void infecthull(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri hulltri; struct otri nexttri; struct otri starttri; struct osub hullsubseg; triangle **deadtriangle; vertex horg, hdest; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose) { printf(" Marking concavities (external triangles) for elimination.\n"); } /* Find a triangle handle on the hull. */ hulltri.tri = m->dummytri; hulltri.orient = 0; symself(hulltri); /* Remember where we started so we know when to stop. */ otricopy(hulltri, starttri); /* Go once counterclockwise around the convex hull. */ do { /* Ignore triangles that are already infected. */ if (!infected(hulltri)) { /* Is the triangle protected by a subsegment? */ tspivot(hulltri, hullsubseg); if (hullsubseg.ss == m->dummysub) { /* The triangle is not protected; infect it. */ if (!infected(hulltri)) { infect(hulltri); deadtriangle = (triangle **) poolalloc(&m->viri); *deadtriangle = hulltri.tri; } } else { /* The triangle is protected; set boundary markers if appropriate. */ if (mark(hullsubseg) == 0) { setmark(hullsubseg, 1); org(hulltri, horg); dest(hulltri, hdest); if (vertexmark(horg) == 0) { setvertexmark(horg, 1); } if (vertexmark(hdest) == 0) { setvertexmark(hdest, 1); } } } } /* To find the next hull edge, go clockwise around the next vertex. */ lnextself(hulltri); oprev(hulltri, nexttri); while (nexttri.tri != m->dummytri) { otricopy(nexttri, hulltri); oprev(hulltri, nexttri); } } while (!otriequal(hulltri, starttri)); } /*****************************************************************************/ /* */ /* plague() Spread the virus from all infected triangles to any neighbors */ /* not protected by subsegments. Delete all infected triangles. */ /* */ /* This is the procedure that actually creates holes and concavities. */ /* */ /* This procedure operates in two phases. The first phase identifies all */ /* the triangles that will die, and marks them as infected. They are */ /* marked to ensure that each triangle is added to the virus pool only */ /* once, so the procedure will terminate. */ /* */ /* The second phase actually eliminates the infected triangles. It also */ /* eliminates orphaned vertices. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void plague(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void plague(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri testtri; struct otri neighbor; triangle **virusloop; triangle **deadtriangle; struct osub neighborsubseg; vertex testvertex; vertex norg, ndest; vertex deadorg, deaddest, deadapex; int killorg; triangle ptr; /* Temporary variable used by sym() and onext(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose) { printf(" Marking neighbors of marked triangles.\n"); } /* Loop through all the infected triangles, spreading the virus to */ /* their neighbors, then to their neighbors' neighbors. */ traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* A triangle is marked as infected by messing with one of its pointers */ /* to subsegments, setting it to an illegal value. Hence, we have to */ /* temporarily uninfect this triangle so that we can examine its */ /* adjacent subsegments. */ uninfect(testtri); if (b->verbose > 2) { /* Assign the triangle an orientation for convenience in */ /* checking its vertices. */ testtri.orient = 0; org(testtri, deadorg); dest(testtri, deaddest); apex(testtri, deadapex); printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", deadorg[0], deadorg[1], deaddest[0], deaddest[1], deadapex[0], deadapex[1]); } /* Check each of the triangle's three neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { /* Find the neighbor. */ sym(testtri, neighbor); /* Check for a subsegment between the triangle and its neighbor. */ tspivot(testtri, neighborsubseg); /* Check if the neighbor is nonexistent or already infected. */ if ((neighbor.tri == m->dummytri) || infected(neighbor)) { if (neighborsubseg.ss != m->dummysub) { /* There is a subsegment separating the triangle from its */ /* neighbor, but both triangles are dying, so the subsegment */ /* dies too. */ subsegdealloc(m, neighborsubseg.ss); if (neighbor.tri != m->dummytri) { /* Make sure the subsegment doesn't get deallocated again */ /* later when the infected neighbor is visited. */ uninfect(neighbor); tsdissolve(neighbor); infect(neighbor); } } } else { /* The neighbor exists and is not infected. */ if (neighborsubseg.ss == m->dummysub) { /* There is no subsegment protecting the neighbor, so */ /* the neighbor becomes infected. */ if (b->verbose > 2) { org(neighbor, deadorg); dest(neighbor, deaddest); apex(neighbor, deadapex); printf( " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", deadorg[0], deadorg[1], deaddest[0], deaddest[1], deadapex[0], deadapex[1]); } infect(neighbor); /* Ensure that the neighbor's neighbors will be infected. */ deadtriangle = (triangle **) poolalloc(&m->viri); *deadtriangle = neighbor.tri; } else { /* The neighbor is protected by a subsegment. */ /* Remove this triangle from the subsegment. */ stdissolve(neighborsubseg); /* The subsegment becomes a boundary. Set markers accordingly. */ if (mark(neighborsubseg) == 0) { setmark(neighborsubseg, 1); } org(neighbor, norg); dest(neighbor, ndest); if (vertexmark(norg) == 0) { setvertexmark(norg, 1); } if (vertexmark(ndest) == 0) { setvertexmark(ndest, 1); } } } } /* Remark the triangle as infected, so it doesn't get added to the */ /* virus pool again. */ infect(testtri); virusloop = (triangle **) traverse(&m->viri); } if (b->verbose) { printf(" Deleting marked triangles.\n"); } traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* Check each of the three corners of the triangle for elimination. */ /* This is done by walking around each vertex, checking if it is */ /* still connected to at least one live triangle. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { org(testtri, testvertex); /* Check if the vertex has already been tested. */ if (testvertex != (vertex) NULL) { killorg = 1; /* Mark the corner of the triangle as having been tested. */ setorg(testtri, NULL); /* Walk counterclockwise about the vertex. */ onext(testtri, neighbor); /* Stop upon reaching a boundary or the starting triangle. */ while ((neighbor.tri != m->dummytri) && (!otriequal(neighbor, testtri))) { if (infected(neighbor)) { /* Mark the corner of this triangle as having been tested. */ setorg(neighbor, NULL); } else { /* A live triangle. The vertex survives. */ killorg = 0; } /* Walk counterclockwise about the vertex. */ onextself(neighbor); } /* If we reached a boundary, we must walk clockwise as well. */ if (neighbor.tri == m->dummytri) { /* Walk clockwise about the vertex. */ oprev(testtri, neighbor); /* Stop upon reaching a boundary. */ while (neighbor.tri != m->dummytri) { if (infected(neighbor)) { /* Mark the corner of this triangle as having been tested. */ setorg(neighbor, NULL); } else { /* A live triangle. The vertex survives. */ killorg = 0; } /* Walk clockwise about the vertex. */ oprevself(neighbor); } } if (killorg) { if (b->verbose > 1) { printf(" Deleting vertex (%.12g, %.12g)\n", testvertex[0], testvertex[1]); } setvertextype(testvertex, UNDEADVERTEX); m->undeads++; } } } /* Record changes in the number of boundary edges, and disconnect */ /* dead triangles from their neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { sym(testtri, neighbor); if (neighbor.tri == m->dummytri) { /* There is no neighboring triangle on this edge, so this edge */ /* is a boundary edge. This triangle is being deleted, so this */ /* boundary edge is deleted. */ m->hullsize--; } else { /* Disconnect the triangle from its neighbor. */ dissolve(neighbor); /* There is a neighboring triangle on this edge, so this edge */ /* becomes a boundary edge when this triangle is deleted. */ m->hullsize++; } } /* Return the dead triangle to the pool of triangles. */ triangledealloc(m, testtri.tri); virusloop = (triangle **) traverse(&m->viri); } /* Empty the virus pool. */ poolrestart(&m->viri); } /*****************************************************************************/ /* */ /* regionplague() Spread regional attributes and/or area constraints */ /* (from a .poly file) throughout the mesh. */ /* */ /* This procedure operates in two phases. The first phase spreads an */ /* attribute and/or an area constraint through a (segment-bounded) region. */ /* The triangles are marked to ensure that each triangle is added to the */ /* virus pool only once, so the procedure will terminate. */ /* */ /* The second phase uninfects all infected triangles, returning them to */ /* normal. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void regionplague(struct mesh *m, struct behavior *b, REAL attribute, REAL area) #else /* not ANSI_DECLARATORS */ void regionplague(m, b, attribute, area) struct mesh *m; struct behavior *b; REAL attribute; REAL area; #endif /* not ANSI_DECLARATORS */ { struct otri testtri; struct otri neighbor; triangle **virusloop; triangle **regiontri; struct osub neighborsubseg; vertex regionorg, regiondest, regionapex; triangle ptr; /* Temporary variable used by sym() and onext(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 1) { printf(" Marking neighbors of marked triangles.\n"); } /* Loop through all the infected triangles, spreading the attribute */ /* and/or area constraint to their neighbors, then to their neighbors' */ /* neighbors. */ traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* A triangle is marked as infected by messing with one of its pointers */ /* to subsegments, setting it to an illegal value. Hence, we have to */ /* temporarily uninfect this triangle so that we can examine its */ /* adjacent subsegments. */ uninfect(testtri); if (b->regionattrib) { /* Set an attribute. */ setelemattribute(testtri, m->eextras, attribute); } if (b->vararea) { /* Set an area constraint. */ setareabound(testtri, area); } if (b->verbose > 2) { /* Assign the triangle an orientation for convenience in */ /* checking its vertices. */ testtri.orient = 0; org(testtri, regionorg); dest(testtri, regiondest); apex(testtri, regionapex); printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", regionorg[0], regionorg[1], regiondest[0], regiondest[1], regionapex[0], regionapex[1]); } /* Check each of the triangle's three neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { /* Find the neighbor. */ sym(testtri, neighbor); /* Check for a subsegment between the triangle and its neighbor. */ tspivot(testtri, neighborsubseg); /* Make sure the neighbor exists, is not already infected, and */ /* isn't protected by a subsegment. */ if ((neighbor.tri != m->dummytri) && !infected(neighbor) && (neighborsubseg.ss == m->dummysub)) { if (b->verbose > 2) { org(neighbor, regionorg); dest(neighbor, regiondest); apex(neighbor, regionapex); printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", regionorg[0], regionorg[1], regiondest[0], regiondest[1], regionapex[0], regionapex[1]); } /* Infect the neighbor. */ infect(neighbor); /* Ensure that the neighbor's neighbors will be infected. */ regiontri = (triangle **) poolalloc(&m->viri); *regiontri = neighbor.tri; } } /* Remark the triangle as infected, so it doesn't get added to the */ /* virus pool again. */ infect(testtri); virusloop = (triangle **) traverse(&m->viri); } /* Uninfect all triangles. */ if (b->verbose > 1) { printf(" Unmarking marked triangles.\n"); } traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; uninfect(testtri); virusloop = (triangle **) traverse(&m->viri); } /* Empty the virus pool. */ poolrestart(&m->viri); } /*****************************************************************************/ /* */ /* carveholes() Find the holes and infect them. Find the area */ /* constraints and infect them. Infect the convex hull. */ /* Spread the infection and kill triangles. Spread the */ /* area constraints. */ /* */ /* This routine mainly calls other routines to carry out all these */ /* functions. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, REAL *regionlist, int regions) #else /* not ANSI_DECLARATORS */ void carveholes(m, b, holelist, holes, regionlist, regions) struct mesh *m; struct behavior *b; REAL *holelist; int holes; REAL *regionlist; int regions; #endif /* not ANSI_DECLARATORS */ { struct otri searchtri; struct otri triangleloop; struct otri *regiontris; triangle **holetri; triangle **regiontri; vertex searchorg, searchdest; enum locateresult intersect; int i; triangle ptr; /* Temporary variable used by sym(). */ if (!(b->quiet || (b->noholes && b->convex))) { printf("Removing unwanted triangles.\n"); if (b->verbose && (holes > 0)) { printf(" Marking holes for elimination.