src/glu/sgi/libtess/mesh.c

   1 /*
   2  * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
   3  * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
   4  *
   5  * Permission is hereby granted, free of charge, to any person obtaining a
   6  * copy of this software and associated documentation files (the "Software"),
   7  * to deal in the Software without restriction, including without limitation
   8  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
   9  * and/or sell copies of the Software, and to permit persons to whom the
  10  * Software is furnished to do so, subject to the following conditions:
  11  *
  12  * The above copyright notice including the dates of first publication and
  13  * either this permission notice or a reference to
  14  * http://oss.sgi.com/projects/FreeB/
  15  * shall be included in all copies or substantial portions of the Software.
  16  *
  17  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  18  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  19  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  20  * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
  21  * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
  22  * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  23  * SOFTWARE.
  24  *
  25  * Except as contained in this notice, the name of Silicon Graphics, Inc.
  26  * shall not be used in advertising or otherwise to promote the sale, use or
  27  * other dealings in this Software without prior written authorization from
  28  * Silicon Graphics, Inc.
  29  */
  30 /*
  31 ** Author: Eric Veach, July 1994.
  32 **
  33 */
  34
  35 #include "gluos.h"
  36 #include <stddef.h>
  37 #include <assert.h>
  38 #include "mesh.h"
  39 #include "memalloc.h"
  40
  41 #define TRUE 1
  42 #define FALSE 0
  43
  44 static GLUvertex *allocVertex()
  45 {
  46    return (GLUvertex *)memAlloc( sizeof( GLUvertex ));
  47 }
  48
  49 static GLUface *allocFace()
  50 {
  51    return (GLUface *)memAlloc( sizeof( GLUface ));
  52 }
  53
  54 /************************ Utility Routines ************************/
  55
  56 /* Allocate and free half-edges in pairs for efficiency.
  57  * The *only* place that should use this fact is allocation/free.
  58  */
  59 typedef struct { GLUhalfEdge e, eSym; } EdgePair;
  60
  61 /* MakeEdge creates a new pair of half-edges which form their own loop.
  62  * No vertex or face structures are allocated, but these must be assigned
  63  * before the current edge operation is completed.
  64  */
  65 static GLUhalfEdge *MakeEdge( GLUhalfEdge *eNext )
  66 {
  67   GLUhalfEdge *e;
  68   GLUhalfEdge *eSym;
  69   GLUhalfEdge *ePrev;
  70   EdgePair *pair = (EdgePair *)memAlloc( sizeof( EdgePair ));
  71   if (pair == NULL) return NULL;
  72
  73   e = &pair->e;
  74   eSym = &pair->eSym;
  75
  76   /* Make sure eNext points to the first edge of the edge pair */
  77   if( eNext->Sym < eNext ) { eNext = eNext->Sym; }
  78
  79   /* Insert in circular doubly-linked list before eNext.
  80    * Note that the prev pointer is stored in Sym->next.
  81    */
  82   ePrev = eNext->Sym->next;
  83   eSym->next = ePrev;
  84   ePrev->Sym->next = e;
  85   e->next = eNext;
  86   eNext->Sym->next = eSym;
  87
  88   e->Sym = eSym;
  89   e->Onext = e;
  90   e->Lnext = eSym;
  91   e->Org = NULL;
  92   e->Lface = NULL;
  93   e->winding = 0;
  94   e->activeRegion = NULL;
  95
  96   eSym->Sym = e;
  97   eSym->Onext = eSym;
  98   eSym->Lnext = e;
  99   eSym->Org = NULL;
 100   eSym->Lface = NULL;
 101   eSym->winding = 0;
 102   eSym->activeRegion = NULL;
 103
 104   return e;
 105 }
 106
 107 /* Splice( a, b ) is best described by the Guibas/Stolfi paper or the
 108  * CS348a notes (see mesh.h).  Basically it modifies the mesh so that
 109  * a->Onext and b->Onext are exchanged.  This can have various effects
 110  * depending on whether a and b belong to different face or vertex rings.
 111  * For more explanation see __gl_meshSplice() below.
