File indexing completed on 2024-04-21 14:46:25

 /*
 ** Author: Eric Veach, July 1994.
 **
 */
 
 #include "gluos.h"
 #include <assert.h>
 #include <stddef.h>
 #include <setjmp.h> /* longjmp */
 #include <limits.h> /* LONG_MAX */
 
 #include "mesh.h"
 #include "geom.h"
 #include "tess.h"
 #include "dict.h"
 #include "priorityq.h"
 #include "memalloc.h"
 #include "sweep.h"
 
 #ifndef TRUE
 #define TRUE 1
 #endif
 #ifndef FALSE
 #define FALSE 0
 #endif
 
 #ifdef FOR_TRITE_TEST_PROGRAM
 extern void DebugEvent(GLUtesselator *tess);
 #else
 #define DebugEvent(tess)
 #endif
 
 /*
  * Invariants for the Edge Dictionary.
  * - each pair of adjacent edges e2=Succ(e1) satisfies EdgeLeq(e1,e2)
  *   at any valid location of the sweep event
  * - if EdgeLeq(e2,e1) as well (at any valid sweep event), then e1 and e2
  *   share a common endpoint
  * - for each e, e->Dst has been processed, but not e->Org
  * - each edge e satisfies VertLeq(e->Dst,event) && VertLeq(event,e->Org)
  *   where "event" is the current sweep line event.
  * - no edge e has zero length
  *
  * Invariants for the Mesh (the processed portion).
  * - the portion of the mesh left of the sweep line is a planar graph,
  *   ie. there is *some* way to embed it in the plane
  * - no processed edge has zero length
  * - no two processed vertices have identical coordinates
  * - each "inside" region is monotone, ie. can be broken into two chains
  *   of monotonically increasing vertices according to VertLeq(v1,v2)
  *   - a non-invariant: these chains may intersect (very slightly)
  *
  * Invariants for the Sweep.
  * - if none of the edges incident to the event vertex have an activeRegion
  *   (ie. none of these edges are in the edge dictionary), then the vertex
  *   has only right-going edges.
  * - if an edge is marked "fixUpperEdge" (it is a temporary edge introduced
  *   by ConnectRightVertex), then it is the only right-going edge from
  *   its associated vertex.  (This says that these edges exist only
  *   when it is necessary.)
  */
 
 #undef MAX
 #undef MIN
 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
 #define MIN(x, y) ((x) <= (y) ? (x) : (y))
 
 /* When we merge two edges into one, we need to compute the combined
  * winding of the new edge.
  */
 #define AddWinding(eDst, eSrc) (eDst->winding += eSrc->winding, eDst->Sym->winding += eSrc->Sym->winding)
 
 static void SweepEvent(GLUtesselator *tess, GLUvertex *vEvent);
 static void WalkDirtyRegions(GLUtesselator *tess, ActiveRegion *regUp);
 static int CheckForRightSplice(GLUtesselator *tess, ActiveRegion *regUp);
 
 static int EdgeLeq(GLUtesselator *tess, ActiveRegion *reg1, ActiveRegion *reg2)
 /*
  * Both edges must be directed from right to left (this is the canonical
  * direction for the upper edge of each region).
  *
  * The strategy is to evaluate a "t" value for each edge at the
  * current sweep line position, given by tess->event.  The calculations
  * are designed to be very stable, but of course they are not perfect.
  *
  * Special case: if both edge destinations are at the sweep event,
  * we sort the edges by slope (they would otherwise compare equally).
  */
 {
     GLUvertex *event = tess->event;
     GLUhalfEdge *e1, *e2;
     GLdouble t1, t2;
 
     e1 = reg1->eUp;
     e2 = reg2->eUp;
 
     if (e1->Dst == event)
     {
         if (e2->Dst == event)
         {
             /* Two edges right of the sweep line which meet at the sweep event.
        * Sort them by slope.
        */
             if (VertLeq(e1->Org, e2->Org))
             {
                 return EdgeSign(e2->Dst, e1->Org, e2->Org) <= 0;
             }
             return EdgeSign(e1->Dst, e2->Org, e1->Org) >= 0;
         }
         return EdgeSign(e2->Dst, event, e2->Org) <= 0;
     }
     if (e2->Dst == event)
     {
         return EdgeSign(e1->Dst, event, e1->Org) >= 0;
     }
 
     /* General case - compute signed distance *from* e1, e2 to event */
     t1 = EdgeEval(e1->Dst, event, e1->Org);
     t2 = EdgeEval(e2->Dst, event, e2->Org);
     return (t1 >= t2);
 }
 
 static void DeleteRegion(GLUtesselator *tess, ActiveRegion *reg)
 {
     if (reg->fixUpperEdge)
     {
         /* It was created with zero winding number, so it better be
      * deleted with zero winding number (ie. it better not get merged
      * with a real edge).
      */
         assert(reg->eUp->winding == 0);
     }
     reg->eUp->activeRegion = NULL;
     dictDelete(tess->dict, reg->nodeUp); /* __gl_dictListDelete */
     memFree(reg);
 }
 
 static int FixUpperEdge(ActiveRegion *reg, GLUhalfEdge *newEdge)
 /*
  * Replace an upper edge which needs fixing (see ConnectRightVertex).
  */
 {
     assert(reg->fixUpperEdge);
     if (!__gl_meshDelete(reg->eUp))
         return 0;
     reg->fixUpperEdge     = FALSE;
     reg->eUp              = newEdge;
     newEdge->activeRegion = reg;
 
     return 1;
 }
 
 static ActiveRegion *TopLeftRegion(ActiveRegion *reg)
 {
     GLUvertex *org = reg->eUp->Org;
     GLUhalfEdge *e;
 
     /* Find the region above the uppermost edge with the same origin */
     do
     {
         reg = RegionAbove(reg);
     } while (reg->eUp->Org == org);
 
     /* If the edge above was a temporary edge introduced by ConnectRightVertex,
    * now is the time to fix it.
    */
     if (reg->fixUpperEdge)
     {
         e = __gl_meshConnect(RegionBelow(reg)->eUp->Sym, reg->eUp->Lnext);
         if (e == NULL)
             return NULL;
         if (!FixUpperEdge(reg, e))
             return NULL;
         reg = RegionAbove(reg);
     }
     return reg;
 }
 
 static ActiveRegion *TopRightRegion(ActiveRegion *reg)
 {
     GLUvertex *dst = reg->eUp->Dst;
 
