SGI SI GLU library

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diff --git a/src/glu/sgi/libtess/sweep.c b/src/glu/sgi/libtess/sweep.c
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+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+** 
+** http://oss.sgi.com/projects/FreeB
+** 
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+** 
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+** 
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+**
+*/
+/*
+** Author: Eric Veach, July 1994.
+**
+** $Date: 2001/03/17 00:25:41 $ $Revision: 1.1 $
+** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libtess/sweep.c,v 1.1 2001/03/17 00:25:41 brianp Exp $
+*/
+
+#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"
+
+#define TRUE 1
+#define FALSE 0
+
+#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.)
+ */
+
+#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*/
+}
+
+
+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 idential 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;
+  int fixedEdges = 0;
+
+  /* __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;
+}