 112  */
 113 static void Splice( GLUhalfEdge *a, GLUhalfEdge *b )
 114 {
 115   GLUhalfEdge *aOnext = a->Onext;
 116   GLUhalfEdge *bOnext = b->Onext;
 117
 118   aOnext->Sym->Lnext = b;
 119   bOnext->Sym->Lnext = a;
 120   a->Onext = bOnext;
 121   b->Onext = aOnext;
 122 }
 123
 124 /* MakeVertex( newVertex, eOrig, vNext ) attaches a new vertex and makes it the
 125  * origin of all edges in the vertex loop to which eOrig belongs. "vNext" gives
 126  * a place to insert the new vertex in the global vertex list.  We insert
 127  * the new vertex *before* vNext so that algorithms which walk the vertex
 128  * list will not see the newly created vertices.
 129  */
 130 static void MakeVertex( GLUvertex *newVertex,
 131                         GLUhalfEdge *eOrig, GLUvertex *vNext )
 132 {
 133   GLUhalfEdge *e;
 134   GLUvertex *vPrev;
 135   GLUvertex *vNew = newVertex;
 136
 137   assert(vNew != NULL);
 138
 139   /* insert in circular doubly-linked list before vNext */
 140   vPrev = vNext->prev;
 141   vNew->prev = vPrev;
 142   vPrev->next = vNew;
 143   vNew->next = vNext;
 144   vNext->prev = vNew;
 145
 146   vNew->anEdge = eOrig;
 147   vNew->data = NULL;
 148   /* leave coords, s, t undefined */
 149
 150   /* fix other edges on this vertex loop */
 151   e = eOrig;
 152   do {
 153     e->Org = vNew;
 154     e = e->Onext;
 155   } while( e != eOrig );
 156 }
 157
 158 /* MakeFace( newFace, eOrig, fNext ) attaches a new face and makes it the left
 159  * face of all edges in the face loop to which eOrig belongs.  "fNext" gives
 160  * a place to insert the new face in the global face list.  We insert
 161  * the new face *before* fNext so that algorithms which walk the face
 162  * list will not see the newly created faces.
 163  */
 164 static void MakeFace( GLUface *newFace, GLUhalfEdge *eOrig, GLUface *fNext )
 165 {
 166   GLUhalfEdge *e;
 167   GLUface *fPrev;
 168   GLUface *fNew = newFace;
 169
 170   assert(fNew != NULL);
 171
 172   /* insert in circular doubly-linked list before fNext */
 173   fPrev = fNext->prev;
 174   fNew->prev = fPrev;
 175   fPrev->next = fNew;
 176   fNew->next = fNext;
 177   fNext->prev = fNew;
 178
 179   fNew->anEdge = eOrig;
 180   fNew->data = NULL;
 181   fNew->trail = NULL;
 182   fNew->marked = FALSE;
 183
 184   /* The new face is marked "inside" if the old one was.  This is a
 185    * convenience for the common case where a face has been split in two.
 186    */
 187   fNew->inside = fNext->inside;
 188
 189   /* fix other edges on this face loop */
 190   e = eOrig;
 191   do {
 192     e->Lface = fNew;
 193     e = e->Lnext;
 194   } while( e != eOrig );
 195 }
 196
 197 /* KillEdge( eDel ) destroys an edge (the half-edges eDel and eDel->Sym),
 198  * and removes from the global edge list.
 199  */
 200 static void KillEdge( GLUhalfEdge *eDel )
 201 {
 202   GLUhalfEdge *ePrev, *eNext;
 203
 204   /* Half-edges are allocated in pairs, see EdgePair above */
 205   if( eDel->Sym < eDel ) { eDel = eDel->Sym; }
 206
 207   /* delete from circular doubly-linked list */
 208   eNext = eDel->next;
 209   ePrev = eDel->Sym->next;
 210   eNext->Sym->next = ePrev;
 211   ePrev->Sym->next = eNext;
 212
 213   memFree( eDel );
 214 }
 215
 216
 217 /* KillVertex( vDel ) destroys a vertex and removes it from the global
 218  * vertex list.  It updates the vertex loop to point to a given new vertex.
 219  */
 220 static void KillVertex( GLUvertex *vDel, GLUvertex *newOrg )
 221 {
 222   GLUhalfEdge *e, *eStart = vDel->anEdge;
 223   GLUvertex *vPrev, *vNext;
 224
 225   /* change the origin of all affected edges */
 226   e = eStart;
 227   do {
 228     e->Org = newOrg;
 229     e = e->Onext;
 230   } while( e != eStart );
 231
 232   /* delete from circular doubly-linked list */
 233   vPrev = vDel->prev;
 234   vNext = vDel->next;
 235   vNext->prev = vPrev;
 236   vPrev->next = vNext;
 237
 238   memFree( vDel );
 239 }
 240
 241 /* KillFace( fDel ) destroys a face and removes it from the global face
 242  * list.  It updates the face loop to point to a given new face.