     /* Find the region above the uppermost edge with the same destination */
     do
     {
         reg = RegionAbove(reg);
     } while (reg->eUp->Dst == dst);
     return reg;
 }
 
 static ActiveRegion *AddRegionBelow(GLUtesselator *tess, ActiveRegion *regAbove, GLUhalfEdge *eNewUp)
 /*
  * Add a new active region to the sweep line, *somewhere* below "regAbove"
  * (according to where the new edge belongs in the sweep-line dictionary).
  * The upper edge of the new region will be "eNewUp".
  * Winding number and "inside" flag are not updated.
  */
 {
     ActiveRegion *regNew = (ActiveRegion *)memAlloc(sizeof(ActiveRegion));
     if (regNew == NULL)
         longjmp(tess->env, 1);
 
     regNew->eUp = eNewUp;
     /* __gl_dictListInsertBefore */
     regNew->nodeUp = dictInsertBefore(tess->dict, regAbove->nodeUp, regNew);
     if (regNew->nodeUp == NULL)
         longjmp(tess->env, 1);
     regNew->fixUpperEdge = FALSE;
     regNew->sentinel     = FALSE;
     regNew->dirty        = FALSE;
 
     eNewUp->activeRegion = regNew;
     return regNew;
 }
 
 static GLboolean IsWindingInside(GLUtesselator *tess, int n)
 {
     switch (tess->windingRule)
     {
         case GLU_TESS_WINDING_ODD:
             return (n & 1);
         case GLU_TESS_WINDING_NONZERO:
             return (n != 0);
         case GLU_TESS_WINDING_POSITIVE:
             return (n > 0);
         case GLU_TESS_WINDING_NEGATIVE:
             return (n < 0);
         case GLU_TESS_WINDING_ABS_GEQ_TWO:
             return (n >= 2) || (n <= -2);
     }
     /*LINTED*/
     assert(FALSE);
     /*NOTREACHED*/
     return GL_FALSE; /* avoid compiler complaints */
 }
 
 static void ComputeWinding(GLUtesselator *tess, ActiveRegion *reg)
 {
     reg->windingNumber = RegionAbove(reg)->windingNumber + reg->eUp->winding;
     reg->inside        = IsWindingInside(tess, reg->windingNumber);
 }
 
 static void FinishRegion(GLUtesselator *tess, ActiveRegion *reg)
 /*
  * Delete a region from the sweep line.  This happens when the upper
  * and lower chains of a region meet (at a vertex on the sweep line).
  * The "inside" flag is copied to the appropriate mesh face (we could
  * not do this before -- since the structure of the mesh is always
  * changing, this face may not have even existed until now).
  */
 {
     GLUhalfEdge *e = reg->eUp;
     GLUface *f     = e->Lface;
 
     f->inside = reg->inside;
     f->anEdge = e; /* optimization for __gl_meshTessellateMonoRegion() */
     DeleteRegion(tess, reg);
 }
 
 static GLUhalfEdge *FinishLeftRegions(GLUtesselator *tess, ActiveRegion *regFirst, ActiveRegion *regLast)
 /*
  * We are given a vertex with one or more left-going edges.  All affected
  * edges should be in the edge dictionary.  Starting at regFirst->eUp,
  * we walk down deleting all regions where both edges have the same
  * origin vOrg.  At the same time we copy the "inside" flag from the
  * active region to the face, since at this point each face will belong
  * to at most one region (this was not necessarily true until this point
  * in the sweep).  The walk stops at the region above regLast; if regLast
  * is NULL we walk as far as possible.  At the same time we relink the
  * mesh if necessary, so that the ordering of edges around vOrg is the
  * same as in the dictionary.
  */
 {
     ActiveRegion *reg, *regPrev;
     GLUhalfEdge *e, *ePrev;
 
     regPrev = regFirst;
     ePrev   = regFirst->eUp;
     while (regPrev != regLast)
     {
         regPrev->fixUpperEdge = FALSE; /* placement was OK */
         reg                   = RegionBelow(regPrev);
         e                     = reg->eUp;
         if (e->Org != ePrev->Org)
         {
             if (!reg->fixUpperEdge)
             {
                 /* Remove the last left-going edge.  Even though there are no further
      * edges in the dictionary with this origin, there may be further
      * such edges in the mesh (if we are adding left edges to a vertex
      * that has already been processed).  Thus it is important to call
      * FinishRegion rather than just DeleteRegion.
      */
                 FinishRegion(tess, regPrev);
                 break;
             }
             /* If the edge below was a temporary edge introduced by
        * ConnectRightVertex, now is the time to fix it.
        */
             e = __gl_meshConnect(ePrev->Lprev, e->Sym);
             if (e == NULL)
                 longjmp(tess->env, 1);
             if (!FixUpperEdge(reg, e))
                 longjmp(tess->env, 1);
         }
 
         /* Relink edges so that ePrev->Onext == e */
         if (ePrev->Onext != e)
         {
             if (!__gl_meshSplice(e->Oprev, e))
                 longjmp(tess->env, 1);
             if (!__gl_meshSplice(ePrev, e))
                 longjmp(tess->env, 1);
         }
         FinishRegion(tess, regPrev); /* may change reg->eUp */
         ePrev   = reg->eUp;
         regPrev = reg;
     }
     return ePrev;
 }
 
 static void AddRightEdges(GLUtesselator *tess, ActiveRegion *regUp, GLUhalfEdge *eFirst, GLUhalfEdge *eLast,
                           GLUhalfEdge *eTopLeft, GLboolean cleanUp)
 /*
  * Purpose: insert right-going edges into the edge dictionary, and update
  * winding numbers and mesh connectivity appropriately.  All right-going
  * edges share a common origin vOrg.  Edges are inserted CCW starting at
  * eFirst; the last edge inserted is eLast->Oprev.  If vOrg has any
  * left-going edges already processed, then eTopLeft must be the edge
  * such that an imaginary upward vertical segment from vOrg would be
  * contained between eTopLeft->Oprev and eTopLeft; otherwise eTopLeft
  * should be NULL.
  */
 {
     ActiveRegion *reg, *regPrev;
     GLUhalfEdge *e, *ePrev;
     int firstTime = TRUE;
 
     /* Insert the new right-going edges in the dictionary */
     e = eFirst;
     do
     {
         assert(VertLeq(e->Org, e->Dst));
         AddRegionBelow(tess, regUp, e->Sym);
         e = e->Onext;
     } while (e != eLast);
 
     /* Walk *all* right-going edges from e->Org, in the dictionary order,
    * updating the winding numbers of each region, and re-linking the mesh
    * edges to match the dictionary ordering (if necessary).
    */
     if (eTopLeft == NULL)
     {
         eTopLeft = RegionBelow(regUp)->eUp->Rprev;
     }
     regPrev = regUp;
     ePrev   = eTopLeft;
     for (;;)
     {
         reg = RegionBelow(regPrev);
         e   = reg->eUp->Sym;
         if (e->Org != ePrev->Org)
             break;
 
         if (e->Onext != ePrev)
         {
             /* Unlink e from its current position, and relink below ePrev */
             if (!__gl_meshSplice(e->Oprev, e))
                 longjmp(tess->env, 1);
             if (!__gl_meshSplice(ePrev->Oprev, e))
                 longjmp(tess->env, 1);
         }
         /* Compute the winding number and "inside" flag for the new regions */
         reg->windingNumber = regPrev->windingNumber - e->winding;
         reg->inside        = IsWindingInside(tess, reg->windingNumber);
 