\n"); } } if (regions > 0) { /* Allocate storage for the triangles in which region points fall. */ regiontris = (struct otri *) trimalloc(regions * sizeof(struct otri)); } if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { /* Initialize a pool of viri to be used for holes, concavities, */ /* regional attributes, and/or regional area constraints. */ poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, POINTER, 0); } if (!b->convex) { /* Mark as infected any unprotected triangles on the boundary. */ /* This is one way by which concavities are created. */ infecthull(m, b); } if ((holes > 0) && !b->noholes) { /* Infect each triangle in which a hole lies. */ for (i = 0; i < 2 * holes; i += 2) { /* Ignore holes that aren't within the bounds of the mesh. */ if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax) && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) { /* Start searching from some triangle on the outer boundary. */ searchtri.tri = m->dummytri; searchtri.orient = 0; symself(searchtri); /* Ensure that the hole is to the left of this boundary edge; */ /* otherwise, locate() will falsely report that the hole */ /* falls within the starting triangle. */ org(searchtri, searchorg); dest(searchtri, searchdest); if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) > 0.0) { /* Find a triangle that contains the hole. */ intersect = locate(m, b, &holelist[i], &searchtri); if ((intersect != OUTSIDE) && (!infected(searchtri))) { /* Infect the triangle. This is done by marking the triangle */ /* as infected and including the triangle in the virus pool. */ infect(searchtri); holetri = (triangle **) poolalloc(&m->viri); *holetri = searchtri.tri; } } } } } /* Now, we have to find all the regions BEFORE we carve the holes, because */ /* locate() won't work when the triangulation is no longer convex. */ /* (Incidentally, this is the reason why regional attributes and area */ /* constraints can't be used when refining a preexisting mesh, which */ /* might not be convex; they can only be used with a freshly */ /* triangulated PSLG.) */ if (regions > 0) { /* Find the starting triangle for each region. */ for (i = 0; i < regions; i++) { regiontris[i].tri = m->dummytri; /* Ignore region points that aren't within the bounds of the mesh. */ if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) && (regionlist[4 * i + 1] >= m->ymin) && (regionlist[4 * i + 1] <= m->ymax)) { /* Start searching from some triangle on the outer boundary. */ searchtri.tri = m->dummytri; searchtri.orient = 0; symself(searchtri); /* Ensure that the region point is to the left of this boundary */ /* edge; otherwise, locate() will falsely report that the */ /* region point falls within the starting triangle. */ org(searchtri, searchorg); dest(searchtri, searchdest); if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) > 0.0) { /* Find a triangle that contains the region point. */ intersect = locate(m, b, ®ionlist[4 * i], &searchtri); if ((intersect != OUTSIDE) && (!infected(searchtri))) { /* Record the triangle for processing after the */ /* holes have been carved. */ otricopy(searchtri, regiontris[i]); } } } } } if (m->viri.items > 0) { /* Carve the holes and concavities. */ plague(m, b); } /* The virus pool should be empty now. */ if (regions > 0) { if (!b->quiet) { if (b->regionattrib) { if (b->vararea) { printf("Spreading regional attributes and area constraints.\n"); } else { printf("Spreading regional attributes.\n"); } } else { printf("Spreading regional area constraints.\n"); } } if (b->regionattrib && !b->refine) { /* Assign every triangle a regional attribute of zero. */ traversalinit(&m->triangles); triangleloop.orient = 0; triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { setelemattribute(triangleloop, m->eextras, 0.0); triangleloop.tri = triangletraverse(m); } } for (i = 0; i < regions; i++) { if (regiontris[i].tri != m->dummytri) { /* Make sure the triangle under consideration still exists. */ /* It may have been eaten by the virus. */ if (!deadtri(regiontris[i].tri)) { /* Put one triangle in the virus pool. */ infect(regiontris[i]); regiontri = (triangle **) poolalloc(&m->viri); *regiontri = regiontris[i].tri; /* Apply one region's attribute and/or area constraint. */ regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]); /* The virus pool should be empty now. */ } } } if (b->regionattrib && !b->refine) { /* Note the fact that each triangle has an additional attribute. */ m->eextras++; } } /* Free up memory. */ if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { pooldeinit(&m->viri); } if (regions > 0) { trifree((VOID *) regiontris); } } /** **/ /** **/ /********* Carving out holes and concavities ends here *********/ /********* Mesh quality maintenance begins here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* tallyencs() Traverse the entire list of subsegments, and check each */ /* to see if it is encroached. If so, add it to the list. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void tallyencs(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void tallyencs(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct osub subsegloop; int dummy; traversalinit(&m->subsegs); subsegloop.ssorient = 0; subsegloop.ss = subsegtraverse(m); while (subsegloop.ss != (subseg *) NULL) { /* If the segment is encroached, add it to the list. */ dummy = checkseg4encroach(m, b, &subsegloop, 0.0); subsegloop.ss = subsegtraverse(m); } } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* precisionerror() Print an error message for precision problems. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY void precisionerror() { printf("Try increasing the area criterion and/or reducing the minimum\n"); printf(" allowable angle so that tiny triangles are not created.\n"); #ifdef SINGLE printf("Alternatively, try recompiling me with double precision\n"); printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); printf(" source file or \"-DSINGLE\" from the makefile).\n"); #endif /* SINGLE */ } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* splitencsegs() Split all the encroached subsegments. */ /* */ /* Each encroached subsegment is repaired by splitting it - inserting a */ /* vertex at or near its midpoint. Newly inserted vertices may encroach */ /* upon other subsegments; these are also repaired. */ /* */ /* `triflaws' is a flag that specifies whether one should take note of new */ /* bad triangles that result from inserting vertices to repair encroached */ /* subsegments. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void splitencsegs(struct mesh *m, struct behavior *b, int triflaws) #else /* not ANSI_DECLARATORS */ void splitencsegs(m, b, triflaws) struct mesh *m; struct behavior *b; int triflaws; #endif /* not ANSI_DECLARATORS */ { struct otri enctri; struct otri testtri; struct osub testsh; struct osub currentenc; struct badsubseg *encloop; vertex eorg, edest, eapex; vertex newvertex; enum insertvertexresult success; REAL segmentlength, nearestpoweroftwo; REAL split; REAL multiplier, divisor; int acuteorg, acuteorg2, acutedest, acutedest2; int dummy; int i; triangle ptr; /* Temporary variable used by stpivot(). */ subseg sptr; /* Temporary variable used by snext(). */ /* Note that steinerleft == -1 if an unlimited number */ /* of Steiner points is allowed. */ while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) { traversalinit(&m->badsubsegs); encloop = badsubsegtraverse(m); while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) { sdecode(encloop->encsubseg, currentenc); sorg(currentenc, eorg); sdest(currentenc, edest); /* Make sure that this segment is still the same segment it was */ /* when it was determined to be encroached. If the segment was */ /* enqueued multiple times (because several newly inserted */ /* vertices encroached it), it may have already been split. */ if (!deadsubseg(currentenc.ss) && (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) { /* To decide where to split a segment, we need to know if the */ /* segment shares an endpoint with an adjacent segment. */ /* The concern is that, if we simply split every encroached */ /* segment in its center, two adjacent segments with a small */ /* angle between them might lead to an infinite loop; each */ /* vertex added to split one segment will encroach upon the */ /* other segment, which must then be split with a vertex that */ /* will encroach upon the first segment, and so on forever. */ /* To avoid this, imagine a set of concentric circles, whose */ /* radii are powers of two, about each segment endpoint. */ /* These concentric circles determine where the segment is */ /* split. (If both endpoints are shared with adjacent */ /* segments, split the segment in the middle, and apply the */ /* concentric circles for later splittings.) */ /* Is the origin shared with another segment? */ stpivot(currentenc, enctri); lnext(enctri, testtri); tspivot(testtri, testsh); acuteorg = testsh.ss != m->dummysub; /* Is the destination shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acutedest = testsh.ss != m->dummysub; /* If we're using diametral lenses (rather than diametral circles) */ /* to define encroachment, delete free vertices from the */ /* subsegment's diametral circle. */ if (!b->nolenses && !acuteorg && !acutedest) { apex(enctri, eapex); while ((vertextype(eapex) == FREEVERTEX) && ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { deletevertex(m, b, &testtri); stpivot(currentenc, enctri); apex(enctri, eapex); lprev(enctri, testtri); } } /* Now, check the other side of the segment, if there's a triangle */ /* there. */ sym(enctri, testtri); if (testtri.tri != m->dummytri) { /* Is the destination shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acutedest2 = testsh.ss != m->dummysub; acutedest = acutedest || acutedest2; /* Is the origin shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acuteorg2 = testsh.ss != m->dummysub; acuteorg = acuteorg || acuteorg2; /* Delete free vertices from the subsegment's diametral circle. */ if (!b->nolenses && !acuteorg2 && !acutedest2) { org(testtri, eapex); while ((vertextype(eapex) == FREEVERTEX) && ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { deletevertex(m, b, &testtri); sym(enctri, testtri); apex(testtri, eapex); lprevself(testtri); } } } /* Use the concentric circles if exactly one endpoint is shared */ /* with another adjacent segment. */ if (acuteorg || acutedest) { segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + (edest[1] - eorg[1]) * (edest[1] - eorg[1])); /* Find the power of two that most evenly splits the segment. */ /* The worst case is a 2:1 ratio between subsegment lengths. */ nearestpoweroftwo = 1.0; while (segmentlength > 3.0 * nearestpoweroftwo) { nearestpoweroftwo *= 2.0; } while (segmentlength < 1.5 * nearestpoweroftwo) { nearestpoweroftwo *= 0.5; } /* Where do we split the segment? */ split = nearestpoweroftwo / segmentlength; if (acutedest) { split = 1.0 - split; } } else { /* If we're not worried about adjacent segments, split */ /* this segment in the middle. */ split = 0.5; } /* Create the new vertex. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate its coordinate and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]); } if (!b->noexact) { /* Roundoff in the above calculation may yield a `newvertex' */ /* that is not precisely collinear with `eorg' and `edest'. */ /* Improve collinearity by one step of iterative refinement. */ multiplier = counterclockwise(m, b, eorg, edest, newvertex); divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) + (eorg[1] - edest[1]) * (eorg[1] - edest[1])); if ((multiplier != 0.0) && (divisor != 0.0)) { multiplier = multiplier / divisor; /* Watch out for NANs. */ if (multiplier == multiplier) { newvertex[0] += multiplier * (edest[1] - eorg[1]); newvertex[1] += multiplier * (eorg[0] - edest[0]); } } } setvertexmark(newvertex, mark(currentenc)); setvertextype(newvertex, SEGMENTVERTEX); if (b->verbose > 1) { printf( " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", eorg[0], eorg[1], edest[0], edest[1], newvertex[0], newvertex[1]); } /* Check whether the new vertex lies on an endpoint. */ if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) || ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) { printf("Error: Ran out of precision at (%.12g, %.12g).\n", newvertex[0], newvertex[1]); printf("I attempted to split a segment to a smaller size than\n"); printf(" can be accommodated by the finite precision of\n"); printf(" floating point arithmetic.\n"); precisionerror(); exit(1); } /* Insert the splitting vertex. This should always succeed. */ success = insertvertex(m, b, newvertex, &enctri, ¤tenc, 1, triflaws, 0.0); if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) { printf("Internal error in splitencsegs():\n"); printf(" Failure to split a segment.\n"); internalerror(); } if (m->steinerleft > 0) { m->steinerleft--; } /* Check the two new subsegments to see if they're encroached. */ dummy = checkseg4encroach(m, b, ¤tenc, 0.0); snextself(currentenc); dummy = checkseg4encroach(m, b, ¤tenc, 0.0); } badsubsegdealloc(m, encloop); encloop = badsubsegtraverse(m); } } } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* tallyfaces() Test every triangle in the mesh for quality measures. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void tallyfaces(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void tallyfaces(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop; if (b->verbose) { printf(" Making a list of bad triangles.\n"); } traversalinit(&m->triangles); triangleloop.orient = 0; triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* If the triangle is bad, enqueue it. */ testtriangle(m, b, &triangleloop); triangleloop.tri = triangletraverse(m); } } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* splittriangle() Inserts a vertex at the circumcenter of a triangle. */ /* Deletes the newly inserted vertex if it encroaches */ /* upon a segment. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void splittriangle(struct mesh *m, struct behavior *b, struct badtriang *badtri) #else /* not ANSI_DECLARATORS */ void splittriangle(m, b, badtri) struct mesh *m; struct behavior *b; struct badtriang *badtri; #endif /* not ANSI_DECLARATORS */ { struct otri badotri; vertex borg, bdest, bapex; vertex newvertex; REAL xi, eta; REAL minedge; enum insertvertexresult success; int errorflag; int i; decode(badtri->poortri, badotri); org(badotri, borg); dest(badotri, bdest); apex(badotri, bapex); /* Make sure that this triangle is still the same triangle it was */ /* when it was tested and determined to be of bad quality. */ /* Subsequent transformations may have made it a different triangle. */ if (!deadtri(badotri.tri) && (borg == badtri->triangorg) && (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { if (b->verbose > 1) { printf(" Splitting this triangle at its circumcenter:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); } errorflag = 0; /* Create a new vertex at the triangle's circumcenter. */ newvertex = (vertex) poolalloc(&m->vertices); findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, &minedge); /* Check whether the new vertex lies on a triangle vertex. */ if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) || ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) || ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) { if (!b->quiet) { printf( "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", newvertex[0], newvertex[1]); errorflag = 1; } vertexdealloc(m, newvertex); } else { for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ newvertex[i] = borg[i] + xi * (bdest[i] - borg[i]) + eta * (bapex[i] - borg[i]); } /* The new vertex must be in the interior, and therefore is a */ /* free vertex with a marker of zero. */ setvertexmark(newvertex, 0); setvertextype(newvertex, FREEVERTEX); /* Ensure that the handle `badotri' does not represent the longest */ /* edge of the triangle. This ensures that the circumcenter must */ /* fall to the left of this edge, so point location will work. */ /* (If the angle org-apex-dest exceeds 90 degrees, then the */ /* circumcenter lies outside the org-dest edge, and eta is */ /* negative. Roundoff error might prevent eta from being */ /* negative when it should be, so I test eta against xi.) */ if (eta < xi) { lprevself(badotri); } /* Insert the circumcenter, searching from the edge of the triangle, */ /* and maintain the Delaunay property of the triangulation. */ success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL, 1, 1, minedge); if (success == SUCCESSFULVERTEX) { if (m->steinerleft > 0) { m->steinerleft--; } } else if (success == ENCROACHINGVERTEX) { /* If the newly inserted vertex encroaches upon a subsegment, */ /* delete the new vertex. */ undovertex(m, b); if (b->verbose > 1) { printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } vertexdealloc(m, newvertex); } else if (success == VIOLATINGVERTEX) { /* Failed to insert the new vertex, but some subsegment was */ /* marked as being encroached. */ vertexdealloc(m, newvertex); } else { /* success == DUPLICATEVERTEX */ /* Couldn't insert the new vertex because a vertex is already there. */ if (!b->quiet) { printf( "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", newvertex[0], newvertex[1]); errorflag = 1; } vertexdealloc(m, newvertex); } } if (errorflag) { if (b->verbose) { printf(" The new vertex is at the circumcenter of triangle\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); } printf("This probably means that I am trying to refine triangles\n"); printf(" to a smaller size than can be accommodated by the finite\n"); printf(" precision of floating point arithmetic. (You can be\n"); printf(" sure of this if I fail to terminate.)\n"); precisionerror(); } } } #endif /* not CDT_ONLY */ /*****************************************************************************/ /* */ /* enforcequality() Remove all the encroached subsegments and bad */ /* triangles from the triangulation. */ /* */ /*****************************************************************************/ #ifndef CDT_ONLY #ifdef ANSI_DECLARATORS void enforcequality(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void enforcequality(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct badtriang *badtri; int i; if (!b->quiet) { printf("Adding Steiner points to enforce quality.\n"); } /* Initialize the pool of encroached subsegments. */ poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK, POINTER, 0); if (b->verbose) { printf(" Looking for encroached subsegments.\n"); } /* Test all segments to see if they're encroached. */ tallyencs(m, b); if (b->verbose && (m->badsubsegs.items > 0)) { printf(" Splitting encroached subsegments.\n"); } /* Fix encroached subsegments without noting bad triangles. */ splitencsegs(m, b, 0); /* At this point, if we haven't run out of Steiner points, the */ /* triangulation should be (conforming) Delaunay. */ /* Next, we worry about enforcing triangle quality. */ if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { /* Initialize the pool of bad triangles. */ poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK, POINTER, 0); /* Initialize the queues of bad triangles. */ for (i = 0; i < 64; i++) { m->queuefront[i] = (struct badtriang *) NULL; } m->firstnonemptyq = -1; /* Test all triangles to see if they're bad. */ tallyfaces(m, b); /* Initialize the pool of recently flipped triangles. */ poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK, POINTER, 0); m->checkquality = 1; if (b->verbose) { printf(" Splitting bad triangles.\n"); } while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) { /* Fix one bad triangle by inserting a vertex at its circumcenter. */ badtri = dequeuebadtriang(m); splittriangle(m, b, badtri); if (m->badsubsegs.items > 0) { /* Put bad triangle back in queue for another try later. */ enqueuebadtriang(m, b, badtri); /* Fix any encroached subsegments that resulted. */ /* Record any new bad triangles that result. */ splitencsegs(m, b, 1); } else { /* Return the bad triangle to the pool. */ pooldealloc(&m->badtriangles, (VOID *) badtri); } } } /* At this point, if we haven't run out of Steiner points, the */ /* triangulation should be (conforming) Delaunay and have no */ /* low-quality triangles. */ /* Might we have run out of Steiner points too soon? */ if (!b->quiet && (m->badsubsegs.items > 0) && (m->steinerleft == 0)) { printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); if (m->badsubsegs.items == 1) { printf(" an encroached subsegment, and therefore might not be truly\n"); } else { printf(" %ld encroached subsegments, and therefore might not be truly\n" , m->badsubsegs.items); } printf(" Delaunay. If the Delaunay property is important to you,\n"); printf(" try increasing the number of Steiner points (controlled by\n"); printf(" the -S switch) slightly and try again.\n\n"); } } #endif /* not CDT_ONLY */ /** **/ /** **/ /********* Mesh quality maintenance ends here *********/ /*****************************************************************************/ /* */ /* highorder() Create extra nodes for quadratic subparametric elements. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void highorder(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void highorder(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop, trisym; struct osub checkmark; vertex newvertex; vertex torg, tdest; int i; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (!b->quiet) { printf("Adding vertices for second-order triangles.\n"); } /* The following line ensures that dead items in the pool of nodes */ /* cannot be allocated for the extra nodes associated with high */ /* order elements. This ensures that the primary nodes (at the */ /* corners of elements) will occur earlier in the output files, and */ /* have lower indices, than the extra nodes. */ m->vertices.deaditemstack = (VOID *) NULL; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { org(triangleloop, torg); dest(triangleloop, tdest); /* Create a new node in the middle of the edge. Interpolate */ /* its attributes. */ newvertex = (vertex) poolalloc(&m->vertices); for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = 0.5 * (torg[i] + tdest[i]); } /* Set the new node's marker to zero or one, depending on */ /* whether it lies on a boundary. */ setvertexmark(newvertex, trisym.tri == m->dummytri); setvertextype(newvertex, trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX); if (b->usesegments) { tspivot(triangleloop, checkmark); /* If this edge is a segment, transfer the marker to the new node. */ if (checkmark.ss != m->dummysub) { setvertexmark(newvertex, mark(checkmark)); setvertextype(newvertex, SEGMENTVERTEX); } } if (b->verbose > 1) { printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* Record the new node in the (one or two) adjacent elements. */ triangleloop.tri[m->highorderindex + triangleloop.orient] = (triangle) newvertex; if (trisym.tri != m->dummytri) { trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex; } } } triangleloop.tri = triangletraverse(m); } } /********* File I/O routines begin here *********/ /** **/ /** **/ /*****************************************************************************/ /* */ /* readline() Read a nonempty line from a file. */ /* */ /* A line is considered "nonempty" if it contains something that looks like */ /* a number. Comments (prefaced by `#') are ignored. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS char *readline(char *string, FILE *infile, char *infilename) #else /* not ANSI_DECLARATORS */ char *readline(string, infile, infilename) char *string; FILE *infile; char *infilename; #endif /* not ANSI_DECLARATORS */ { char *result; /* Search for something that looks like a number. */ do { result = fgets(string, INPUTLINESIZE, infile); if (result == (char *) NULL) { printf(" Error: Unexpected end of file in %s.\n", infilename); exit(1); } /* Skip anything that doesn't look like a number, a comment, */ /* or the end of a line. */ while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } /* If it's a comment or end of line, read another line and try again. */ } while ((*result == '#') || (*result == '\0')); return result; } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* findfield() Find the next field of a string. */ /* */ /* Jumps past the current field by searching for whitespace, then jumps */ /* past the whitespace to find the next field. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS char *findfield(char *string) #else /* not ANSI_DECLARATORS */ char *findfield(string) char *string; #endif /* not ANSI_DECLARATORS */ { char *result; result = string; /* Skip the current field. Stop upon reaching whitespace. */ while ((*result != '\0') && (*result != '#') && (*result != ' ') && (*result != '\t')) { result++; } /* Now skip the whitespace and anything else that doesn't look like a */ /* number, a comment, or the end of a line. */ while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } /* Check for a comment (prefixed with `#'). */ if (*result == '#') { *result = '\0'; } return result; } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* readnodes() Read the vertices from a file, which may be a .node or */ /* .poly file. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS void readnodes(struct mesh *m, struct behavior *b, char *nodefilename, char *polyfilename, FILE **polyfile) #else /* not ANSI_DECLARATORS */ void readnodes(m, b, nodefilename, polyfilename, polyfile) struct mesh *m; struct behavior *b; char *nodefilename; char *polyfilename; FILE **polyfile; #endif /* not ANSI_DECLARATORS */ { FILE *infile; vertex vertexloop; char inputline[INPUTLINESIZE]; char *stringptr; char *infilename; REAL x, y; int firstnode; int nodemarkers; int currentmarker; int i, j; if (b->poly) { /* Read the vertices from a .poly file. */ if (!b->quiet) { printf("Opening %s.\n", polyfilename); } *polyfile = fopen(polyfilename, "r"); if (*polyfile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", polyfilename); exit(1); } /* Read number of vertices, number of dimensions, number of vertex */ /* attributes, and number of boundary markers. */ stringptr = readline(inputline, *polyfile, polyfilename); m->invertices = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { m->mesh_dim = 2; } else { m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->nextras = 0; } else { m->nextras = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { nodemarkers = 0; } else { nodemarkers = (int) strtol(stringptr, &stringptr, 0); } if (m->invertices > 0) { infile = *polyfile; infilename = polyfilename; m->readnodefile = 0; } else { /* If the .poly file claims there are zero vertices, that means that */ /* the vertices should be read from a separate .node file. */ m->readnodefile = 1; infilename = nodefilename; } } else { m->readnodefile = 1; infilename = nodefilename; *polyfile = (FILE *) NULL; } if (m->readnodefile) { /* Read the vertices from a .node file. */ if (!b->quiet) { printf("Opening %s.