 243  */
 244 static void KillFace( GLUface *fDel, GLUface *newLface )
 245 {
 246   GLUhalfEdge *e, *eStart = fDel->anEdge;
 247   GLUface *fPrev, *fNext;
 248
 249   /* change the left face of all affected edges */
 250   e = eStart;
 251   do {
 252     e->Lface = newLface;
 253     e = e->Lnext;
 254   } while( e != eStart );
 255
 256   /* delete from circular doubly-linked list */
 257   fPrev = fDel->prev;
 258   fNext = fDel->next;
 259   fNext->prev = fPrev;
 260   fPrev->next = fNext;
 261
 262   memFree( fDel );
 263 }
 264
 265
 266 /****************** Basic Edge Operations **********************/
 267
 268 /* __gl_meshMakeEdge creates one edge, two vertices, and a loop (face).
 269  * The loop consists of the two new half-edges.
 270  */
 271 GLUhalfEdge *__gl_meshMakeEdge( GLUmesh *mesh )
 272 {
 273   GLUvertex *newVertex1= allocVertex();
 274   GLUvertex *newVertex2= allocVertex();
 275   GLUface *newFace= allocFace();
 276   GLUhalfEdge *e;
 277
 278   /* if any one is null then all get freed */
 279   if (newVertex1 == NULL || newVertex2 == NULL || newFace == NULL) {
 280      if (newVertex1 != NULL) memFree(newVertex1);
 281      if (newVertex2 != NULL) memFree(newVertex2);
 282      if (newFace != NULL) memFree(newFace);
 283      return NULL;
 284   }
 285
 286   e = MakeEdge( &mesh->eHead );
 287   if (e == NULL) return NULL;
 288
 289   MakeVertex( newVertex1, e, &mesh->vHead );
 290   MakeVertex( newVertex2, e->Sym, &mesh->vHead );
 291   MakeFace( newFace, e, &mesh->fHead );
 292   return e;
 293 }
 294
 295
 296 /* __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
 297  * mesh connectivity and topology.  It changes the mesh so that
 298  *      eOrg->Onext <- OLD( eDst->Onext )
 299  *      eDst->Onext <- OLD( eOrg->Onext )
 300  * where OLD(...) means the value before the meshSplice operation.
 301  *
 302  * This can have two effects on the vertex structure:
 303  *  - if eOrg->Org != eDst->Org, the two vertices are merged together
 304  *  - if eOrg->Org == eDst->Org, the origin is split into two vertices
 305  * In both cases, eDst->Org is changed and eOrg->Org is untouched.
 306  *
 307  * Similarly (and independently) for the face structure,
 308  *  - if eOrg->Lface == eDst->Lface, one loop is split into two
 309  *  - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
 310  * In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
 311  *
 312  * Some special cases:
 313  * If eDst == eOrg, the operation has no effect.
 314  * If eDst == eOrg->Lnext, the new face will have a single edge.
 315  * If eDst == eOrg->Lprev, the old face will have a single edge.
 316  * If eDst == eOrg->Onext, the new vertex will have a single edge.
 317  * If eDst == eOrg->Oprev, the old vertex will have a single edge.
 318  */
 319 int __gl_meshSplice( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
 320 {
 321   int joiningLoops = FALSE;
 322   int joiningVertices = FALSE;
 323
 324   if( eOrg == eDst ) return 1;
 325
 326   if( eDst->Org != eOrg->Org ) {
 327     /* We are merging two disjoint vertices -- destroy eDst->Org */
 328     joiningVertices = TRUE;
 329     KillVertex( eDst->Org, eOrg->Org );
 330   }
 331   if( eDst->Lface != eOrg->Lface ) {
 332     /* We are connecting two disjoint loops -- destroy eDst->Lface */
 333     joiningLoops = TRUE;
 334     KillFace( eDst->Lface, eOrg->Lface );
 335   }
 336
 337   /* Change the edge structure */
 338   Splice( eDst, eOrg );
 339
 340   if( ! joiningVertices ) {
 341     GLUvertex *newVertex= allocVertex();
 342     if (newVertex == NULL) return 0;
 343
 344     /* We split one vertex into two -- the new vertex is eDst->Org.