         /* Check for two outgoing edges with same slope -- process these
      * before any intersection tests (see example in __gl_computeInterior).
      */
         regPrev->dirty = TRUE;
         if (!firstTime && CheckForRightSplice(tess, regPrev))
         {
             AddWinding(e, ePrev);
             DeleteRegion(tess, regPrev);
             if (!__gl_meshDelete(ePrev))
                 longjmp(tess->env, 1);
         }
         firstTime = FALSE;
         regPrev   = reg;
         ePrev     = e;
     }
     regPrev->dirty = TRUE;
     assert(regPrev->windingNumber - e->winding == reg->windingNumber);
 
     if (cleanUp)
     {
         /* Check for intersections between newly adjacent edges. */
         WalkDirtyRegions(tess, regPrev);
     }
 }
 
 static void CallCombine(GLUtesselator *tess, GLUvertex *isect, void *data[4], GLfloat weights[4], int needed)
 {
     GLdouble coords[3];
 
     /* Copy coord data in case the callback changes it. */
     coords[0] = isect->coords[0];
     coords[1] = isect->coords[1];
     coords[2] = isect->coords[2];
 
     isect->data = NULL;
     CALL_COMBINE_OR_COMBINE_DATA(coords, data, weights, &isect->data);
     if (isect->data == NULL)
     {
         if (!needed)
         {
             isect->data = data[0];
         }
         else if (!tess->fatalError)
         {
             /* The only way fatal error is when two edges are found to intersect,
        * but the user has not provided the callback necessary to handle
        * generated intersection points.
        */
             CALL_ERROR_OR_ERROR_DATA(GLU_TESS_NEED_COMBINE_CALLBACK);
             tess->fatalError = TRUE;
         }
     }
 }
 
 static void SpliceMergeVertices(GLUtesselator *tess, GLUhalfEdge *e1, GLUhalfEdge *e2)
 /*
  * Two vertices with identical coordinates are combined into one.
  * e1->Org is kept, while e2->Org is discarded.
  */
 {
     void *data[4]      = { NULL, NULL, NULL, NULL };
     GLfloat weights[4] = { 0.5, 0.5, 0.0, 0.0 };
 
     data[0] = e1->Org->data;
     data[1] = e2->Org->data;
     CallCombine(tess, e1->Org, data, weights, FALSE);
     if (!__gl_meshSplice(e1, e2))
         longjmp(tess->env, 1);
 }
 
 static void VertexWeights(GLUvertex *isect, GLUvertex *org, GLUvertex *dst, GLfloat *weights)
 /*
  * Find some weights which describe how the intersection vertex is
  * a linear combination of "org" and "dest".  Each of the two edges
  * which generated "isect" is allocated 50% of the weight; each edge
  * splits the weight between its org and dst according to the
  * relative distance to "isect".
  */
 {
     GLdouble t1 = VertL1dist(org, isect);
     GLdouble t2 = VertL1dist(dst, isect);
 
     weights[0] = 0.5 * t2 / (t1 + t2);
     weights[1] = 0.5 * t1 / (t1 + t2);
     isect->coords[0] += weights[0] * org->coords[0] + weights[1] * dst->coords[0];
     isect->coords[1] += weights[0] * org->coords[1] + weights[1] * dst->coords[1];
     isect->coords[2] += weights[0] * org->coords[2] + weights[1] * dst->coords[2];
 }
 
 static void GetIntersectData(GLUtesselator *tess, GLUvertex *isect, GLUvertex *orgUp, GLUvertex *dstUp,
                              GLUvertex *orgLo, GLUvertex *dstLo)
 /*
  * We've computed a new intersection point, now we need a "data" pointer
  * from the user so that we can refer to this new vertex in the
  * rendering callbacks.
  */
 {
     void *data[4];
     GLfloat weights[4];
 
     data[0] = orgUp->data;
     data[1] = dstUp->data;
     data[2] = orgLo->data;
     data[3] = dstLo->data;
 
     isect->coords[0] = isect->coords[1] = isect->coords[2] = 0;
     VertexWeights(isect, orgUp, dstUp, &weights[0]);
     VertexWeights(isect, orgLo, dstLo, &weights[2]);
 
     CallCombine(tess, isect, data, weights, TRUE);
 }
 
 static int CheckForRightSplice(GLUtesselator *tess, ActiveRegion *regUp)
 /*
  * Check the upper and lower edge of "regUp", to make sure that the
  * eUp->Org is above eLo, or eLo->Org is below eUp (depending on which
  * origin is leftmost).
  *
  * The main purpose is to splice right-going edges with the same
  * dest vertex and nearly identical slopes (ie. we can't distinguish
  * the slopes numerically).  However the splicing can also help us
  * to recover from numerical errors.  For example, suppose at one
  * point we checked eUp and eLo, and decided that eUp->Org is barely
  * above eLo.  Then later, we split eLo into two edges (eg. from
  * a splice operation like this one).  This can change the result of
  * our test so that now eUp->Org is incident to eLo, or barely below it.
  * We must correct this condition to maintain the dictionary invariants.
  *
  * One possibility is to check these edges for intersection again
  * (ie. CheckForIntersect).  This is what we do if possible.  However
  * CheckForIntersect requires that tess->event lies between eUp and eLo,
  * so that it has something to fall back on when the intersection
  * calculation gives us an unusable answer.  So, for those cases where
  * we can't check for intersection, this routine fixes the problem
  * by just splicing the offending vertex into the other edge.
  * This is a guaranteed solution, no matter how degenerate things get.
  * Basically this is a combinatorial solution to a numerical problem.
  */
 {
     ActiveRegion *regLo = RegionBelow(regUp);
     GLUhalfEdge *eUp    = regUp->eUp;
     GLUhalfEdge *eLo    = regLo->eUp;
 
     if (VertLeq(eUp->Org, eLo->Org))
     {
         if (EdgeSign(eLo->Dst, eUp->Org, eLo->Org) > 0)
             return FALSE;
 
         /* eUp->Org appears to be below eLo */
         if (!VertEq(eUp->Org, eLo->Org))
         {
             /* Splice eUp->Org into eLo */
             if (__gl_meshSplitEdge(eLo->Sym) == NULL)
                 longjmp(tess->env, 1);
             if (!__gl_meshSplice(eUp, eLo->Oprev))
                 longjmp(tess->env, 1);
             regUp->dirty = regLo->dirty = TRUE;
         }
         else if (eUp->Org != eLo->Org)
         {
             /* merge the two vertices, discarding eUp->Org */
             pqDelete(tess->pq, eUp->Org->pqHandle); /* __gl_pqSortDelete */
             SpliceMergeVertices(tess, eLo->Oprev, eUp);
         }
     }
     else
     {
         if (EdgeSign(eUp->Dst, eLo->Org, eUp->Org) < 0)
             return FALSE;
 