\n", nodefilename); } infile = fopen(nodefilename, "r"); if (infile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", nodefilename); exit(1); } /* Read number of vertices, number of dimensions, number of vertex */ /* attributes, and number of boundary markers. */ stringptr = readline(inputline, infile, nodefilename); m->invertices = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { m->mesh_dim = 2; } else { m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->nextras = 0; } else { m->nextras = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { nodemarkers = 0; } else { nodemarkers = (int) strtol(stringptr, &stringptr, 0); } } if (m->invertices < 3) { printf("Error: Input must have at least three input vertices.\n"); exit(1); } if (m->mesh_dim != 2) { printf("Error: Triangle only works with two-dimensional meshes.\n"); exit(1); } if (m->nextras == 0) { b->weighted = 0; } initializevertexpool(m, b); /* Read the vertices. */ for (i = 0; i < m->invertices; i++) { vertexloop = (vertex) poolalloc(&m->vertices); stringptr = readline(inputline, infile, infilename); if (i == 0) { firstnode = (int) strtol(stringptr, &stringptr, 0); if ((firstnode == 0) || (firstnode == 1)) { b->firstnumber = firstnode; } } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i); exit(1); } x = (REAL) strtod(stringptr, &stringptr); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i); exit(1); } y = (REAL) strtod(stringptr, &stringptr); vertexloop[0] = x; vertexloop[1] = y; /* Read the vertex attributes. */ for (j = 2; j < 2 + m->nextras; j++) { stringptr = findfield(stringptr); if (*stringptr == '\0') { vertexloop[j] = 0.0; } else { vertexloop[j] = (REAL) strtod(stringptr, &stringptr); } } if (nodemarkers) { /* Read a vertex marker. */ stringptr = findfield(stringptr); if (*stringptr == '\0') { setvertexmark(vertexloop, 0); } else { currentmarker = (int) strtol(stringptr, &stringptr, 0); setvertexmark(vertexloop, currentmarker); } } else { /* If no markers are specified in the file, they default to zero. */ setvertexmark(vertexloop, 0); } setvertextype(vertexloop, INPUTVERTEX); /* Determine the smallest and largest x and y coordinates. */ if (i == 0) { m->xmin = m->xmax = x; m->ymin = m->ymax = y; } else { m->xmin = (x < m->xmin) ? x : m->xmin; m->xmax = (x > m->xmax) ? x : m->xmax; m->ymin = (y < m->ymin) ? y : m->ymin; m->ymax = (y > m->ymax) ? y : m->ymax; } } if (m->readnodefile) { fclose(infile); } /* Nonexistent x value used as a flag to mark circle events in sweepline */ /* Delaunay algorithm. */ m->xminextreme = 10 * m->xmin - 9 * m->xmax; } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* transfernodes() Read the vertices from memory. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist, REAL *pointattriblist, int *pointmarkerlist, int numberofpoints, int numberofpointattribs) #else /* not ANSI_DECLARATORS */ void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist, numberofpoints, numberofpointattribs) struct mesh *m; struct behavior *b; REAL *pointlist; REAL *pointattriblist; int *pointmarkerlist; int numberofpoints; int numberofpointattribs; #endif /* not ANSI_DECLARATORS */ { vertex vertexloop; REAL x, y; int i, j; int coordindex; int attribindex; m->invertices = numberofpoints; m->mesh_dim = 2; m->nextras = numberofpointattribs; m->readnodefile = 0; if (m->invertices < 3) { printf("Error: Input must have at least three input vertices.\n"); exit(1); } if (m->nextras == 0) { b->weighted = 0; } initializevertexpool(m, b); /* Read the vertices. */ coordindex = 0; attribindex = 0; for (i = 0; i < m->invertices; i++) { vertexloop = (vertex) poolalloc(&m->vertices); /* Read the vertex coordinates. */ x = vertexloop[0] = pointlist[coordindex++]; y = vertexloop[1] = pointlist[coordindex++]; /* Read the vertex attributes. */ for (j = 0; j < numberofpointattribs; j++) { vertexloop[2 + j] = pointattriblist[attribindex++]; } if (pointmarkerlist != (int *) NULL) { /* Read a vertex marker. */ setvertexmark(vertexloop, pointmarkerlist[i]); } else { /* If no markers are specified, they default to zero. */ setvertexmark(vertexloop, 0); } setvertextype(vertexloop, INPUTVERTEX); /* Determine the smallest and largest x and y coordinates. */ if (i == 0) { m->xmin = m->xmax = x; m->ymin = m->ymax = y; } else { m->xmin = (x < m->xmin) ? x : m->xmin; m->xmax = (x > m->xmax) ? x : m->xmax; m->ymin = (y < m->ymin) ? y : m->ymin; m->ymax = (y > m->ymax) ? y : m->ymax; } } /* Nonexistent x value used as a flag to mark circle events in sweepline */ /* Delaunay algorithm. */ m->xminextreme = 10 * m->xmin - 9 * m->xmax; } #endif /* TRILIBRARY */ /*****************************************************************************/ /* */ /* readholes() Read the holes, and possibly regional attributes and area */ /* constraints, from a .poly file. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS void readholes(struct mesh *m, struct behavior *b, FILE *polyfile, char *polyfilename, REAL **hlist, int *holes, REAL **rlist, int *regions) #else /* not ANSI_DECLARATORS */ void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions) struct mesh *m; struct behavior *b; FILE *polyfile; char *polyfilename; REAL **hlist; int *holes; REAL **rlist; int *regions; #endif /* not ANSI_DECLARATORS */ { REAL *holelist; REAL *regionlist; char inputline[INPUTLINESIZE]; char *stringptr; int index; int i; /* Read the holes. */ stringptr = readline(inputline, polyfile, polyfilename); *holes = (int) strtol(stringptr, &stringptr, 0); if (*holes > 0) { holelist = (REAL *) trimalloc(2 * *holes * sizeof(REAL)); *hlist = holelist; for (i = 0; i < 2 * *holes; i += 2) { stringptr = readline(inputline, polyfile, polyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no x coordinate.\n", b->firstnumber + (i >> 1)); exit(1); } else { holelist[i] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no y coordinate.\n", b->firstnumber + (i >> 1)); exit(1); } else { holelist[i + 1] = (REAL) strtod(stringptr, &stringptr); } } } else { *hlist = (REAL *) NULL; } #ifndef CDT_ONLY if ((b->regionattrib || b->vararea) && !b->refine) { /* Read the area constraints. */ stringptr = readline(inputline, polyfile, polyfilename); *regions = (int) strtol(stringptr, &stringptr, 0); if (*regions > 0) { regionlist = (REAL *) trimalloc(4 * *regions * sizeof(REAL)); *rlist = regionlist; index = 0; for (i = 0; i < *regions; i++) { stringptr = readline(inputline, polyfile, polyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no x coordinate.\n", b->firstnumber + i); exit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no y coordinate.\n", b->firstnumber + i); exit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf( "Error: Region %d has no region attribute or area constraint.\n", b->firstnumber + i); exit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { regionlist[index] = regionlist[index - 1]; } else { regionlist[index] = (REAL) strtod(stringptr, &stringptr); } index++; } } } else { /* Set `*regions' to zero to avoid an accidental free() later. */ *regions = 0; *rlist = (REAL *) NULL; } #endif /* not CDT_ONLY */ fclose(polyfile); } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* finishfile() Write the command line to the output file so the user */ /* can remember how the file was generated. Close the file. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS void finishfile(FILE *outfile, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void finishfile(outfile, argc, argv) FILE *outfile; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ { int i; fprintf(outfile, "# Generated by"); for (i = 0; i < argc; i++) { fprintf(outfile, " "); fputs(argv[i], outfile); } fprintf(outfile, "\n"); fclose(outfile); } #endif /* not TRILIBRARY */ /*****************************************************************************/ /* */ /* writenodes() Number the vertices and write them to a .node file. */ /* */ /* To save memory, the vertex numbers are written over the boundary markers */ /* after the vertices are written to a file. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, REAL **pointattriblist, int **pointmarkerlist) #else /* not ANSI_DECLARATORS */ void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist) struct mesh *m; struct behavior *b; REAL **pointlist; REAL **pointattriblist; int **pointmarkerlist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writenodes(struct mesh *m, struct behavior *b, char *nodefilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writenodes(m, b, nodefilename, argc, argv) struct mesh *m; struct behavior *b; char *nodefilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY REAL *plist; REAL *palist; int *pmlist; int coordindex; int attribindex; #else /* not TRILIBRARY */ FILE *outfile; #endif /* not TRILIBRARY */ vertex vertexloop; long outvertices; int vertexnumber; int i; if (b->jettison) { outvertices = m->vertices.items - m->undeads; } else { outvertices = m->vertices.items; } #ifdef TRILIBRARY if (!b->quiet) { printf("Writing vertices.\n"); } /* Allocate memory for output vertices if necessary. */ if (*pointlist == (REAL *) NULL) { *pointlist = (REAL *) trimalloc(outvertices * 2 * sizeof(REAL)); } /* Allocate memory for output vertex attributes if necessary. */ if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) { *pointattriblist = (REAL *) trimalloc(outvertices * m->nextras * sizeof(REAL)); } /* Allocate memory for output vertex markers if necessary. */ if (!b->nobound && (*pointmarkerlist == (int *) NULL)) { *pointmarkerlist = (int *) trimalloc(outvertices * sizeof(int)); } plist = *pointlist; palist = *pointattriblist; pmlist = *pointmarkerlist; coordindex = 0; attribindex = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", nodefilename); } outfile = fopen(nodefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", nodefilename); exit(1); } /* Number of vertices, number of dimensions, number of vertex attributes, */ /* and number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim, m->nextras, 1 - b->nobound); #endif /* not TRILIBRARY */ traversalinit(&m->vertices); vertexnumber = b->firstnumber; vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { #ifdef TRILIBRARY /* X and y coordinates. */ plist[coordindex++] = vertexloop[0]; plist[coordindex++] = vertexloop[1]; /* Vertex attributes. */ for (i = 0; i < m->nextras; i++) { palist[attribindex++] = vertexloop[2 + i]; } if (!b->nobound) { /* Copy the boundary marker. */ pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop); } #else /* not TRILIBRARY */ /* Vertex number, x and y coordinates. */ fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0], vertexloop[1]); for (i = 0; i < m->nextras; i++) { /* Write an attribute. */ fprintf(outfile, " %.17g", vertexloop[i + 2]); } if (b->nobound) { fprintf(outfile, "\n"); } else { /* Write the boundary marker. */ fprintf(outfile, " %d\n", vertexmark(vertexloop)); } #endif /* not TRILIBRARY */ setvertexmark(vertexloop, vertexnumber); vertexnumber++; } vertexloop = vertextraverse(m); } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } /*****************************************************************************/ /* */ /* numbernodes() Number the vertices. */ /* */ /* Each vertex is assigned a marker equal to its number. */ /* */ /* Used when writenodes() is not called because no .node file is written. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void numbernodes(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void numbernodes(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { vertex vertexloop; int vertexnumber; traversalinit(&m->vertices); vertexnumber = b->firstnumber; vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { setvertexmark(vertexloop, vertexnumber); if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { vertexnumber++; } vertexloop = vertextraverse(m); } } /*****************************************************************************/ /* */ /* writeelements() Write the triangles to an .ele file. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writeelements(struct mesh *m, struct behavior *b, int **trianglelist, REAL **triangleattriblist) #else /* not ANSI_DECLARATORS */ void writeelements(m, b, trianglelist, triangleattriblist) struct mesh *m; struct behavior *b; int **trianglelist; REAL **triangleattriblist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writeelements(struct mesh *m, struct behavior *b, char *elefilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writeelements(m, b, elefilename, argc, argv) struct mesh *m; struct behavior *b; char *elefilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY int *tlist; REAL *talist; int vertexindex; int attribindex; #else /* not TRILIBRARY */ FILE *outfile; #endif /* not TRILIBRARY */ struct otri triangleloop; vertex p1, p2, p3; vertex mid1, mid2, mid3; long elementnumber; int i; #ifdef TRILIBRARY if (!b->quiet) { printf("Writing triangles.