 345      * Make sure the old vertex points to a valid half-edge.
 346      */
 347     MakeVertex( newVertex, eDst, eOrg->Org );
 348     eOrg->Org->anEdge = eOrg;
 349   }
 350   if( ! joiningLoops ) {
 351     GLUface *newFace= allocFace();
 352     if (newFace == NULL) return 0;
 353
 354     /* We split one loop into two -- the new loop is eDst->Lface.
 355      * Make sure the old face points to a valid half-edge.
 356      */
 357     MakeFace( newFace, eDst, eOrg->Lface );
 358     eOrg->Lface->anEdge = eOrg;
 359   }
 360
 361   return 1;
 362 }
 363
 364
 365 /* __gl_meshDelete( eDel ) removes the edge eDel.  There are several cases:
 366  * if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
 367  * eDel->Lface is deleted.  Otherwise, we are splitting one loop into two;
 368  * the newly created loop will contain eDel->Dst.  If the deletion of eDel
 369  * would create isolated vertices, those are deleted as well.
 370  *
 371  * This function could be implemented as two calls to __gl_meshSplice
 372  * plus a few calls to memFree, but this would allocate and delete
 373  * unnecessary vertices and faces.
 374  */
 375 int __gl_meshDelete( GLUhalfEdge *eDel )
 376 {
 377   GLUhalfEdge *eDelSym = eDel->Sym;
 378   int joiningLoops = FALSE;
 379
 380   /* First step: disconnect the origin vertex eDel->Org.  We make all
 381    * changes to get a consistent mesh in this "intermediate" state.
 382    */
 383   if( eDel->Lface != eDel->Rface ) {
 384     /* We are joining two loops into one -- remove the left face */
 385     joiningLoops = TRUE;
 386     KillFace( eDel->Lface, eDel->Rface );
 387   }
 388
 389   if( eDel->Onext == eDel ) {
 390     KillVertex( eDel->Org, NULL );
 391   } else {
 392     /* Make sure that eDel->Org and eDel->Rface point to valid half-edges */
 393     eDel->Rface->anEdge = eDel->Oprev;
 394     eDel->Org->anEdge = eDel->Onext;
 395
 396     Splice( eDel, eDel->Oprev );
 397     if( ! joiningLoops ) {
 398       GLUface *newFace= allocFace();
 399       if (newFace == NULL) return 0;
 400
 401       /* We are splitting one loop into two -- create a new loop for eDel. */
 402       MakeFace( newFace, eDel, eDel->Lface );
 403     }
 404   }
 405
 406   /* Claim: the mesh is now in a consistent state, except that eDel->Org
 407    * may have been deleted.  Now we disconnect eDel->Dst.
 408    */
 409   if( eDelSym->Onext == eDelSym ) {
 410     KillVertex( eDelSym->Org, NULL );
 411     KillFace( eDelSym->Lface, NULL );
 412   } else {
 413     /* Make sure that eDel->Dst and eDel->Lface point to valid half-edges */
 414     eDel->Lface->anEdge = eDelSym->Oprev;
 415     eDelSym->Org->anEdge = eDelSym->Onext;
 416     Splice( eDelSym, eDelSym->Oprev );
 417   }
 418
 419   /* Any isolated vertices or faces have already been freed. */
 420   KillEdge( eDel );
 421
 422   return 1;
 423 }
 424
 425
 426 /******************** Other Edge Operations **********************/
 427
 428 /* All these routines can be implemented with the basic edge
 429  * operations above.  They are provided for convenience and efficiency.
 430  */
 431
 432
 433 /* __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
 434  * eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
 435  * eOrg and eNew will have the same left face.
 436  */
 437 GLUhalfEdge *__gl_meshAddEdgeVertex( GLUhalfEdge *eOrg )
 438 {
 439   GLUhalfEdge *eNewSym;
 440   GLUhalfEdge *eNew = MakeEdge( eOrg );
 441   if (eNew == NULL) return NULL;
 442
 443   eNewSym = eNew->Sym;
 444
 445   /* Connect the new edge appropriately */
 446   Splice( eNew, eOrg->Lnext );
 447
 448   /* Set the vertex and face information */
 449   eNew->Org = eOrg->Dst;
 450   {
 451     GLUvertex *newVertex= allocVertex();
 452     if (newVertex == NULL) return NULL;
 453
 454     MakeVertex( newVertex, eNewSym, eNew->Org );
 455   }
 456   eNew->Lface = eNewSym->Lface = eOrg->Lface;
 457
 458   return eNew;
 459 }
 460
 461
 462 /* __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
 463  * such that eNew == eOrg->Lnext.  The new vertex is eOrg->Dst == eNew->Org.