         /* eLo->Org appears to be above eUp, so splice eLo->Org into eUp */
         RegionAbove(regUp)->dirty = regUp->dirty = TRUE;
         if (__gl_meshSplitEdge(eUp->Sym) == NULL)
             longjmp(tess->env, 1);
         if (!__gl_meshSplice(eLo->Oprev, eUp))
             longjmp(tess->env, 1);
     }
     return TRUE;
 }
 
 static int CheckForLeftSplice(GLUtesselator *tess, ActiveRegion *regUp)
 /*
  * Check the upper and lower edge of "regUp", to make sure that the
  * eUp->Dst is above eLo, or eLo->Dst is below eUp (depending on which
  * destination is rightmost).
  *
  * Theoretically, this should always be true.  However, splitting an edge
  * into two pieces can change the results of previous tests.  For example,
  * suppose at one point we checked eUp and eLo, and decided that eUp->Dst
  * is barely above eLo.  Then later, we split eLo into two edges (eg. from
  * a splice operation like this one).  This can change the result of
  * the test so that now eUp->Dst is incident to eLo, or barely below it.
  * We must correct this condition to maintain the dictionary invariants
  * (otherwise new edges might get inserted in the wrong place in the
  * dictionary, and bad stuff will happen).
  *
  * We fix the problem by just splicing the offending vertex into the
  * other edge.
  */
 {
     ActiveRegion *regLo = RegionBelow(regUp);
     GLUhalfEdge *eUp    = regUp->eUp;
     GLUhalfEdge *eLo    = regLo->eUp;
     GLUhalfEdge *e;
 
     assert(!VertEq(eUp->Dst, eLo->Dst));
 
     if (VertLeq(eUp->Dst, eLo->Dst))
     {
         if (EdgeSign(eUp->Dst, eLo->Dst, eUp->Org) < 0)
             return FALSE;
 
         /* eLo->Dst is above eUp, so splice eLo->Dst into eUp */
         RegionAbove(regUp)->dirty = regUp->dirty = TRUE;
         e                                        = __gl_meshSplitEdge(eUp);
         if (e == NULL)
             longjmp(tess->env, 1);
         if (!__gl_meshSplice(eLo->Sym, e))
             longjmp(tess->env, 1);
         e->Lface->inside = regUp->inside;
     }
     else
     {
         if (EdgeSign(eLo->Dst, eUp->Dst, eLo->Org) > 0)
             return FALSE;
 
         /* eUp->Dst is below eLo, so splice eUp->Dst into eLo */
         regUp->dirty = regLo->dirty = TRUE;
         e                           = __gl_meshSplitEdge(eLo);
         if (e == NULL)
             longjmp(tess->env, 1);
         if (!__gl_meshSplice(eUp->Lnext, eLo->Sym))
             longjmp(tess->env, 1);
         e->Rface->inside = regUp->inside;
     }
     return TRUE;
 }
 
 static int CheckForIntersect(GLUtesselator *tess, ActiveRegion *regUp)
 /*
  * Check the upper and lower edges of the given region to see if
  * they intersect.  If so, create the intersection and add it
  * to the data structures.
  *
  * Returns TRUE if adding the new intersection resulted in a recursive
  * call to AddRightEdges(); in this case all "dirty" regions have been
  * checked for intersections, and possibly regUp has been deleted.
  */
 {
     ActiveRegion *regLo = RegionBelow(regUp);
     GLUhalfEdge *eUp    = regUp->eUp;
     GLUhalfEdge *eLo    = regLo->eUp;
     GLUvertex *orgUp    = eUp->Org;
     GLUvertex *orgLo    = eLo->Org;
     GLUvertex *dstUp    = eUp->Dst;
     GLUvertex *dstLo    = eLo->Dst;
     GLdouble tMinUp, tMaxLo;
     GLUvertex isect, *orgMin;
     GLUhalfEdge *e;
 
     assert(!VertEq(dstLo, dstUp));
     assert(EdgeSign(dstUp, tess->event, orgUp) <= 0);
     assert(EdgeSign(dstLo, tess->event, orgLo) >= 0);
     assert(orgUp != tess->event && orgLo != tess->event);
     assert(!regUp->fixUpperEdge && !regLo->fixUpperEdge);
 
     if (orgUp == orgLo)
         return FALSE; /* right endpoints are the same */
 
     tMinUp = MIN(orgUp->t, dstUp->t);
     tMaxLo = MAX(orgLo->t, dstLo->t);
     if (tMinUp > tMaxLo)
         return FALSE; /* t ranges do not overlap */
 
     if (VertLeq(orgUp, orgLo))
     {
         if (EdgeSign(dstLo, orgUp, orgLo) > 0)
             return FALSE;
     }
     else
     {
         if (EdgeSign(dstUp, orgLo, orgUp) < 0)
             return FALSE;
     }
 
     /* At this point the edges intersect, at least marginally */
     DebugEvent(tess);
 
     __gl_edgeIntersect(dstUp, orgUp, dstLo, orgLo, &isect);
     /* The following properties are guaranteed: */
     assert(MIN(orgUp->t, dstUp->t) <= isect.t);
     assert(isect.t <= MAX(orgLo->t, dstLo->t));
     assert(MIN(dstLo->s, dstUp->s) <= isect.s);
     assert(isect.s <= MAX(orgLo->s, orgUp->s));
 
     if (VertLeq(&isect, tess->event))
     {
         /* The intersection point lies slightly to the left of the sweep line,
      * so move it until it''s slightly to the right of the sweep line.
      * (If we had perfect numerical precision, this would never happen
      * in the first place).  The easiest and safest thing to do is
      * replace the intersection by tess->event.
      */
         isect.s = tess->event->s;
         isect.t = tess->event->t;
     }
     /* Similarly, if the computed intersection lies to the right of the
    * rightmost origin (which should rarely happen), it can cause
    * unbelievable inefficiency on sufficiently degenerate inputs.
    * (If you have the test program, try running test54.d with the
    * "X zoom" option turned on).
    */
     orgMin = VertLeq(orgUp, orgLo) ? orgUp : orgLo;
     if (VertLeq(orgMin, &isect))
     {
         isect.s = orgMin->s;
         isect.t = orgMin->t;
     }
 
     if (VertEq(&isect, orgUp) || VertEq(&isect, orgLo))
     {
         /* Easy case -- intersection at one of the right endpoints */
         (void)CheckForRightSplice(tess, regUp);
         return FALSE;
     }
 
