mesh

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// see license file for original license.
 
#ifndef tools_glutess_mesh
#define tools_glutess_mesh
 
#include "_glu"
 
typedef struct GLUmesh GLUmesh; 
 
typedef struct GLUvertex GLUvertex;
typedef struct GLUface GLUface;
typedef struct GLUhalfEdge GLUhalfEdge;
 
typedef struct ActiveRegion ActiveRegion;   /* Internal data */
 
/* The mesh structure is similar in spirit, notation, and operations
 * to the "quad-edge" structure (see L. Guibas and J. Stolfi, Primitives
 * for the manipulation of general subdivisions and the computation of
 * Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985).
 * For a simplified description, see the course notes for CS348a,
 * "Mathematical Foundations of Computer Graphics", available at the
 * Stanford bookstore (and taught during the fall quarter).
 * The implementation also borrows a tiny subset of the graph-based approach
 * use in Mantyla's Geometric Work Bench (see M. Mantyla, An Introduction
 * to Sold Modeling, Computer Science Press, Rockville, Maryland, 1988).
 *
 * The fundamental data structure is the "half-edge".  Two half-edges
 * go together to make an edge, but they point in opposite directions.
 * Each half-edge has a pointer to its mate (the "symmetric" half-edge Sym),
 * its origin vertex (Org), the face on its left side (Lface), and the
 * adjacent half-edges in the CCW direction around the origin vertex
 * (Onext) and around the left face (Lnext).  There is also a "next"
 * pointer for the global edge list (see below).
 *
 * The notation used for mesh navigation:
 *  Sym   = the mate of a half-edge (same edge, but opposite direction)
 *  Onext = edge CCW around origin vertex (keep same origin)
 *  Dnext = edge CCW around destination vertex (keep same dest)
 *  Lnext = edge CCW around left face (dest becomes new origin)
 *  Rnext = edge CCW around right face (origin becomes new dest)
 *
 * "prev" means to substitute CW for CCW in the definitions above.
 *
 * The mesh keeps global lists of all vertices, faces, and edges,
 * stored as doubly-linked circular lists with a dummy header node.
 * The mesh stores pointers to these dummy headers (vHead, fHead, eHead).
 *
 * The circular edge list is special; since half-edges always occur
 * in pairs (e and e->Sym), each half-edge stores a pointer in only
 * one direction.  Starting at eHead and following the e->next pointers
 * will visit each *edge* once (ie. e or e->Sym, but not both).
 * e->Sym stores a pointer in the opposite direction, thus it is
 * always true that e->Sym->next->Sym->next == e.
 *
 * Each vertex has a pointer to next and previous vertices in the
 * circular list, and a pointer to a half-edge with this vertex as
 * the origin (NULL if this is the dummy header).  There is also a
 * field "data" for client data.
 *
 * Each face has a pointer to the next and previous faces in the
 * circular list, and a pointer to a half-edge with this face as
 * the left face (NULL if this is the dummy header).  There is also
 * a field "data" for client data.
 *
 * Note that what we call a "face" is really a loop; faces may consist
 * of more than one loop (ie. not simply connected), but there is no
 * record of this in the data structure.  The mesh may consist of
 * several disconnected regions, so it may not be possible to visit
 * the entire mesh by starting at a half-edge and traversing the edge
 * structure.
 *
 * The mesh does NOT support isolated vertices; a vertex is deleted along
 * with its last edge.  Similarly when two faces are merged, one of the
 * faces is deleted (see __gl_meshDelete below).  For mesh operations,
 * all face (loop) and vertex pointers must not be NULL.  However, once
 * mesh manipulation is finished, __gl_MeshZapFace can be used to delete
 * faces of the mesh, one at a time.  All external faces can be "zapped"
 * before the mesh is returned to the client; then a NULL face indicates
 * a region which is not part of the output polygon.
 */
 
struct GLUvertex {
  GLUvertex *next;      /* next vertex (never NULL) */
  GLUvertex *prev;      /* previous vertex (never NULL) */
  GLUhalfEdge   *anEdge;    /* a half-edge with this origin */
  void      *data;      /* client's data */
 