 464  * eOrg and eNew will have the same left face.
 465  */
 466 GLUhalfEdge *__gl_meshSplitEdge( GLUhalfEdge *eOrg )
 467 {
 468   GLUhalfEdge *eNew;
 469   GLUhalfEdge *tempHalfEdge= __gl_meshAddEdgeVertex( eOrg );
 470   if (tempHalfEdge == NULL) return NULL;
 471
 472   eNew = tempHalfEdge->Sym;
 473
 474   /* Disconnect eOrg from eOrg->Dst and connect it to eNew->Org */
 475   Splice( eOrg->Sym, eOrg->Sym->Oprev );
 476   Splice( eOrg->Sym, eNew );
 477
 478   /* Set the vertex and face information */
 479   eOrg->Dst = eNew->Org;
 480   eNew->Dst->anEdge = eNew->Sym;        /* may have pointed to eOrg->Sym */
 481   eNew->Rface = eOrg->Rface;
 482   eNew->winding = eOrg->winding;        /* copy old winding information */
 483   eNew->Sym->winding = eOrg->Sym->winding;
 484
 485   return eNew;
 486 }
 487
 488
 489 /* __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
 490  * to eDst->Org, and returns the corresponding half-edge eNew.
 491  * If eOrg->Lface == eDst->Lface, this splits one loop into two,
 492  * and the newly created loop is eNew->Lface.  Otherwise, two disjoint
 493  * loops are merged into one, and the loop eDst->Lface is destroyed.
 494  *
 495  * If (eOrg == eDst), the new face will have only two edges.
 496  * If (eOrg->Lnext == eDst), the old face is reduced to a single edge.
 497  * If (eOrg->Lnext->Lnext == eDst), the old face is reduced to two edges.
 498  */
 499 GLUhalfEdge *__gl_meshConnect( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
 500 {
 501   GLUhalfEdge *eNewSym;
 502   int joiningLoops = FALSE;
 503   GLUhalfEdge *eNew = MakeEdge( eOrg );
 504   if (eNew == NULL) return NULL;
 505
 506   eNewSym = eNew->Sym;
 507
 508   if( eDst->Lface != eOrg->Lface ) {
 509     /* We are connecting two disjoint loops -- destroy eDst->Lface */
 510     joiningLoops = TRUE;
 511     KillFace( eDst->Lface, eOrg->Lface );
 512   }
 513
 514   /* Connect the new edge appropriately */
 515   Splice( eNew, eOrg->Lnext );
 516   Splice( eNewSym, eDst );
 517
 518   /* Set the vertex and face information */
 519   eNew->Org = eOrg->Dst;
 520   eNewSym->Org = eDst->Org;
 521   eNew->Lface = eNewSym->Lface = eOrg->Lface;
 522
 523   /* Make sure the old face points to a valid half-edge */
 524   eOrg->Lface->anEdge = eNewSym;
 525
 526   if( ! joiningLoops ) {
 527     GLUface *newFace= allocFace();
 528     if (newFace == NULL) return NULL;
 529
 530     /* We split one loop into two -- the new loop is eNew->Lface */
 531     MakeFace( newFace, eNew, eOrg->Lface );
 532   }
 533   return eNew;
 534 }
 535
 536
 537 /******************** Other Operations **********************/
 538
 539 /* __gl_meshZapFace( fZap ) destroys a face and removes it from the
 540  * global face list.  All edges of fZap will have a NULL pointer as their
 541  * left face.  Any edges which also have a NULL pointer as their right face
 542  * are deleted entirely (along with any isolated vertices this produces).
 543  * An entire mesh can be deleted by zapping its faces, one at a time,
 544  * in any order.  Zapped faces cannot be used in further mesh operations!