     if ((!VertEq(dstUp, tess->event) && EdgeSign(dstUp, tess->event, &isect) >= 0) ||
         (!VertEq(dstLo, tess->event) && EdgeSign(dstLo, tess->event, &isect) <= 0))
     {
         /* Very unusual -- the new upper or lower edge would pass on the
      * wrong side of the sweep event, or through it.  This can happen
      * due to very small numerical errors in the intersection calculation.
      */
         if (dstLo == tess->event)
         {
             /* Splice dstLo into eUp, and process the new region(s) */
             if (__gl_meshSplitEdge(eUp->Sym) == NULL)
                 longjmp(tess->env, 1);
             if (!__gl_meshSplice(eLo->Sym, eUp))
                 longjmp(tess->env, 1);
             regUp = TopLeftRegion(regUp);
             if (regUp == NULL)
                 longjmp(tess->env, 1);
             eUp = RegionBelow(regUp)->eUp;
             FinishLeftRegions(tess, RegionBelow(regUp), regLo);
             AddRightEdges(tess, regUp, eUp->Oprev, eUp, eUp, TRUE);
             return TRUE;
         }
         if (dstUp == tess->event)
         {
             /* Splice dstUp into eLo, and process the new region(s) */
             if (__gl_meshSplitEdge(eLo->Sym) == NULL)
                 longjmp(tess->env, 1);
             if (!__gl_meshSplice(eUp->Lnext, eLo->Oprev))
                 longjmp(tess->env, 1);
             regLo      = regUp;
             regUp      = TopRightRegion(regUp);
             e          = RegionBelow(regUp)->eUp->Rprev;
             regLo->eUp = eLo->Oprev;
             eLo        = FinishLeftRegions(tess, regLo, NULL);
             AddRightEdges(tess, regUp, eLo->Onext, eUp->Rprev, e, TRUE);
             return TRUE;
         }
         /* Special case: called from ConnectRightVertex.  If either
      * edge passes on the wrong side of tess->event, split it
      * (and wait for ConnectRightVertex to splice it appropriately).
      */
         if (EdgeSign(dstUp, tess->event, &isect) >= 0)
         {
             RegionAbove(regUp)->dirty = regUp->dirty = TRUE;
             if (__gl_meshSplitEdge(eUp->Sym) == NULL)
                 longjmp(tess->env, 1);
             eUp->Org->s = tess->event->s;
             eUp->Org->t = tess->event->t;
         }
         if (EdgeSign(dstLo, tess->event, &isect) <= 0)
         {
             regUp->dirty = regLo->dirty = TRUE;
             if (__gl_meshSplitEdge(eLo->Sym) == NULL)
                 longjmp(tess->env, 1);
             eLo->Org->s = tess->event->s;
             eLo->Org->t = tess->event->t;
         }
         /* leave the rest for ConnectRightVertex */
         return FALSE;
     }
 
     /* General case -- split both edges, splice into new vertex.
    * When we do the splice operation, the order of the arguments is
    * arbitrary as far as correctness goes.  However, when the operation
    * creates a new face, the work done is proportional to the size of
    * the new face.  We expect the faces in the processed part of
    * the mesh (ie. eUp->Lface) to be smaller than the faces in the
    * unprocessed original contours (which will be eLo->Oprev->Lface).
    */
     if (__gl_meshSplitEdge(eUp->Sym) == NULL)
         longjmp(tess->env, 1);
     if (__gl_meshSplitEdge(eLo->Sym) == NULL)
         longjmp(tess->env, 1);
     if (!__gl_meshSplice(eLo->Oprev, eUp))
         longjmp(tess->env, 1);
     eUp->Org->s        = isect.s;
     eUp->Org->t        = isect.t;
     eUp->Org->pqHandle = pqInsert(tess->pq, eUp->Org); /* __gl_pqSortInsert */
     if (eUp->Org->pqHandle == LONG_MAX)
     {
         pqDeletePriorityQ(tess->pq); /* __gl_pqSortDeletePriorityQ */
         tess->pq = NULL;
         longjmp(tess->env, 1);
     }
     GetIntersectData(tess, eUp->Org, orgUp, dstUp, orgLo, dstLo);
     RegionAbove(regUp)->dirty = regUp->dirty = regLo->dirty = TRUE;
     return FALSE;
 }
 
 static void WalkDirtyRegions(GLUtesselator *tess, ActiveRegion *regUp)
 /*
  * When the upper or lower edge of any region changes, the region is
  * marked "dirty".  This routine walks through all the dirty regions
  * and makes sure that the dictionary invariants are satisfied
  * (see the comments at the beginning of this file).  Of course
  * new dirty regions can be created as we make changes to restore
  * the invariants.
  */
 {
     ActiveRegion *regLo = RegionBelow(regUp);
     GLUhalfEdge *eUp, *eLo;
 
     for (;;)
     {
         /* Find the lowest dirty region (we walk from the bottom up). */
         while (regLo->dirty)
         {
             regUp = regLo;
             regLo = RegionBelow(regLo);
         }
         if (!regUp->dirty)
         {
             regLo = regUp;
             regUp = RegionAbove(regUp);
             if (regUp == NULL || !regUp->dirty)
             {
                 /* We've walked all the dirty regions */
                 return;
             }
         }
         regUp->dirty = FALSE;
         eUp          = regUp->eUp;
         eLo          = regLo->eUp;
 
         if (eUp->Dst != eLo->Dst)
         {
             /* Check that the edge ordering is obeyed at the Dst vertices. */
             if (CheckForLeftSplice(tess, regUp))
             {
                 /* If the upper or lower edge was marked fixUpperEdge, then
      * we no longer need it (since these edges are needed only for
      * vertices which otherwise have no right-going edges).
      */
                 if (regLo->fixUpperEdge)
                 {
                     DeleteRegion(tess, regLo);
                     if (!__gl_meshDelete(eLo))
                         longjmp(tess->env, 1);
                     regLo = RegionBelow(regUp);
                     eLo   = regLo->eUp;
                 }
                 else if (regUp->fixUpperEdge)
                 {
                     DeleteRegion(tess, regUp);
                     if (!__gl_meshDelete(eUp))
                         longjmp(tess->env, 1);
                     regUp = RegionAbove(regLo);
                     eUp   = regUp->eUp;
                 }
             }
         }
         if (eUp->Org != eLo->Org)
         {
             if (eUp->Dst != eLo->Dst && !regUp->fixUpperEdge && !regLo->fixUpperEdge &&
                 (eUp->Dst == tess->event || eLo->Dst == tess->event))
             {
                 /* When all else fails in CheckForIntersect(), it uses tess->event
      * as the intersection location.  To make this possible, it requires
      * that tess->event lie between the upper and lower edges, and also
      * that neither of these is marked fixUpperEdge (since in the worst
      * case it might splice one of these edges into tess->event, and
      * violate the invariant that fixable edges are the only right-going
      * edge from their associated vertex).
      */
                 if (CheckForIntersect(tess, regUp))
                 {
                     /* WalkDirtyRegions() was called recursively; we're done */
                     return;
                 }
             }
             else
             {
                 /* Even though we can't use CheckForIntersect(), the Org vertices
      * may violate the dictionary edge ordering.  Check and correct this.
      */
                 (void)CheckForRightSplice(tess, regUp);
             }
         }
         if (eUp->Org == eLo->Org && eUp->Dst == eLo->Dst)
         {
             /* A degenerate loop consisting of only two edges -- delete it. */
             AddWinding(eLo, eUp);
             DeleteRegion(tess, regUp);
             if (!__gl_meshDelete(eUp))
                 longjmp(tess->env, 1);
             regUp = RegionAbove(regLo);
         }
     }
 }
 