\n"); } /* Allocate memory for output triangles if necessary. */ if (*trianglelist == (int *) NULL) { *trianglelist = (int *) trimalloc(m->triangles.items * ((b->order + 1) * (b->order + 2) / 2) * sizeof(int)); } /* Allocate memory for output triangle attributes if necessary. */ if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) { *triangleattriblist = (REAL *) trimalloc(m->triangles.items * m->eextras * sizeof(REAL)); } tlist = *trianglelist; talist = *triangleattriblist; vertexindex = 0; attribindex = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", elefilename); } outfile = fopen(elefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", elefilename); exit(1); } /* Number of triangles, vertices per triangle, attributes per triangle. */ fprintf(outfile, "%ld %d %d\n", m->triangles.items, (b->order + 1) * (b->order + 2) / 2, m->eextras); #endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p1); dest(triangleloop, p2); apex(triangleloop, p3); if (b->order == 1) { #ifdef TRILIBRARY tlist[vertexindex++] = vertexmark(p1); tlist[vertexindex++] = vertexmark(p2); tlist[vertexindex++] = vertexmark(p3); #else /* not TRILIBRARY */ /* Triangle number, indices for three vertices. */ fprintf(outfile, "%4ld %4d %4d %4d", elementnumber, vertexmark(p1), vertexmark(p2), vertexmark(p3)); #endif /* not TRILIBRARY */ } else { mid1 = (vertex) triangleloop.tri[m->highorderindex + 1]; mid2 = (vertex) triangleloop.tri[m->highorderindex + 2]; mid3 = (vertex) triangleloop.tri[m->highorderindex]; #ifdef TRILIBRARY tlist[vertexindex++] = vertexmark(p1); tlist[vertexindex++] = vertexmark(p2); tlist[vertexindex++] = vertexmark(p3); tlist[vertexindex++] = vertexmark(mid1); tlist[vertexindex++] = vertexmark(mid2); tlist[vertexindex++] = vertexmark(mid3); #else /* not TRILIBRARY */ /* Triangle number, indices for six vertices. */ fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber, vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1), vertexmark(mid2), vertexmark(mid3)); #endif /* not TRILIBRARY */ } #ifdef TRILIBRARY for (i = 0; i < m->eextras; i++) { talist[attribindex++] = elemattribute(triangleloop, i); } #else /* not TRILIBRARY */ for (i = 0; i < m->eextras; i++) { fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); } fprintf(outfile, "\n"); #endif /* not TRILIBRARY */ triangleloop.tri = triangletraverse(m); elementnumber++; } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } /*****************************************************************************/ /* */ /* writepoly() Write the segments and holes to a .poly file. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writepoly(struct mesh *m, struct behavior *b, int **segmentlist, int **segmentmarkerlist) #else /* not ANSI_DECLARATORS */ void writepoly(m, b, segmentlist, segmentmarkerlist) struct mesh *m; struct behavior *b; int **segmentlist; int **segmentmarkerlist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writepoly(struct mesh *m, struct behavior *b, char *polyfilename, REAL *holelist, int holes, REAL *regionlist, int regions, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions, argc, argv) struct mesh *m; struct behavior *b; char *polyfilename; REAL *holelist; int holes; REAL *regionlist; int regions; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY int *slist; int *smlist; int index; #else /* not TRILIBRARY */ FILE *outfile; long holenumber, regionnumber; #endif /* not TRILIBRARY */ struct osub subsegloop; vertex endpoint1, endpoint2; long subsegnumber; #ifdef TRILIBRARY if (!b->quiet) { printf("Writing segments.\n"); } /* Allocate memory for output segments if necessary. */ if (*segmentlist == (int *) NULL) { *segmentlist = (int *) trimalloc(m->subsegs.items * 2 * sizeof(int)); } /* Allocate memory for output segment markers if necessary. */ if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) { *segmentmarkerlist = (int *) trimalloc(m->subsegs.items * sizeof(int)); } slist = *segmentlist; smlist = *segmentmarkerlist; index = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", polyfilename); } outfile = fopen(polyfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", polyfilename); exit(1); } /* The zero indicates that the vertices are in a separate .node file. */ /* Followed by number of dimensions, number of vertex attributes, */ /* and number of boundary markers (zero or one). */ fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras, 1 - b->nobound); /* Number of segments, number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound); #endif /* not TRILIBRARY */ traversalinit(&m->subsegs); subsegloop.ss = subsegtraverse(m); subsegloop.ssorient = 0; subsegnumber = b->firstnumber; while (subsegloop.ss != (subseg *) NULL) { sorg(subsegloop, endpoint1); sdest(subsegloop, endpoint2); #ifdef TRILIBRARY /* Copy indices of the segment's two endpoints. */ slist[index++] = vertexmark(endpoint1); slist[index++] = vertexmark(endpoint2); if (!b->nobound) { /* Copy the boundary marker. */ smlist[subsegnumber - b->firstnumber] = mark(subsegloop); } #else /* not TRILIBRARY */ /* Segment number, indices of its two endpoints, and possibly a marker. */ if (b->nobound) { fprintf(outfile, "%4ld %4d %4d\n", subsegnumber, vertexmark(endpoint1), vertexmark(endpoint2)); } else { fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber, vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop)); } #endif /* not TRILIBRARY */ subsegloop.ss = subsegtraverse(m); subsegnumber++; } #ifndef TRILIBRARY #ifndef CDT_ONLY fprintf(outfile, "%d\n", holes); if (holes > 0) { for (holenumber = 0; holenumber < holes; holenumber++) { /* Hole number, x and y coordinates. */ fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber, holelist[2 * holenumber], holelist[2 * holenumber + 1]); } } if (regions > 0) { fprintf(outfile, "%d\n", regions); for (regionnumber = 0; regionnumber < regions; regionnumber++) { /* Region number, x and y coordinates, attribute, maximum area. */ fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n", b->firstnumber + regionnumber, regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1], regionlist[4 * regionnumber + 2], regionlist[4 * regionnumber + 3]); } } #endif /* not CDT_ONLY */ finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } /*****************************************************************************/ /* */ /* writeedges() Write the edges to an .edge file. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writeedges(struct mesh *m, struct behavior *b, int **edgelist, int **edgemarkerlist) #else /* not ANSI_DECLARATORS */ void writeedges(m, b, edgelist, edgemarkerlist) struct mesh *m; struct behavior *b; int **edgelist; int **edgemarkerlist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writeedges(struct mesh *m, struct behavior *b, char *edgefilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writeedges(m, b, edgefilename, argc, argv) struct mesh *m; struct behavior *b; char *edgefilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY int *elist; int *emlist; int index; #else /* not TRILIBRARY */ FILE *outfile; #endif /* not TRILIBRARY */ struct otri triangleloop, trisym; struct osub checkmark; vertex p1, p2; long edgenumber; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ #ifdef TRILIBRARY if (!b->quiet) { printf("Writing edges.\n"); } /* Allocate memory for edges if necessary. */ if (*edgelist == (int *) NULL) { *edgelist = (int *) trimalloc(m->edges * 2 * sizeof(int)); } /* Allocate memory for edge markers if necessary. */ if (!b->nobound && (*edgemarkerlist == (int *) NULL)) { *edgemarkerlist = (int *) trimalloc(m->edges * sizeof(int)); } elist = *edgelist; emlist = *edgemarkerlist; index = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", edgefilename); } outfile = fopen(edgefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", edgefilename); exit(1); } /* Number of edges, number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound); #endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); edgenumber = b->firstnumber; /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { org(triangleloop, p1); dest(triangleloop, p2); #ifdef TRILIBRARY elist[index++] = vertexmark(p1); elist[index++] = vertexmark(p2); #endif /* TRILIBRARY */ if (b->nobound) { #ifndef TRILIBRARY /* Edge number, indices of two endpoints. */ fprintf(outfile, "%4ld %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2)); #endif /* not TRILIBRARY */ } else { /* Edge number, indices of two endpoints, and a boundary marker. */ /* If there's no subsegment, the boundary marker is zero. */ if (b->usesegments) { tspivot(triangleloop, checkmark); if (checkmark.ss == m->dummysub) { #ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = 0; #else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), 0); #endif /* not TRILIBRARY */ } else { #ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = mark(checkmark); #else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), mark(checkmark)); #endif /* not TRILIBRARY */ } } else { #ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri; #else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri); #endif /* not TRILIBRARY */ } } edgenumber++; } } triangleloop.tri = triangletraverse(m); } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } /*****************************************************************************/ /* */ /* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */ /* file. */ /* */ /* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */ /* Hence, the Voronoi vertices are listed by traversing the Delaunay */ /* triangles, and the Voronoi edges are listed by traversing the Delaunay */ /* edges. */ /* */ /* WARNING: In order to assign numbers to the Voronoi vertices, this */ /* procedure messes up the subsegments or the extra nodes of every */ /* element. Hence, you should call this procedure last. */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist, REAL **vpointattriblist, int **vpointmarkerlist, int **vedgelist, int **vedgemarkerlist, REAL **vnormlist) #else /* not ANSI_DECLARATORS */ void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist, vedgelist, vedgemarkerlist, vnormlist) struct mesh *m; struct behavior *b; REAL **vpointlist; REAL **vpointattriblist; int **vpointmarkerlist; int **vedgelist; int **vedgemarkerlist; REAL **vnormlist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename, char *vedgefilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv) struct mesh *m; struct behavior *b; char *vnodefilename; char *vedgefilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY REAL *plist; REAL *palist; int *elist; REAL *normlist; int coordindex; int attribindex; #else /* not TRILIBRARY */ FILE *outfile; #endif /* not TRILIBRARY */ struct otri triangleloop, trisym; vertex torg, tdest, tapex; REAL circumcenter[2]; REAL xi, eta; REAL dum; long vnodenumber, vedgenumber; int p1, p2; int i; triangle ptr; /* Temporary variable used by sym(). */ #ifdef TRILIBRARY if (!b->quiet) { printf("Writing Voronoi vertices.\n"); } /* Allocate memory for Voronoi vertices if necessary. */ if (*vpointlist == (REAL *) NULL) { *vpointlist = (REAL *) trimalloc(m->triangles.items * 2 * sizeof(REAL)); } /* Allocate memory for Voronoi vertex attributes if necessary. */ if (*vpointattriblist == (REAL *) NULL) { *vpointattriblist = (REAL *) trimalloc(m->triangles.items * m->nextras * sizeof(REAL)); } *vpointmarkerlist = (int *) NULL; plist = *vpointlist; palist = *vpointattriblist; coordindex = 0; attribindex = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", vnodefilename); } outfile = fopen(vnodefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", vnodefilename); exit(1); } /* Number of triangles, two dimensions, number of vertex attributes, */ /* no markers. */ fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0); #endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; vnodenumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, torg); dest(triangleloop, tdest); apex(triangleloop, tapex); findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, &dum); #ifdef TRILIBRARY /* X and y coordinates. */ plist[coordindex++] = circumcenter[0]; plist[coordindex++] = circumcenter[1]; for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) + eta * (tapex[i] - torg[i]); } #else /* not TRILIBRARY */ /* Voronoi vertex number, x and y coordinates. */ fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0], circumcenter[1]); for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) + eta * (tapex[i] - torg[i])); } fprintf(outfile, "\n"); #endif /* not TRILIBRARY */ * (int *) (triangleloop.tri + 6) = (int) vnodenumber; triangleloop.tri = triangletraverse(m); vnodenumber++; } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ #ifdef TRILIBRARY if (!b->quiet) { printf("Writing Voronoi edges.