 545  */
 546 void __gl_meshZapFace( GLUface *fZap )
 547 {
 548   GLUhalfEdge *eStart = fZap->anEdge;
 549   GLUhalfEdge *e, *eNext, *eSym;
 550   GLUface *fPrev, *fNext;
 551
 552   /* walk around face, deleting edges whose right face is also NULL */
 553   eNext = eStart->Lnext;
 554   do {
 555     e = eNext;
 556     eNext = e->Lnext;
 557
 558     e->Lface = NULL;
 559     if( e->Rface == NULL ) {
 560       /* delete the edge -- see __gl_MeshDelete above */
 561
 562       if( e->Onext == e ) {
 563         KillVertex( e->Org, NULL );
 564       } else {
 565         /* Make sure that e->Org points to a valid half-edge */
 566         e->Org->anEdge = e->Onext;
 567         Splice( e, e->Oprev );
 568       }
 569       eSym = e->Sym;
 570       if( eSym->Onext == eSym ) {
 571         KillVertex( eSym->Org, NULL );
 572       } else {
 573         /* Make sure that eSym->Org points to a valid half-edge */
 574         eSym->Org->anEdge = eSym->Onext;
 575         Splice( eSym, eSym->Oprev );
 576       }
 577       KillEdge( e );
 578     }
 579   } while( e != eStart );
 580
 581   /* delete from circular doubly-linked list */
 582   fPrev = fZap->prev;
 583   fNext = fZap->next;
 584   fNext->prev = fPrev;
 585   fPrev->next = fNext;
 586
 587   memFree( fZap );
 588 }
 589
 590
 591 /* __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
 592  * and no loops (what we usually call a "face").
 593  */
 594 GLUmesh *__gl_meshNewMesh( void )
 595 {
 596   GLUvertex *v;
 597   GLUface *f;
 598   GLUhalfEdge *e;
 599   GLUhalfEdge *eSym;
 600   GLUmesh *mesh = (GLUmesh *)memAlloc( sizeof( GLUmesh ));
 601   if (mesh == NULL) {
 602      return NULL;
 603   }
 604
 605   v = &mesh->vHead;
 606   f = &mesh->fHead;
 607   e = &mesh->eHead;
 608   eSym = &mesh->eHeadSym;
 609
 610   v->next = v->prev = v;
 611   v->anEdge = NULL;
 612   v->data = NULL;
 613
 614   f->next = f->prev = f;
 615   f->anEdge = NULL;
 616   f->data = NULL;
 617   f->trail = NULL;
 618   f->marked = FALSE;
 619   f->inside = FALSE;
 620
 621   e->next = e;
 622   e->Sym = eSym;
 623   e->Onext = NULL;
 624   e->Lnext = NULL;
 625   e->Org = NULL;
 626   e->Lface = NULL;
 627   e->winding = 0;
 628   e->activeRegion = NULL;
 629
 630   eSym->next = eSym;
 631   eSym->Sym = e;
 632   eSym->Onext = NULL;
 633   eSym->Lnext = NULL;
 634   eSym->Org = NULL;
 635   eSym->Lface = NULL;
 636   eSym->winding = 0;
 637   eSym->activeRegion = NULL;
 638
 639   return mesh;
 640 }
 641
 642
 643 /* __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
 644  * both meshes, and returns the new mesh (the old meshes are destroyed).