 static void ConnectRightVertex(GLUtesselator *tess, ActiveRegion *regUp, GLUhalfEdge *eBottomLeft)
 /*
  * Purpose: connect a "right" vertex vEvent (one where all edges go left)
  * to the unprocessed portion of the mesh.  Since there are no right-going
  * edges, two regions (one above vEvent and one below) are being merged
  * into one.  "regUp" is the upper of these two regions.
  *
  * There are two reasons for doing this (adding a right-going edge):
  *  - if the two regions being merged are "inside", we must add an edge
  *    to keep them separated (the combined region would not be monotone).
  *  - in any case, we must leave some record of vEvent in the dictionary,
  *    so that we can merge vEvent with features that we have not seen yet.
  *    For example, maybe there is a vertical edge which passes just to
  *    the right of vEvent; we would like to splice vEvent into this edge.
  *
  * However, we don't want to connect vEvent to just any vertex.  We don''t
  * want the new edge to cross any other edges; otherwise we will create
  * intersection vertices even when the input data had no self-intersections.
  * (This is a bad thing; if the user's input data has no intersections,
  * we don't want to generate any false intersections ourselves.)
  *
  * Our eventual goal is to connect vEvent to the leftmost unprocessed
  * vertex of the combined region (the union of regUp and regLo).
  * But because of unseen vertices with all right-going edges, and also
  * new vertices which may be created by edge intersections, we don''t
  * know where that leftmost unprocessed vertex is.  In the meantime, we
  * connect vEvent to the closest vertex of either chain, and mark the region
  * as "fixUpperEdge".  This flag says to delete and reconnect this edge
  * to the next processed vertex on the boundary of the combined region.
  * Quite possibly the vertex we connected to will turn out to be the
  * closest one, in which case we won''t need to make any changes.
  */
 {
     GLUhalfEdge *eNew;
     GLUhalfEdge *eTopLeft = eBottomLeft->Onext;
     ActiveRegion *regLo   = RegionBelow(regUp);
     GLUhalfEdge *eUp      = regUp->eUp;
     GLUhalfEdge *eLo      = regLo->eUp;
     int degenerate        = FALSE;
 
     if (eUp->Dst != eLo->Dst)
     {
         (void)CheckForIntersect(tess, regUp);
     }
 
     /* Possible new degeneracies: upper or lower edge of regUp may pass
    * through vEvent, or may coincide with new intersection vertex
    */
     if (VertEq(eUp->Org, tess->event))
     {
         if (!__gl_meshSplice(eTopLeft->Oprev, eUp))
             longjmp(tess->env, 1);
         regUp = TopLeftRegion(regUp);
         if (regUp == NULL)
             longjmp(tess->env, 1);
         eTopLeft = RegionBelow(regUp)->eUp;
         FinishLeftRegions(tess, RegionBelow(regUp), regLo);
         degenerate = TRUE;
     }
     if (VertEq(eLo->Org, tess->event))
     {
         if (!__gl_meshSplice(eBottomLeft, eLo->Oprev))
             longjmp(tess->env, 1);
         eBottomLeft = FinishLeftRegions(tess, regLo, NULL);
         degenerate  = TRUE;
     }
     if (degenerate)
     {
         AddRightEdges(tess, regUp, eBottomLeft->Onext, eTopLeft, eTopLeft, TRUE);
         return;
     }
 
     /* Non-degenerate situation -- need to add a temporary, fixable edge.
    * Connect to the closer of eLo->Org, eUp->Org.
    */
     if (VertLeq(eLo->Org, eUp->Org))
     {
         eNew = eLo->Oprev;
     }
     else
     {
         eNew = eUp;
     }
     eNew = __gl_meshConnect(eBottomLeft->Lprev, eNew);
     if (eNew == NULL)
         longjmp(tess->env, 1);
 
     /* Prevent cleanup, otherwise eNew might disappear before we've even
    * had a chance to mark it as a temporary edge.
    */
     AddRightEdges(tess, regUp, eNew, eNew->Onext, eNew->Onext, FALSE);
     eNew->Sym->activeRegion->fixUpperEdge = TRUE;
     WalkDirtyRegions(tess, regUp);
 }
 
 /* Because vertices at exactly the same location are merged together
  * before we process the sweep event, some degenerate cases can't occur.
  * However if someone eventually makes the modifications required to
  * merge features which are close together, the cases below marked
  * TOLERANCE_NONZERO will be useful.  They were debugged before the
  * code to merge identical vertices in the main loop was added.
  */
 #define TOLERANCE_NONZERO FALSE
 
 static void ConnectLeftDegenerate(GLUtesselator *tess, ActiveRegion *regUp, GLUvertex *vEvent)
 /*
  * The event vertex lies exacty on an already-processed edge or vertex.
  * Adding the new vertex involves splicing it into the already-processed
  * part of the mesh.
  */
 {
     GLUhalfEdge *e, *eTopLeft, *eTopRight, *eLast;
     ActiveRegion *reg;
 
     e = regUp->eUp;
     if (VertEq(e->Org, vEvent))
     {
         /* e->Org is an unprocessed vertex - just combine them, and wait
      * for e->Org to be pulled from the queue
      */
         assert(TOLERANCE_NONZERO);
         SpliceMergeVertices(tess, e, vEvent->anEdge);
         return;
     }
 
     if (!VertEq(e->Dst, vEvent))
     {
         /* General case -- splice vEvent into edge e which passes through it */
         if (__gl_meshSplitEdge(e->Sym) == NULL)
             longjmp(tess->env, 1);
         if (regUp->fixUpperEdge)
         {
             /* This edge was fixable -- delete unused portion of original edge */
             if (!__gl_meshDelete(e->Onext))
                 longjmp(tess->env, 1);
             regUp->fixUpperEdge = FALSE;
         }
         if (!__gl_meshSplice(vEvent->anEdge, e))
             longjmp(tess->env, 1);
         SweepEvent(tess, vEvent); /* recurse */
         return;
     }
 
     /* vEvent coincides with e->Dst, which has already been processed.
    * Splice in the additional right-going edges.
    */
     assert(TOLERANCE_NONZERO);
     regUp     = TopRightRegion(regUp);
     reg       = RegionBelow(regUp);
     eTopRight = reg->eUp->Sym;
     eTopLeft = eLast = eTopRight->Onext;
     if (reg->fixUpperEdge)
     {
         /* Here e->Dst has only a single fixable edge going right.
      * We can delete it since now we have some real right-going edges.
      */
         assert(eTopLeft != eTopRight); /* there are some left edges too */
         DeleteRegion(tess, reg);
         if (!__gl_meshDelete(eTopRight))
             longjmp(tess->env, 1);
         eTopRight = eTopLeft->Oprev;
     }
     if (!__gl_meshSplice(vEvent->anEdge, eTopRight))
         longjmp(tess->env, 1);
     if (!EdgeGoesLeft(eTopLeft))
     {
         /* e->Dst had no left-going edges -- indicate this to AddRightEdges() */
         eTopLeft = NULL;
     }
     AddRightEdges(tess, regUp, eTopRight->Onext, eLast, eTopLeft, TRUE);
 }
 
 static void ConnectLeftVertex(GLUtesselator *tess, GLUvertex *vEvent)
 /*
  * Purpose: connect a "left" vertex (one where both edges go right)
  * to the processed portion of the mesh.  Let R be the active region
  * containing vEvent, and let U and L be the upper and lower edge
  * chains of R.  There are two possibilities:
  *
  * - the normal case: split R into two regions, by connecting vEvent to
  *   the rightmost vertex of U or L lying to the left of the sweep line
  *
  * - the degenerate case: if vEvent is close enough to U or L, we
  *   merge vEvent into that edge chain.  The subcases are:
  *  - merging with the rightmost vertex of U or L
  *  - merging with the active edge of U or L
  *  - merging with an already-processed portion of U or L
  */
 {
     ActiveRegion *regUp, *regLo, *reg;
     GLUhalfEdge *eUp, *eLo, *eNew;
     ActiveRegion tmp;
 