\n"); } /* Allocate memory for output Voronoi edges if necessary. */ if (*vedgelist == (int *) NULL) { *vedgelist = (int *) trimalloc(m->edges * 2 * sizeof(int)); } *vedgemarkerlist = (int *) NULL; /* Allocate memory for output Voronoi norms if necessary. */ if (*vnormlist == (REAL *) NULL) { *vnormlist = (REAL *) trimalloc(m->edges * 2 * sizeof(REAL)); } elist = *vedgelist; normlist = *vnormlist; coordindex = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", vedgefilename); } outfile = fopen(vedgefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", vedgefilename); exit(1); } /* Number of edges, zero boundary markers. */ fprintf(outfile, "%ld %d\n", m->edges, 0); #endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); vedgenumber = b->firstnumber; /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { /* Find the number of this triangle (and Voronoi vertex). */ p1 = * (int *) (triangleloop.tri + 6); if (trisym.tri == m->dummytri) { org(triangleloop, torg); dest(triangleloop, tdest); #ifdef TRILIBRARY /* Copy an infinite ray. Index of one endpoint, and -1. */ elist[coordindex] = p1; normlist[coordindex++] = tdest[1] - torg[1]; elist[coordindex] = -1; normlist[coordindex++] = torg[0] - tdest[0]; #else /* not TRILIBRARY */ /* Write an infinite ray. Edge number, index of one endpoint, -1, */ /* and x and y coordinates of a vector representing the */ /* direction of the ray. */ fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber, p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]); #endif /* not TRILIBRARY */ } else { /* Find the number of the adjacent triangle (and Voronoi vertex). */ p2 = * (int *) (trisym.tri + 6); /* Finite edge. Write indices of two endpoints. */ #ifdef TRILIBRARY elist[coordindex] = p1; normlist[coordindex++] = 0.0; elist[coordindex] = p2; normlist[coordindex++] = 0.0; #else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2); #endif /* not TRILIBRARY */ } vedgenumber++; } } triangleloop.tri = triangletraverse(m); } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist) #else /* not ANSI_DECLARATORS */ void writeneighbors(m, b, neighborlist) struct mesh *m; struct behavior *b; int **neighborlist; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writeneighbors(m, b, neighborfilename, argc, argv) struct mesh *m; struct behavior *b; char *neighborfilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { #ifdef TRILIBRARY int *nlist; int index; #else /* not TRILIBRARY */ FILE *outfile; #endif /* not TRILIBRARY */ struct otri triangleloop, trisym; long elementnumber; int neighbor1, neighbor2, neighbor3; triangle ptr; /* Temporary variable used by sym(). */ #ifdef TRILIBRARY if (!b->quiet) { printf("Writing neighbors.\n"); } /* Allocate memory for neighbors if necessary. */ if (*neighborlist == (int *) NULL) { *neighborlist = (int *) trimalloc(m->triangles.items * 3 * sizeof(int)); } nlist = *neighborlist; index = 0; #else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", neighborfilename); } outfile = fopen(neighborfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", neighborfilename); exit(1); } /* Number of triangles, three neighbors per triangle. */ fprintf(outfile, "%ld %d\n", m->triangles.items, 3); #endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { * (int *) (triangleloop.tri + 6) = (int) elementnumber; triangleloop.tri = triangletraverse(m); elementnumber++; } * (int *) (m->dummytri + 6) = -1; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { triangleloop.orient = 1; sym(triangleloop, trisym); neighbor1 = * (int *) (trisym.tri + 6); triangleloop.orient = 2; sym(triangleloop, trisym); neighbor2 = * (int *) (trisym.tri + 6); triangleloop.orient = 0; sym(triangleloop, trisym); neighbor3 = * (int *) (trisym.tri + 6); #ifdef TRILIBRARY nlist[index++] = neighbor1; nlist[index++] = neighbor2; nlist[index++] = neighbor3; #else /* not TRILIBRARY */ /* Triangle number, neighboring triangle numbers. */ fprintf(outfile, "%4ld %d %d %d\n", elementnumber, neighbor1, neighbor2, neighbor3); #endif /* not TRILIBRARY */ triangleloop.tri = triangletraverse(m); elementnumber++; } #ifndef TRILIBRARY finishfile(outfile, argc, argv); #endif /* not TRILIBRARY */ } /*****************************************************************************/ /* */ /* writeoff() Write the triangulation to an .off file. */ /* */ /* OFF stands for the Object File Format, a format used by the Geometry */ /* Center's Geomview package. */ /* */ /*****************************************************************************/ #ifndef TRILIBRARY #ifdef ANSI_DECLARATORS void writeoff(struct mesh *m, struct behavior *b, char *offfilename, int argc, char **argv) #else /* not ANSI_DECLARATORS */ void writeoff(m, b, offfilename, argc, argv) struct mesh *m; struct behavior *b; char *offfilename; int argc; char **argv; #endif /* not ANSI_DECLARATORS */ { FILE *outfile; struct otri triangleloop; vertex vertexloop; vertex p1, p2, p3; long outvertices; if (!b->quiet) { printf("Writing %s.\n", offfilename); } if (b->jettison) { outvertices = m->vertices.items - m->undeads; } else { outvertices = m->vertices.items; } outfile = fopen(offfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", offfilename); exit(1); } /* Number of vertices, triangles, and edges. */ fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items, m->edges); /* Write the vertices. */ traversalinit(&m->vertices); vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { /* The "0.0" is here because the OFF format uses 3D coordinates. */ fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1], 0.0); } vertexloop = vertextraverse(m); } /* Write the triangles. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p1); dest(triangleloop, p2); apex(triangleloop, p3); /* The "3" means a three-vertex polygon. */ fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - 1, vertexmark(p2) - 1, vertexmark(p3) - 1); triangleloop.tri = triangletraverse(m); } finishfile(outfile, argc, argv); } #endif /* not TRILIBRARY */ /** **/ /** **/ /********* File I/O routines end here *********/ /*****************************************************************************/ /* */ /* quality_statistics() Print statistics about the quality of the mesh. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void quality_statistics(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void quality_statistics(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { struct otri triangleloop; vertex p[3]; REAL cossquaretable[8]; REAL ratiotable[16]; REAL dx[3], dy[3]; REAL edgelength[3]; REAL dotproduct; REAL cossquare; REAL triarea; REAL shortest, longest; REAL trilongest2; REAL smallestarea, biggestarea; REAL triminaltitude2; REAL minaltitude; REAL triaspect2; REAL worstaspect; REAL smallestangle, biggestangle; REAL radconst, degconst; int angletable[18]; int aspecttable[16]; int aspectindex; int tendegree; int acutebiggest; int i, ii, j, k; printf("Mesh quality statistics:\n\n"); radconst = PI / 18.0; degconst = 180.0 / PI; for (i = 0; i < 8; i++) { cossquaretable[i] = cos(radconst * (REAL) (i + 1)); cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; } for (i = 0; i < 18; i++) { angletable[i] = 0; } ratiotable[0] = 1.5; ratiotable[1] = 2.0; ratiotable[2] = 2.5; ratiotable[3] = 3.0; ratiotable[4] = 4.0; ratiotable[5] = 6.0; ratiotable[6] = 10.0; ratiotable[7] = 15.0; ratiotable[8] = 25.0; ratiotable[9] = 50.0; ratiotable[10] = 100.0; ratiotable[11] = 300.0; ratiotable[12] = 1000.0; ratiotable[13] = 10000.0; ratiotable[14] = 100000.0; ratiotable[15] = 0.0; for (i = 0; i < 16; i++) { aspecttable[i] = 0; } worstaspect = 0.0; minaltitude = m->xmax - m->xmin + m->ymax - m->ymin; minaltitude = minaltitude * minaltitude; shortest = minaltitude; longest = 0.0; smallestarea = minaltitude; biggestarea = 0.0; worstaspect = 0.0; smallestangle = 0.0; biggestangle = 2.0; acutebiggest = 1; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p[0]); dest(triangleloop, p[1]); apex(triangleloop, p[2]); trilongest2 = 0.0; for (i = 0; i < 3; i++) { j = plus1mod3[i]; k = minus1mod3[i]; dx[i] = p[j][0] - p[k][0]; dy[i] = p[j][1] - p[k][1]; edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; if (edgelength[i] > trilongest2) { trilongest2 = edgelength[i]; } if (edgelength[i] > longest) { longest = edgelength[i]; } if (edgelength[i] < shortest) { shortest = edgelength[i]; } } triarea = counterclockwise(m, b, p[0], p[1], p[2]); if (triarea < smallestarea) { smallestarea = triarea; } if (triarea > biggestarea) { biggestarea = triarea; } triminaltitude2 = triarea * triarea / trilongest2; if (triminaltitude2 < minaltitude) { minaltitude = triminaltitude2; } triaspect2 = trilongest2 / triminaltitude2; if (triaspect2 > worstaspect) { worstaspect = triaspect2; } aspectindex = 0; while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) && (aspectindex < 15)) { aspectindex++; } aspecttable[aspectindex]++; for (i = 0; i < 3; i++) { j = plus1mod3[i]; k = minus1mod3[i]; dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); tendegree = 8; for (ii = 7; ii >= 0; ii--) { if (cossquare > cossquaretable[ii]) { tendegree = ii; } } if (dotproduct <= 0.0) { angletable[tendegree]++; if (cossquare > smallestangle) { smallestangle = cossquare; } if (acutebiggest && (cossquare < biggestangle)) { biggestangle = cossquare; } } else { angletable[17 - tendegree]++; if (acutebiggest || (cossquare > biggestangle)) { biggestangle = cossquare; acutebiggest = 0; } } } triangleloop.tri = triangletraverse(m); } shortest = sqrt(shortest); longest = sqrt(longest); minaltitude = sqrt(minaltitude); worstaspect = sqrt(worstaspect); smallestarea *= 0.5; biggestarea *= 0.5; if (smallestangle >= 1.0) { smallestangle = 0.0; } else { smallestangle = degconst * acos(sqrt(smallestangle)); } if (biggestangle >= 1.0) { biggestangle = 180.0; } else { if (acutebiggest) { biggestangle = degconst * acos(sqrt(biggestangle)); } else { biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); } } printf(" Smallest area: %16.5g | Largest area: %16.5g\n", smallestarea, biggestarea); printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", shortest, longest); printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", minaltitude, worstaspect); printf(" Triangle aspect ratio histogram:\n"); printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], aspecttable[8]); for (i = 1; i < 7; i++) { printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", ratiotable[i - 1], ratiotable[i], aspecttable[i], ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); } printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], aspecttable[15]); printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n"); printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", smallestangle, biggestangle); printf(" Angle histogram:\n"); for (i = 0; i < 9; i++) { printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", i * 10, i * 10 + 10, angletable[i], i * 10 + 90, i * 10 + 100, angletable[i + 9]); } printf("\n"); } /*****************************************************************************/ /* */ /* statistics() Print all sorts of cool facts. */ /* */ /*****************************************************************************/ #ifdef ANSI_DECLARATORS void statistics(struct mesh *m, struct behavior *b) #else /* not ANSI_DECLARATORS */ void statistics(m, b) struct mesh *m; struct behavior *b; #endif /* not ANSI_DECLARATORS */ { printf("\nStatistics:\n\n"); printf(" Input vertices: %d\n", m->invertices); if (b->refine) { printf(" Input triangles: %d\n", m->inelements); } if (b->poly) { printf(" Input segments: %d\n", m->insegments); if (!b->refine) { printf(" Input holes: %d\n", m->holes); } } printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads); printf(" Mesh triangles: %ld\n", m->triangles.items); printf(" Mesh edges: %ld\n", m->edges); printf(" Mesh exterior boundary edges: %ld\n", m->hullsize); if (b->poly || b->refine) { printf(" Mesh interior boundary edges: %ld\n", m->subsegs.items - m->hullsize); printf(" Mesh subsegments (constrained edges): %ld\n", m->subsegs.items); } printf("\n"); if (b->verbose) { quality_statistics(m, b); printf("Memory allocation statistics:\n\n"); printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems); printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems); if (m->subsegs.maxitems > 0) { printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems); } if (m->viri.maxitems > 0) { printf(" Maximum number of viri: %ld\n", m->viri.maxitems); } if (m->badsubsegs.maxitems > 0) { printf(" Maximum number of encroached subsegments: %ld\n", m->badsubsegs.maxitems); } if (m->badtriangles.maxitems > 0) { printf(" Maximum number of bad triangles: %ld\n", m->badtriangles.maxitems); } if (m->flipstackers.maxitems > 0) { printf(" Maximum number of stacked triangle flips: %ld\n", m->flipstackers.maxitems); } if (m->splaynodes.maxitems > 0) { printf(" Maximum number of splay tree nodes: %ld\n", m->splaynodes.maxitems); } printf(" Approximate heap memory use (bytes): %ld\n\n", m->vertices.maxitems * m->vertices.itembytes + m->triangles.maxitems * m->triangles.itembytes + m->subsegs.maxitems * m->subsegs.itembytes + m->viri.maxitems * m->viri.itembytes + m->badsubsegs.maxitems * m->badsubsegs.itembytes + m->badtriangles.maxitems * m->badtriangles.itembytes + m->flipstackers.maxitems * m->flipstackers.itembytes + m->splaynodes.maxitems * m->splaynodes.itembytes); printf("Algorithmic statistics:\n\n"); if (!b->weighted) { printf(" Number of incircle tests: %ld\n", m->incirclecount); } else { printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount); } printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount); if (m->hyperbolacount > 0) { printf(" Number of right-of-hyperbola tests: %ld\n", m->hyperbolacount); } if (m->circletopcount > 0) { printf(" Number of circle top computations: %ld\n", m->circletopcount); } if (m->circumcentercount > 0) { printf(" Number of triangle circumcenter computations: %ld\n", m->circumcentercount); } printf("\n"); } } /*****************************************************************************/ /* */ /* main() or triangulate() Gosh, do everything. */ /* */ /* The sequence is roughly as follows. Many of these steps can be skipped, */ /* depending on the command line switches. */ /* */ /* - Initialize constants and parse the command line. */ /* - Read the vertices from a file and either */ /* - triangulate them (no -r), or */ /* - read an old mesh from files and reconstruct it (-r). */ /* - Insert the PSLG segments (-p), and possibly segments on the convex */ /* hull (-c). */ /* - Read the holes (-p), regional attributes (-pA), and regional area */ /* constraints (-pa). Carve the holes and concavities, and spread the */ /* regional attributes and area constraints. */ /* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */ /* Also enforce the conforming Delaunay property (-q and -a). */ /* - Compute the number of edges in the resulting mesh. */ /* - Promote the mesh's linear triangles to higher order elements (-o). */ /* - Write the output files and print the statistics. */ /* - Check the consistency and Delaunay property of the mesh (-C). */ /* */ /*****************************************************************************/ #ifdef TRILIBRARY #ifdef ANSI_DECLARATORS void triangulate(char *triswitches, struct triangulateio *in, struct triangulateio *out, struct triangulateio *vorout) #else /* not ANSI_DECLARATORS */ void triangulate(triswitches, in, out, vorout) char *triswitches; struct triangulateio *in; struct triangulateio *out; struct triangulateio *vorout; #endif /* not ANSI_DECLARATORS */ #else /* not TRILIBRARY */ #ifdef ANSI_DECLARATORS int main(int argc, char **argv) #else /* not ANSI_DECLARATORS */ int main(argc, argv) int argc; char **argv; #endif /* not ANSI_DECLARATORS */ #endif /* not TRILIBRARY */ { struct mesh m; struct behavior b; REAL *holearray; /* Array of holes. */ REAL *regionarray; /* Array of regional attributes and area constraints. */ #ifndef TRILIBRARY FILE *polyfile; #endif /* not TRILIBRARY */ #ifndef NO_TIMER /* Variables for timing the performance of Triangle. The types are */ /* defined in sys/time.h. */ struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; struct timezone tz; #endif /* not NO_TIMER */ #ifndef NO_TIMER gettimeofday(&tv0, &tz); #endif /* not NO_TIMER */ triangleinit(&m); #ifdef TRILIBRARY parsecommandline(1, &triswitches, &b); #else /* not TRILIBRARY */ parsecommandline(argc, argv, &b); #endif /* not TRILIBRARY */ m.steinerleft = b.steiner; #ifdef TRILIBRARY transfernodes(&m, &b, in->pointlist, in->pointattributelist, in->pointmarkerlist, in->numberofpoints, in->numberofpointattributes); #else /* not TRILIBRARY */ readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile); #endif /* not TRILIBRARY */ #ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv1, &tz); } #endif /* not NO_TIMER */ #ifdef CDT_ONLY m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ #else /* not CDT_ONLY */ if (b.refine) { /* Read and reconstruct a mesh. */ #ifdef TRILIBRARY m.hullsize = reconstruct(&m, &b, in->trianglelist, in->triangleattributelist, in->trianglearealist, in->numberoftriangles, in->numberofcorners, in->numberoftriangleattributes, in->segmentlist, in->segmentmarkerlist, in->numberofsegments); #else /* not TRILIBRARY */ m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename, b.inpolyfilename, polyfile); #endif /* not TRILIBRARY */ } else { m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ } #endif /* not CDT_ONLY */ #ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv2, &tz); if (b.refine) { printf("Mesh reconstruction"); } else { printf("Delaunay"); } printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + (tv2.tv_usec - tv1.tv_usec) / 1000l); } #endif /* not NO_TIMER */ /* Ensure that no vertex can be mistaken for a triangular bounding */ /* box vertex in insertvertex(). */ m.infvertex1 = (vertex) NULL; m.infvertex2 = (vertex) NULL; m.infvertex3 = (vertex) NULL; if (b.usesegments) { m.checksegments = 1; /* Segments will be introduced next. */ if (!b.refine) { /* Insert PSLG segments and/or convex hull segments. */ #ifdef TRILIBRARY formskeleton(&m, &b, in->segmentlist, in->segmentmarkerlist, in->numberofsegments); #else /* not TRILIBRARY */ formskeleton(&m, &b, polyfile, b.inpolyfilename); #endif /* not TRILIBRARY */ } } #ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv3, &tz); if (b.usesegments && !b.refine) { printf("Segment milliseconds: %ld\n", 1000l * (tv3.tv_sec - tv2.tv_sec) + (tv3.tv_usec - tv2.tv_usec) / 1000l); } } #endif /* not NO_TIMER */ if (b.poly && (m.triangles.items > 0)) { #ifdef TRILIBRARY holearray = in->holelist; m.holes = in->numberofholes; regionarray = in->regionlist; m.regions = in->numberofregions; #else /* not TRILIBRARY */ readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes, ®ionarray, &m.regions); #endif /* not TRILIBRARY */ if (!b.refine) { /* Carve out holes and concavities. */ carveholes(&m, &b, holearray, m.holes, regionarray, m.regions); } } else { /* Without a PSLG, there can be no holes or regional attributes */ /* or area constraints. The following are set to zero to avoid */ /* an accidental free() later. */ m.holes = 0; m.regions = 0; } #ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv4, &tz); if (b.poly && !b.refine) { printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + (tv4.tv_usec - tv3.tv_usec) / 1000l); } } #endif /* not NO_TIMER */ #ifndef CDT_ONLY if (b.quality && (m.triangles.items > 0)) { enforcequality(&m, &b); /* Enforce angle and area constraints. */ } #endif /* not CDT_ONLY */ #ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv5, &tz); #ifndef CDT_ONLY if (b.quality) { printf("Quality milliseconds: %ld\n", 1000l * (tv5.tv_sec - tv4.tv_sec) + (tv5.tv_usec - tv4.tv_usec) / 1000l); } #endif /* not CDT_ONLY */ } #endif /* not NO_TIMER */ /* Calculate the number of edges. */ m.edges = (3l * m.triangles.items + m.hullsize) / 2l; if (b.order > 1) { highorder(&m, &b); /* Promote elements to higher polynomial order. */ } if (!b.quiet) { printf("\n"); } #ifdef TRILIBRARY out->numberofpoints = m.vertices.items; out->numberofpointattributes = m.nextras; out->numberoftriangles = m.triangles.items; out->numberofcorners = (b.order + 1) * (b.order + 2) / 2; out->numberoftriangleattributes = m.eextras; out->numberofedges = m.edges; if (b.usesegments) { out->numberofsegments = m.subsegs.items; } else { out->numberofsegments = m.hullsize; } if (vorout != (struct triangulateio *) NULL) { vorout->numberofpoints = m.triangles.items; vorout->numberofpointattributes = m.nextras; vorout->numberofedges = m.edges; } #endif /* TRILIBRARY */ /* If not using iteration numbers, don't write a .node file if one was */ /* read, because the original one would be overwritten! */ if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) { if (!b.quiet) { #ifdef TRILIBRARY printf("NOT writing vertices.\n"); #else /* not TRILIBRARY */ printf("NOT writing a .node file.\n"); #endif /* not TRILIBRARY */ } numbernodes(&m, &b); /* We must remember to number the vertices. */ } else { /* writenodes() numbers the vertices too. */ #ifdef TRILIBRARY writenodes(&m, &b, &out->pointlist, &out->pointattributelist, &out->pointmarkerlist); #else /* not TRILIBRARY */ writenodes(&m, &b, b.outnodefilename, argc, argv); #endif /* TRILIBRARY */ } if (b.noelewritten) { if (!b.quiet) { #ifdef TRILIBRARY printf("NOT writing triangles.\n"); #else /* not TRILIBRARY */ printf("NOT writing an .ele file.\n"); #endif /* not TRILIBRARY */ } } else { #ifdef TRILIBRARY writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist); #else /* not TRILIBRARY */ writeelements(&m, &b, b.outelefilename, argc, argv); #endif /* not TRILIBRARY */ } /* The -c switch (convex switch) causes a PSLG to be written */ /* even if none was read. */ if (b.poly || b.convex) { /* If not using iteration numbers, don't overwrite the .poly file. */ if (b.nopolywritten || b.noiterationnum) { if (!b.quiet) { #ifdef TRILIBRARY printf("NOT writing segments.\n"); #else /* not TRILIBRARY */ printf("NOT writing a .poly file.\n"); #endif /* not TRILIBRARY */ } } else { #ifdef TRILIBRARY writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist); out->numberofholes = m.holes; out->numberofregions = m.regions; if (b.poly) { out->holelist = in->holelist; out->regionlist = in->regionlist; } else { out->holelist = (REAL *) NULL; out->regionlist = (REAL *) NULL; } #else /* not TRILIBRARY */ writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray, m.regions, argc, argv); #endif /* not TRILIBRARY */ } } #ifndef TRILIBRARY #ifndef CDT_ONLY if (m.regions > 0) { trifree((VOID *) regionarray); } #endif /* not CDT_ONLY */ if (m.holes > 0) { trifree((VOID *) holearray); } if (b.geomview) { writeoff(&m, &b, b.offfilename, argc, argv); } #endif /* not TRILIBRARY */ if (b.edgesout) { #ifdef TRILIBRARY writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist); #else /* not TRILIBRARY */ writeedges(&m, &b, b.edgefilename, argc, argv); #endif /* not TRILIBRARY */ } if (b.voronoi) { #ifdef TRILIBRARY writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist, &vorout->pointmarkerlist, &vorout->edgelist, &vorout->edgemarkerlist, &vorout->normlist); #else /* not TRILIBRARY */ writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv); #endif /* not TRILIBRARY */ } if (b.neighbors) { #ifdef TRILIBRARY writeneighbors(&m, &b, &out->neighborlist); #else /* not TRILIBRARY */ writeneighbors(&m, &b, b.neighborfilename, argc, argv); #endif /* not TRILIBRARY */ } if (!b.quiet) { #ifndef NO_TIMER gettimeofday(&tv6, &tz); printf("\nOutput milliseconds: %ld\n", 1000l * (tv6.tv_sec - tv5.tv_sec) + (tv6.tv_usec - tv5.tv_usec) / 1000l); printf("Total running milliseconds: %ld\n", 1000l * (tv6.tv_sec - tv0.tv_sec) + (tv6.tv_usec - tv0.tv_usec) / 1000l); #endif /* not NO_TIMER */ statistics(&m, &b); } #ifndef REDUCED if (b.docheck) { checkmesh(&m, &b); checkdelaunay(&m, &b); } #endif /* not REDUCED */ triangledeinit(&m, &b); #ifndef TRILIBRARY return 0; #endif /* not TRILIBRARY */ } pyangle-0.90/src/triangle.h0000644000175000001440000005265210135233704015430 0ustar akusers00000000000000#ifndef __TRIANGLE_H #define __TRIANGLE_H #ifdef __cplusplus extern "C" { #endif /*****************************************************************************/ /* */ /* (triangle.h) */ /* */ /* Include file for programs that call Triangle. */ /* */ /* Accompanies Triangle Versions 1.3 and 1.4 */ /* July 19, 1996 */ /* */ /* Copyright 1996 */ /* Jonathan Richard Shewchuk */ /* 2360 Woolsey #H */ /* Berkeley, California 94705-1927 */ /* jrs@cs.berkeley.edu */ /* */ /*****************************************************************************/ /*****************************************************************************/ /* */ /* How to call Triangle from another program */ /* */ /* */ /* If you haven't read Triangle's instructions (run "triangle -h" to read */ /* them), you won't understand what follows. */ /* */ /* Triangle must be compiled into an object file (triangle.o) with the */ /* TRILIBRARY symbol defined (preferably by using the -DTRILIBRARY compiler */ /* switch). The makefile included with Triangle will do this for you if */ /* you run "make trilibrary". The resulting object file can be called via */ /* the procedure triangulate(). */ /* */ /* If the size of the object file is important to you, you may wish to */ /* generate a reduced version of triangle.o. The REDUCED symbol gets rid */ /* of all features that are primarily of research interest. Specifically, */ /* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */ /* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */ /* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */ /* eliminates Triangle's -r, -q, -a, -S, and -s switches. */ /* */ /* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */ /* made in the makefile or in triangle.c itself. Putting these definitions */ /* in this file will not create the desired effect. */ /* */ /* */ /* The calling convention for triangulate() follows. */ /* */ /* void triangulate(triswitches, in, out, vorout) */ /* char *triswitches; */ /* struct triangulateio *in; */ /* struct triangulateio *out; */ /* struct triangulateio *vorout; */ /* */ /* `triswitches' is a string containing the command line switches you wish */ /* to invoke. No initial dash is required. Some suggestions: */ /* */ /* - You'll probably find it convenient to use the `z' switch so that */ /* points (and other items) are numbered from zero. This simplifies */ /* indexing, because the first item of any type always starts at index */ /* [0] of the corresponding array, whether that item's number is zero or */ /* one. */ /* - You'll probably want to use the `Q' (quiet) switch in your final code, */ /* but you can take advantage of Triangle's printed output (including the */ /* `V' switch) while debugging. */ /* - If you are not using the `q' or `a' switches, then the output points */ /* will be identical to the input points, except possibly for the */ /* boundary markers. If you don't need the boundary markers, you should */ /* use the `N' (no nodes output) switch to save memory. (If you do need */ /* boundary markers, but need to save memory, a good nasty trick is to */ /* set out->pointlist equal to in->pointlist before calling triangulate(),*/ /* so that Triangle overwrites the input points with identical copies.) */ /* - The `I' (no iteration numbers) and `g' (.off file output) switches */ /* have no effect when Triangle is compiled with TRILIBRARY defined. */ /* */ /* `in', `out', and `vorout' are descriptions of the input, the output, */ /* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */ /* `vorout' may be NULL. `in' and `out' may never be NULL. */ /* */ /* Certain fields of the input and output structures must be initialized, */ /* as described below. */ /* */ /*****************************************************************************/ /*****************************************************************************/ /* */ /* The `triangulateio' structure. */ /* */ /* Used to pass data into and out of the triangulate() procedure. */ /* */ /* */ /* Arrays are used to store points, triangles, markers, and so forth. In */ /* all cases, the first item in any array is stored starting at index [0]. */ /* However, that item is item number `1' unless the `z' switch is used, in */ /* which case it is item number `0'. Hence, you may find it easier to */ /* index points (and triangles in the neighbor list) if you use the `z' */ /* switch. Unless, of course, you're calling Triangle from a Fortran */ /* program. */ /* */ /* Description of fields (except the `numberof' fields, which are obvious): */ /* */ /* `pointlist': An array of point coordinates. The first point's x */ /* coordinate is at index [0] and its y coordinate at index [1], followed */ /* by the coordinates of the remaining points. Each point occupies two */ /* REALs. */ /* `pointattributelist': An array of point attributes. Each point's */ /* attributes occupy `numberofpointattributes' REALs. */ /* `pointmarkerlist': An array of point markers; one int per point. */ /* */ /* `trianglelist': An array of triangle corners. The first triangle's */ /* first corner is at index [0], followed by its other two corners in */ /* counterclockwise order, followed by any other nodes if the triangle */ /* represents a nonlinear element. Each triangle occupies */ /* `numberofcorners' ints. */ /* `triangleattributelist': An array of triangle attributes. Each */ /* triangle's attributes occupy `numberoftriangleattributes' REALs. */ /* `trianglearealist': An array of triangle area constraints; one REAL per */ /* triangle. Input only. */ /* `neighborlist': An array of triangle neighbors; three ints per */ /* triangle. Output only. */ /* */ /* `segmentlist': An array of segment endpoints. The first segment's */ /* endpoints are at indices [0] and [1], followed by the remaining */ /* segments. Two ints per segment. */ /* `segmentmarkerlist': An array of segment markers; one int per segment. */ /* */ /* `holelist': An array of holes. The first hole's x and y coordinates */ /* are at indices [0] and [1], followed by the remaining holes. Two */ /* REALs per hole. Input only, although the pointer is copied to the */ /* output structure for your convenience. */ /* */ /* `regionlist': An array of regional attributes and area constraints. */ /* The first constraint's x and y coordinates are at indices [0] and [1], */ /* followed by the regional attribute and index [2], followed by the */ /* maximum area at index [3], followed by the remaining area constraints. */ /* Four REALs per area constraint. Note that each regional attribute is */ /* used only if you select the `A' switch, and each area constraint is */ /* used only if you select the `a' switch (with no number following), but */ /* omitting one of these switches does not change the memory layout. */ /* Input only, although the pointer is copied to the output structure for */ /* your convenience. */ /* */ /* `edgelist': An array of edge endpoints. The first edge's endpoints are */ /* at indices [0] and [1], followed by the remaining edges. Two ints per */ /* edge. Output only. */ /* `edgemarkerlist': An array of edge markers; one int per edge. Output */ /* only. */ /* `normlist': An array of normal vectors, used for infinite rays in */ /* Voronoi diagrams. The first normal vector's x and y magnitudes are */ /* at indices [0] and [1], followed by the remaining vectors. For each */ /* finite edge in a Voronoi diagram, the normal vector written is the */ /* zero vector. Two REALs per edge. Output only. */ /* */ /* */ /* Any input fields that Triangle will examine must be initialized. */ /* Furthermore, for each output array that Triangle will write to, you */ /* must either provide space by setting the appropriate pointer to point */ /* to the space you want the data written to, or you must initialize the */ /* pointer to NULL, which tells Triangle to allocate space for the results. */ /* The latter option is preferable, because Triangle always knows exactly */ /* how much space to allocate. The former option is provided mainly for */ /* people who need to call Triangle from Fortran code, though it also makes */ /* possible some nasty space-saving tricks, like writing the output to the */ /* same arrays as the input. */ /* */ /* Triangle will not free() any input or output arrays, including those it */ /* allocates itself; that's up to you. */ /* */ /* Here's a guide to help you decide which fields you must initialize */ /* before you call triangulate(). */ /* */ /* `in': */ /* */ /* - `pointlist' must always point to a list of points; `numberofpoints' */ /* and `numberofpointattributes' must be properly set. */ /* `pointmarkerlist' must either be set to NULL (in which case all */ /* markers default to zero), or must point to a list of markers. If */ /* `numberofpointattributes' is not zero, `pointattributelist' must */ /* point to a list of point attributes. */ /* - If the `r' switch is used, `trianglelist' must point to a list of */ /* triangles, and `numberoftriangles', `numberofcorners', and */ /* `numberoftriangleattributes' must be properly set. If */ /* `numberoftriangleattributes' is not zero, `triangleattributelist' */ /* must point to a list of triangle attributes. If the `a' switch is */ /* used (with no number following), `trianglearealist' must point to a */ /* list of triangle area constraints. `neighborlist' may be ignored. */ /* - If the `p' switch is used, `segmentlist' must point to a list of */ /* segments, `numberofsegments' must be properly set, and */ /* `segmentmarkerlist' must either be set to NULL (in which case all */ /* markers default to zero), or must point to a list of markers. */ /* - If the `p' switch is used without the `r' switch, then */ /* `numberofholes' and `numberofregions' must be properly set. If */ /* `numberofholes' is not zero, `holelist' must point to a list of */ /* holes. If `numberofregions' is not zero, `regionlist' must point to */ /* a list of region constraints. */ /* - If the `p' switch is used, `holelist', `numberofholes', */ /* `regionlist', and `numberofregions' is copied to `out'. (You can */ /* nonetheless get away with not initializing them if the `r' switch is */ /* used.) */ /* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */ /* ignored. */ /* */ /* `out': */ /* */ /* - `pointlist' must be initialized (NULL or pointing to memory) unless */ /* the `N' switch is used. `pointmarkerlist' must be initialized */ /* unless the `N' or `B' switch is used. If `N' is not used and */ /* `in->numberofpointattributes' is not zero, `pointattributelist' must */ /* be initialized. */ /* - `trianglelist' must be initialized unless the `E' switch is used. */ /* `neighborlist' must be initialized if the `n' switch is used. If */ /* the `E' switch is not used and (`in->numberofelementattributes' is */ /* not zero or the `A' switch is used), `elementattributelist' must be */ /* initialized. `trianglearealist' may be ignored. */ /* - `segmentlist' must be initialized if the `p' or `c' switch is used, */ /* and the `P' switch is not used. `segmentmarkerlist' must also be */ /* initialized under these circumstances unless the `B' switch is used. */ /* - `edgelist' must be initialized if the `e' switch is used. */ /* `edgemarkerlist' must be initialized if the `e' switch is used and */ /* the `B' switch is not. */ /* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/ /* */ /* `vorout' (only needed if `v' switch is used): */ /* */ /* - `pointlist' must be initialized. If `in->numberofpointattributes' */ /* is not zero, `pointattributelist' must be initialized. */ /* `pointmarkerlist' may be ignored. */ /* - `edgelist' and `normlist' must both be initialized. */ /* `edgemarkerlist' may be ignored. */ /* - Everything else may be ignored. */ /* */ /* After a call to triangulate(), the valid fields of `out' and `vorout' */ /* will depend, in an obvious way, on the choice of switches used. Note */ /* that when the `p' switch is used, the pointers `holelist' and */ /* `regionlist' are copied from `in' to `out', but no new space is */ /* allocated; be careful that you don't free() the same array twice. On */ /* the other hand, Triangle will never copy the `pointlist' pointer (or any */ /* others); new space is allocated for `out->pointlist', or if the `N' */ /* switch is used, `out->pointlist' remains uninitialized. */ /* */ /* All of the meaningful `numberof' fields will be properly set; for */ /* instance, `numberofedges' will represent the number of edges in the */ /* triangulation whether or not the edges were written. If segments are */ /* not used, `numberofsegments' will indicate the number of boundary edges. */ /* */ /*****************************************************************************/ typedef double REAL; struct triangulateio { REAL *pointlist; /* In / out */ REAL *pointattributelist; /* In / out */ int *pointmarkerlist; /* In / out */ int numberofpoints; /* In / out */ int numberofpointattributes; /* In / out */ int *trianglelist; /* In / out */ REAL *triangleattributelist; /* In / out */ REAL *trianglearealist; /* In only */ int *neighborlist; /* Out only */ int numberoftriangles; /* In / out */ int numberofcorners; /* In / out */ int numberoftriangleattributes; /* In / out */ int *segmentlist; /* In / out */ int *segmentmarkerlist; /* In / out */ int numberofsegments; /* In / out */ REAL *holelist; /* In / pointer to array copied out */ int numberofholes; /* In / copied out */ REAL *regionlist; /* In / pointer to array copied out */ int numberofregions; /* In / copied out */ int *edgelist; /* Out only */ int *edgemarkerlist; /* Not used with Voronoi diagram; out only */ REAL *normlist; /* Used only with Voronoi diagram; out only */ int numberofedges; /* Out only */ }; void triangulate(char *, struct triangulateio *, struct triangulateio *, struct triangulateio *); /* external refinement test */ typedef REAL *vertex; int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area); #ifdef __cplusplus } #endif #endif pyangle-0.90/test/0000755000175000001440000000000010135235533013632 5ustar akusers00000000000000pyangle-0.90/test/test_pyangle.py0000644000175000001440000000213710135233704016703 0ustar akusers00000000000000import pyangle import math import pickle segments = 50 points = [ (1,0),(1,1),(-1,1),(-1,-1),(1,-1),(1,0) ] for i in range( 0, segments + 1 ): angle = i * 2 * math.pi / segments points.append( ( 0.5 * math.cos( angle ), 0.5 * math.sin( angle ) ) ) def roundTripConnect(start, end): result = [] for i in range(start, end): result.append((i, i+1)) result.append((end, start)) return result def needsRefinement( vert_origin, vert_destination, vert_apex, area ): bary_x = ( vert_origin.x() + vert_destination.x() + vert_apex.x() ) / 3 bary_y = ( vert_origin.y() + vert_destination.y() + vert_apex.y() ) / 3 dist_center = math.sqrt( bary_x**2 + bary_y**2 ) max_area = math.fabs( 0.002 * (dist_center-0.5) ) + 0.0001 return area > max_area in_p = pyangle.tTriangulationParameters() pyangle.setPoints(in_p, points) pyangle.setHoles(in_p, [(0,0)]) pyangle.setSegments(in_p, roundTripConnect(0, len(points)-1)) out_p = pyangle.triangulate(in_p, refinement_func = needsRefinement ) pickled = pickle.dumps(out_p) out_p_2 = pickle.loads(pickled) pyangle.writeGnuplotMesh( "+tris.dat", out_p_2 ) pyangle-0.90/README0000644000175000001440000000047610135235403013536 0ustar akusers00000000000000Build steps: 1. Customize setup.py, especially boost_path and library_dirs. 2. Run "python setup.py build". 3. Run "python setup.py install" as root. 4. Go to the test/ subdirectory. 5. Run "python test_pyangle.py". 6. Run "gnuplot". 7. At the "gnuplot>", prompt, type gnuplot> plot "+tris.dat" with lines 8. Done. pyangle-0.90/setup.py0000644000175000001440000000176010135234357014374 0ustar akusers00000000000000#!/usr/bin/env python import os from distutils.core import setup,Extension home = os.getenv("HOME") boost_path = "%s/work/boost" % home include_dirs = [boost_path, "src"] library_dirs = ["%s/pool/lib" % home] libraries = ["boost_python"] define_macros = [ ( "EXTERNAL_TEST", 1 ), ( "ANSI_DECLARATORS", 1 ), ( "TRILIBRARY", 1 ) ] setup(name="pyangle", version="0.90", description="A wrapper around the Triangle 1.4 Mesh generator by Richard Shewchuk", author="Andreas Kloeckner", author_email="inducer@users.sf.net", license = "The Triangle License (~Free if not included in commercial software)", url="http://tiker.net/software/#pyangle", packages = [ "pyangle" ], ext_modules = [ Extension( "pyangle.internals", ["src/pyangle.cpp","src/triangle.c"], include_dirs = include_dirs, library_dirs = library_dirs, libraries = libraries, define_macros = define_macros )] ) pyangle-0.90/PKG-INFO0000644000175000001440000000053710135235533013755 0ustar akusers00000000000000Metadata-Version: 1.0 Name: pyangle Version: 0.90 Summary: A wrapper around the Triangle 1.4 Mesh generator by Richard Shewchuk Home-page: http://tiker.net/software/#pyangle Author: Andreas Kloeckner Author-email: inducer@users.sf.net License: The Triangle License (~Free if not included in commercial software) Description: UNKNOWN Platform: UNKNOWN