 645  */
 646 GLUmesh *__gl_meshUnion( GLUmesh *mesh1, GLUmesh *mesh2 )
 647 {
 648   GLUface *f1 = &mesh1->fHead;
 649   GLUvertex *v1 = &mesh1->vHead;
 650   GLUhalfEdge *e1 = &mesh1->eHead;
 651   GLUface *f2 = &mesh2->fHead;
 652   GLUvertex *v2 = &mesh2->vHead;
 653   GLUhalfEdge *e2 = &mesh2->eHead;
 654
 655   /* Add the faces, vertices, and edges of mesh2 to those of mesh1 */
 656   if( f2->next != f2 ) {
 657     f1->prev->next = f2->next;
 658     f2->next->prev = f1->prev;
 659     f2->prev->next = f1;
 660     f1->prev = f2->prev;
 661   }
 662
 663   if( v2->next != v2 ) {
 664     v1->prev->next = v2->next;
 665     v2->next->prev = v1->prev;
 666     v2->prev->next = v1;
 667     v1->prev = v2->prev;
 668   }
 669
 670   if( e2->next != e2 ) {
 671     e1->Sym->next->Sym->next = e2->next;
 672     e2->next->Sym->next = e1->Sym->next;
 673     e2->Sym->next->Sym->next = e1;
 674     e1->Sym->next = e2->Sym->next;
 675   }
 676
 677   memFree( mesh2 );
 678   return mesh1;
 679 }
 680
 681
 682 #ifdef DELETE_BY_ZAPPING
 683
 684 /* __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
 685  */
 686 void __gl_meshDeleteMesh( GLUmesh *mesh )
 687 {
 688   GLUface *fHead = &mesh->fHead;
 689
 690   while( fHead->next != fHead ) {
 691     __gl_meshZapFace( fHead->next );
 692   }
 693   assert( mesh->vHead.next == &mesh->vHead );
 694
 695   memFree( mesh );
 696 }
 697
 698 #else
 699
 700 /* __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
 701  */
 702 void __gl_meshDeleteMesh( GLUmesh *mesh )
 703 {
 704   GLUface *f, *fNext;
 705   GLUvertex *v, *vNext;
 706   GLUhalfEdge *e, *eNext;
 707
 708   for( f = mesh->fHead.next; f != &mesh->fHead; f = fNext ) {
 709     fNext = f->next;
 710     memFree( f );
 711   }
 712
 713   for( v = mesh->vHead.next; v != &mesh->vHead; v = vNext ) {
 714     vNext = v->next;
 715     memFree( v );
 716   }
 717
 718   for( e = mesh->eHead.next; e != &mesh->eHead; e = eNext ) {
 719     /* One call frees both e and e->Sym (see EdgePair above) */
 720     eNext = e->next;
 721     memFree( e );
 722   }
 723
 724   memFree( mesh );
 725 }
 726
 727 #endif
 728
 729 #ifndef NDEBUG
 730
 731 /* __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
 732  */
 733 void __gl_meshCheckMesh( GLUmesh *mesh )
 734 {
 735   GLUface *fHead = &mesh->fHead;
 736   GLUvertex *vHead = &mesh->vHead;
 737   GLUhalfEdge *eHead = &mesh->eHead;
 738   GLUface *f, *fPrev;
 739   GLUvertex *v, *vPrev;
 740   GLUhalfEdge *e, *ePrev;
 741
 742   fPrev = fHead;
 743   for( fPrev = fHead ; (f = fPrev->next) != fHead; fPrev = f) {
 744     assert( f->prev == fPrev );
 745     e = f->anEdge;
 746     do {
 747       assert( e->Sym != e );
 748       assert( e->Sym->Sym == e );
 749       assert( e->Lnext->Onext->Sym == e );
 750       assert( e->Onext->Sym->Lnext == e );
 751       assert( e->Lface == f );
 752       e = e->Lnext;
 753     } while( e != f->anEdge );
 754   }
 755   assert( f->prev == fPrev && f->anEdge == NULL && f->data == NULL );
 756
 757   vPrev = vHead;
 758   for( vPrev = vHead ; (v = vPrev->next) != vHead; vPrev = v) {
 759     assert( v->prev == vPrev );
 760     e = v->anEdge;
 761     do {
 762       assert( e->Sym != e );
 763       assert( e->Sym->Sym == e );
 764       assert( e->Lnext->Onext->Sym == e );
 765       assert( e->Onext->Sym->Lnext == e );
 766       assert( e->Org == v );
 767       e = e->Onext;
 768     } while( e != v->anEdge );
 769   }
 770   assert( v->prev == vPrev && v->anEdge == NULL && v->data == NULL );
 771
 772   ePrev = eHead;
 773   for( ePrev = eHead ; (e = ePrev->next) != eHead; ePrev = e) {
 774     assert( e->Sym->next == ePrev->Sym );
 775     assert( e->Sym != e );
 776     assert( e->Sym->Sym == e );
 777     assert( e->Org != NULL );
 778     assert( e->Dst != NULL );
 779     assert( e->Lnext->Onext->Sym == e );
 780     assert( e->Onext->Sym->Lnext == e );
 781   }
 782   assert( e->Sym->next == ePrev->Sym
 783        && e->Sym == &mesh->eHeadSym
 784        && e->Sym->Sym == e
 785        && e->Org == NULL && e->Dst == NULL
 786        && e->Lface == NULL && e->Rface == NULL );
 787 }
 788
 789 #endif