     /* assert( vEvent->anEdge->Onext->Onext == vEvent->anEdge ); */
 
     /* Get a pointer to the active region containing vEvent */
     tmp.eUp = vEvent->anEdge->Sym;
     /* __GL_DICTLISTKEY */ /* __gl_dictListSearch */
     regUp = (ActiveRegion *)dictKey(dictSearch(tess->dict, &tmp));
     regLo = RegionBelow(regUp);
     eUp   = regUp->eUp;
     eLo   = regLo->eUp;
 
     /* Try merging with U or L first */
     if (EdgeSign(eUp->Dst, vEvent, eUp->Org) == 0)
     {
         ConnectLeftDegenerate(tess, regUp, vEvent);
         return;
     }
 
     /* Connect vEvent to rightmost processed vertex of either chain.
    * e->Dst is the vertex that we will connect to vEvent.
    */
     reg = VertLeq(eLo->Dst, eUp->Dst) ? regUp : regLo;
 
     if (regUp->inside || reg->fixUpperEdge)
     {
         if (reg == regUp)
         {
             eNew = __gl_meshConnect(vEvent->anEdge->Sym, eUp->Lnext);
             if (eNew == NULL)
                 longjmp(tess->env, 1);
         }
         else
         {
             GLUhalfEdge *tempHalfEdge = __gl_meshConnect(eLo->Dnext, vEvent->anEdge);
             if (tempHalfEdge == NULL)
                 longjmp(tess->env, 1);
 
             eNew = tempHalfEdge->Sym;
         }
         if (reg->fixUpperEdge)
         {
             if (!FixUpperEdge(reg, eNew))
                 longjmp(tess->env, 1);
         }
         else
         {
             ComputeWinding(tess, AddRegionBelow(tess, regUp, eNew));
         }
         SweepEvent(tess, vEvent);
     }
     else
     {
         /* The new vertex is in a region which does not belong to the polygon.
      * We don''t need to connect this vertex to the rest of the mesh.
      */
         AddRightEdges(tess, regUp, vEvent->anEdge, vEvent->anEdge, NULL, TRUE);
     }
 }
 
 static void SweepEvent(GLUtesselator *tess, GLUvertex *vEvent)
 /*
  * Does everything necessary when the sweep line crosses a vertex.
  * Updates the mesh and the edge dictionary.
  */
 {
     ActiveRegion *regUp, *reg;
     GLUhalfEdge *e, *eTopLeft, *eBottomLeft;
 
     tess->event = vEvent; /* for access in EdgeLeq() */
     DebugEvent(tess);
 
     /* Check if this vertex is the right endpoint of an edge that is
    * already in the dictionary.  In this case we don't need to waste
    * time searching for the location to insert new edges.
    */
     e = vEvent->anEdge;
     while (e->activeRegion == NULL)
     {
         e = e->Onext;
         if (e == vEvent->anEdge)
         {
             /* All edges go right -- not incident to any processed edges */
             ConnectLeftVertex(tess, vEvent);
             return;
         }
     }
 
     /* Processing consists of two phases: first we "finish" all the
    * active regions where both the upper and lower edges terminate
    * at vEvent (ie. vEvent is closing off these regions).
    * We mark these faces "inside" or "outside" the polygon according
    * to their winding number, and delete the edges from the dictionary.
    * This takes care of all the left-going edges from vEvent.
    */
     regUp = TopLeftRegion(e->activeRegion);
     if (regUp == NULL)
         longjmp(tess->env, 1);
     reg         = RegionBelow(regUp);
     eTopLeft    = reg->eUp;
     eBottomLeft = FinishLeftRegions(tess, reg, NULL);
 
     /* Next we process all the right-going edges from vEvent.  This
    * involves adding the edges to the dictionary, and creating the
    * associated "active regions" which record information about the
    * regions between adjacent dictionary edges.
    */
     if (eBottomLeft->Onext == eTopLeft)
     {
         /* No right-going edges -- add a temporary "fixable" edge */
         ConnectRightVertex(tess, regUp, eBottomLeft);
     }
     else
     {
         AddRightEdges(tess, regUp, eBottomLeft->Onext, eTopLeft, eTopLeft, TRUE);
     }
 }
 
 /* Make the sentinel coordinates big enough that they will never be
  * merged with real input features.  (Even with the largest possible
  * input contour and the maximum tolerance of 1.0, no merging will be
  * done with coordinates larger than 3 * GLU_TESS_MAX_COORD).
  */
 #define SENTINEL_COORD (4 * GLU_TESS_MAX_COORD)
 
 static void AddSentinel(GLUtesselator *tess, GLdouble t)
 /*
  * We add two sentinel edges above and below all other edges,
  * to avoid special cases at the top and bottom.
  */
 {
     GLUhalfEdge *e;
     ActiveRegion *reg = (ActiveRegion *)memAlloc(sizeof(ActiveRegion));
     if (reg == NULL)
         longjmp(tess->env, 1);
 
     e = __gl_meshMakeEdge(tess->mesh);
     if (e == NULL)
         longjmp(tess->env, 1);
 
     e->Org->s   = SENTINEL_COORD;
     e->Org->t   = t;
     e->Dst->s   = -SENTINEL_COORD;
     e->Dst->t   = t;
     tess->event = e->Dst; /* initialize it */
 
     reg->eUp           = e;
     reg->windingNumber = 0;
     reg->inside        = FALSE;
     reg->fixUpperEdge  = FALSE;
     reg->sentinel      = TRUE;
     reg->dirty         = FALSE;
     reg->nodeUp        = dictInsert(tess->dict, reg); /* __gl_dictListInsertBefore */
     if (reg->nodeUp == NULL)
         longjmp(tess->env, 1);
 }
 
 static void InitEdgeDict(GLUtesselator *tess)
 /*
  * We maintain an ordering of edge intersections with the sweep line.
  * This order is maintained in a dynamic dictionary.
  */
 {
     /* __gl_dictListNewDict */
     tess->dict = dictNewDict(tess, (int (*)(void *, DictKey, DictKey))EdgeLeq);
     if (tess->dict == NULL)
         longjmp(tess->env, 1);
 
     AddSentinel(tess, -SENTINEL_COORD);
     AddSentinel(tess, SENTINEL_COORD);
 }
 
 static void DoneEdgeDict(GLUtesselator *tess)
 {
     ActiveRegion *reg;
 #ifndef NDEBUG
     int fixedEdges = 0;
 #endif
 