  /* Internal data (keep hidden) */
  GLUdouble coords[3];  /* vertex location in 3D */
  GLUdouble s, t;       /* projection onto the sweep plane */
  long      pqHandle;   /* to allow deletion from priority queue */
};
 
struct GLUface {
  GLUface   *next;      /* next face (never NULL) */
  GLUface   *prev;      /* previous face (never NULL) */
  GLUhalfEdge   *anEdge;    /* a half edge with this left face */
  void      *data;      /* room for client's data */
 
  /* Internal data (keep hidden) */
  GLUface   *trail;     /* "stack" for conversion to strips */
  GLUboolean    marked;     /* flag for conversion to strips */
  GLUboolean    inside;     /* this face is in the polygon interior */
};
 
struct GLUhalfEdge {
  GLUhalfEdge   *next;      /* doubly-linked list (prev==Sym->next) */
  GLUhalfEdge   *Sym;       /* same edge, opposite direction */
  GLUhalfEdge   *Onext;     /* next edge CCW around origin */
  GLUhalfEdge   *Lnext;     /* next edge CCW around left face */
  GLUvertex *Org;       /* origin vertex (Overtex too long) */
  GLUface   *Lface;     /* left face */
 
  /* Internal data (keep hidden) */
  ActiveRegion  *activeRegion;  /* a region with this upper edge (sweep.c) */
  int       winding;    /* change in winding number when crossing
                                   from the right face to the left face */
};
 
#define Rface   Sym->Lface
#define Dst Sym->Org
 
#define Oprev   Sym->Lnext
#define Lprev   Onext->Sym
#define Dprev   Lnext->Sym
#define Rprev   Sym->Onext
#define Dnext   Rprev->Sym  /* 3 pointers */
#define Rnext   Oprev->Sym  /* 3 pointers */
 
 
struct GLUmesh {
  GLUvertex vHead;      /* dummy header for vertex list */
  GLUface   fHead;      /* dummy header for face list */
  GLUhalfEdge   eHead;      /* dummy header for edge list */
  GLUhalfEdge   eHeadSym;   /* and its symmetric counterpart */
};
 
/* The mesh operations below have three motivations: completeness,
 * convenience, and efficiency.  The basic mesh operations are MakeEdge,
 * Splice, and Delete.  All the other edge operations can be implemented
 * in terms of these.  The other operations are provided for convenience
 * and/or efficiency.
 *
 * When a face is split or a vertex is added, they are inserted into the
 * global list *before* the existing vertex or face (ie. e->Org or e->Lface).
 * This makes it easier to process all vertices or faces in the global lists
 * without worrying about processing the same data twice.  As a convenience,
 * when a face is split, the "inside" flag is copied from the old face.
 * Other internal data (v->data, v->activeRegion, f->data, f->marked,
 * f->trail, e->winding) is set to zero.
 *
 * ********************** Basic Edge Operations **************************
 *
 * __gl_meshMakeEdge( mesh ) creates one edge, two vertices, and a loop.
 * The loop (face) consists of the two new half-edges.
 *
 * __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
 * mesh connectivity and topology.  It changes the mesh so that
 *  eOrg->Onext <- OLD( eDst->Onext )
 *  eDst->Onext <- OLD( eOrg->Onext )
 * where OLD(...) means the value before the meshSplice operation.
 *
 * This can have two effects on the vertex structure:
 *  - if eOrg->Org != eDst->Org, the two vertices are merged together
 *  - if eOrg->Org == eDst->Org, the origin is split into two vertices
 * In both cases, eDst->Org is changed and eOrg->Org is untouched.
 *
 * Similarly (and independently) for the face structure,
 *  - if eOrg->Lface == eDst->Lface, one loop is split into two
 *  - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
 * In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
 *
 * __gl_meshDelete( eDel ) removes the edge eDel.  There are several cases:
 * if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
 * eDel->Lface is deleted.  Otherwise, we are splitting one loop into two;
 * the newly created loop will contain eDel->Dst.  If the deletion of eDel
 * would create isolated vertices, those are deleted as well.
 *
 * ********************** Other Edge Operations **************************
 *
 * __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
 * eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
 * eOrg and eNew will have the same left face.
 *
 * __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
 * such that eNew == eOrg->Lnext.  The new vertex is eOrg->Dst == eNew->Org.
 * eOrg and eNew will have the same left face.
 *
 * __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
 * to eDst->Org, and returns the corresponding half-edge eNew.
 * If eOrg->Lface == eDst->Lface, this splits one loop into two,
 * and the newly created loop is eNew->Lface.  Otherwise, two disjoint
 * loops are merged into one, and the loop eDst->Lface is destroyed.
 *
 * ************************ Other Operations *****************************
 *
 * __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
 * and no loops (what we usually call a "face").
 *
 * __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
 * both meshes, and returns the new mesh (the old meshes are destroyed).
 *
 * __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
 *
 * __gl_meshZapFace( fZap ) destroys a face and removes it from the
 * global face list.  All edges of fZap will have a NULL pointer as their
 * left face.  Any edges which also have a NULL pointer as their right face
 * are deleted entirely (along with any isolated vertices this produces).
 * An entire mesh can be deleted by zapping its faces, one at a time,
 * in any order.  Zapped faces cannot be used in further mesh operations!
 *
 * __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
 */
 