     /* __GL_DICTLISTKEY */ /* __GL_DICTLISTMIN */
     while ((reg = (ActiveRegion *)dictKey(dictMin(tess->dict))) != NULL)
     {
         /*
      * At the end of all processing, the dictionary should contain
      * only the two sentinel edges, plus at most one "fixable" edge
      * created by ConnectRightVertex().
      */
         if (!reg->sentinel)
         {
             assert(reg->fixUpperEdge);
             assert(++fixedEdges == 1);
         }
         assert(reg->windingNumber == 0);
         DeleteRegion(tess, reg);
         /*    __gl_meshDelete( reg->eUp );*/
     }
     dictDeleteDict(tess->dict); /* __gl_dictListDeleteDict */
 }
 
 static void RemoveDegenerateEdges(GLUtesselator *tess)
 /*
  * Remove zero-length edges, and contours with fewer than 3 vertices.
  */
 {
     GLUhalfEdge *e, *eNext, *eLnext;
     GLUhalfEdge *eHead = &tess->mesh->eHead;
 
     /*LINTED*/
     for (e = eHead->next; e != eHead; e = eNext)
     {
         eNext  = e->next;
         eLnext = e->Lnext;
 
         if (VertEq(e->Org, e->Dst) && e->Lnext->Lnext != e)
         {
             /* Zero-length edge, contour has at least 3 edges */
 
             SpliceMergeVertices(tess, eLnext, e); /* deletes e->Org */
             if (!__gl_meshDelete(e))
                 longjmp(tess->env, 1); /* e is a self-loop */
             e      = eLnext;
             eLnext = e->Lnext;
         }
         if (eLnext->Lnext == e)
         {
             /* Degenerate contour (one or two edges) */
 
             if (eLnext != e)
             {
                 if (eLnext == eNext || eLnext == eNext->Sym)
                 {
                     eNext = eNext->next;
                 }
                 if (!__gl_meshDelete(eLnext))
                     longjmp(tess->env, 1);
             }
             if (e == eNext || e == eNext->Sym)
             {
                 eNext = eNext->next;
             }
             if (!__gl_meshDelete(e))
                 longjmp(tess->env, 1);
         }
     }
 }
 
 static int InitPriorityQ(GLUtesselator *tess)
 /*
  * Insert all vertices into the priority queue which determines the
  * order in which vertices cross the sweep line.
  */
 {
     PriorityQ *pq;
     GLUvertex *v, *vHead;
 
     /* __gl_pqSortNewPriorityQ */
     pq = tess->pq = pqNewPriorityQ((int (*)(PQkey, PQkey))__gl_vertLeq);
     if (pq == NULL)
         return 0;
 
     vHead = &tess->mesh->vHead;
     for (v = vHead->next; v != vHead; v = v->next)
     {
         v->pqHandle = pqInsert(pq, v); /* __gl_pqSortInsert */
         if (v->pqHandle == LONG_MAX)
             break;
     }
     if (v != vHead || !pqInit(pq))
     {                                /* __gl_pqSortInit */
         pqDeletePriorityQ(tess->pq); /* __gl_pqSortDeletePriorityQ */
         tess->pq = NULL;
         return 0;
     }
 
     return 1;
 }
 
 static void DonePriorityQ(GLUtesselator *tess)
 {
     pqDeletePriorityQ(tess->pq); /* __gl_pqSortDeletePriorityQ */
 }
 
 static int RemoveDegenerateFaces(GLUmesh *mesh)
 /*
  * Delete any degenerate faces with only two edges.  WalkDirtyRegions()
  * will catch almost all of these, but it won't catch degenerate faces
  * produced by splice operations on already-processed edges.
  * The two places this can happen are in FinishLeftRegions(), when
  * we splice in a "temporary" edge produced by ConnectRightVertex(),
  * and in CheckForLeftSplice(), where we splice already-processed
  * edges to ensure that our dictionary invariants are not violated
  * by numerical errors.
  *
  * In both these cases it is *very* dangerous to delete the offending
  * edge at the time, since one of the routines further up the stack
  * will sometimes be keeping a pointer to that edge.
  */
 {
     GLUface *f, *fNext;
     GLUhalfEdge *e;
 
     /*LINTED*/
     for (f = mesh->fHead.next; f != &mesh->fHead; f = fNext)
     {
         fNext = f->next;
         e     = f->anEdge;
         assert(e->Lnext != e);
 
         if (e->Lnext->Lnext == e)
         {
             /* A face with only two edges */
             AddWinding(e->Onext, e);
             if (!__gl_meshDelete(e))
                 return 0;
         }
     }
     return 1;
 }
 
 int __gl_computeInterior(GLUtesselator *tess)
 /*
  * __gl_computeInterior( tess ) computes the planar arrangement specified
  * by the given contours, and further subdivides this arrangement
  * into regions.  Each region is marked "inside" if it belongs
  * to the polygon, according to the rule given by tess->windingRule.
  * Each interior region is guaranteed be monotone.
  */
 {
     GLUvertex *v, *vNext;
 
     tess->fatalError = FALSE;
 
     /* Each vertex defines an event for our sweep line.  Start by inserting
    * all the vertices in a priority queue.  Events are processed in
    * lexicographic order, ie.
    *
    *    e1 < e2  iff  e1.x < e2.x || (e1.x == e2.x && e1.y < e2.y)
    */
     RemoveDegenerateEdges(tess);
     if (!InitPriorityQ(tess))
         return 0; /* if error */
     InitEdgeDict(tess);
 
     /* __gl_pqSortExtractMin */
     while ((v = (GLUvertex *)pqExtractMin(tess->pq)) != NULL)
     {
         for (;;)
         {
             vNext = (GLUvertex *)pqMinimum(tess->pq); /* __gl_pqSortMinimum */
             if (vNext == NULL || !VertEq(vNext, v))
                 break;
 
             /* Merge together all vertices at exactly the same location.
        * This is more efficient than processing them one at a time,
        * simplifies the code (see ConnectLeftDegenerate), and is also
        * important for correct handling of certain degenerate cases.
        * For example, suppose there are two identical edges A and B
        * that belong to different contours (so without this code they would
        * be processed by separate sweep events).  Suppose another edge C
        * crosses A and B from above.  When A is processed, we split it
        * at its intersection point with C.  However this also splits C,
        * so when we insert B we may compute a slightly different
        * intersection point.  This might leave two edges with a small
        * gap between them.  This kind of error is especially obvious
        * when using boundary extraction (GLU_TESS_BOUNDARY_ONLY).
        */
             vNext = (GLUvertex *)pqExtractMin(tess->pq); /* __gl_pqSortExtractMin*/
             SpliceMergeVertices(tess, v->anEdge, vNext->anEdge);
         }
         SweepEvent(tess, v);
     }
 
     /* Set tess->event for debugging purposes */
     /* __GL_DICTLISTKEY */ /* __GL_DICTLISTMIN */
     tess->event = ((ActiveRegion *)dictKey(dictMin(tess->dict)))->eUp->Org;
     DebugEvent(tess);
     DoneEdgeDict(tess);
     DonePriorityQ(tess);
 
     if (!RemoveDegenerateFaces(tess->mesh))
         return 0;
     __gl_meshCheckMesh(tess->mesh);
 
     return 1;
 }