 
//#include "gluos"
#include <cstddef>
#include <cassert>
#include "memalloc"
 
inline/*static*/ GLUvertex *static_allocVertex()
{
   return (GLUvertex *)memAlloc( sizeof( GLUvertex ));
}
 
inline/*static*/ GLUface *static_allocFace()
{
   return (GLUface *)memAlloc( sizeof( GLUface ));
}
 
/************************ Utility Routines ************************/
 
/* Allocate and free half-edges in pairs for efficiency.
 * The *only* place that should use this fact is allocation/free.
 */
typedef struct { GLUhalfEdge e, eSym; } EdgePair;
 
/* MakeEdge creates a new pair of half-edges which form their own loop.
 * No vertex or face structures are allocated, but these must be assigned
 * before the current edge operation is completed.
 */
inline/*static*/ GLUhalfEdge *static_MakeEdge( GLUhalfEdge *eNext )
{
  GLUhalfEdge *e;
  GLUhalfEdge *eSym;
  GLUhalfEdge *ePrev;
  EdgePair *pair = (EdgePair *)memAlloc( sizeof( EdgePair ));
  if (pair == NULL) return NULL;
 
  e = &pair->e;
  eSym = &pair->eSym;
 
  /* Make sure eNext points to the first edge of the edge pair */
  if( eNext->Sym < eNext ) { eNext = eNext->Sym; }
 
  /* Insert in circular doubly-linked list before eNext.
   * Note that the prev pointer is stored in Sym->next.
   */
  ePrev = eNext->Sym->next;
  eSym->next = ePrev;
  ePrev->Sym->next = e;
  e->next = eNext;
  eNext->Sym->next = eSym;
 
  e->Sym = eSym;
  e->Onext = e;
  e->Lnext = eSym;
  e->Org = NULL;
  e->Lface = NULL;
  e->winding = 0;
  e->activeRegion = NULL;
 
  eSym->Sym = e;
  eSym->Onext = eSym;
  eSym->Lnext = e;
  eSym->Org = NULL;
  eSym->Lface = NULL;
  eSym->winding = 0;
  eSym->activeRegion = NULL;
 
  return e;
}
 
/* Splice( a, b ) is best described by the Guibas/Stolfi paper or the
 * CS348a notes (see mesh.h).  Basically it modifies the mesh so that
 * a->Onext and b->Onext are exchanged.  This can have various effects
 * depending on whether a and b belong to different face or vertex rings.
 * For more explanation see __gl_meshSplice() below.
 */
inline/*static*/ void static_Splice( GLUhalfEdge *a, GLUhalfEdge *b )
{
  GLUhalfEdge *aOnext = a->Onext;
  GLUhalfEdge *bOnext = b->Onext;
 
  aOnext->Sym->Lnext = b;
  bOnext->Sym->Lnext = a;
  a->Onext = bOnext;
  b->Onext = aOnext;
}
 
/* MakeVertex( newVertex, eOrig, vNext ) attaches a new vertex and makes it the
 * origin of all edges in the vertex loop to which eOrig belongs. "vNext" gives
 * a place to insert the new vertex in the global vertex list.  We insert
 * the new vertex *before* vNext so that algorithms which walk the vertex
 * list will not see the newly created vertices.
 */
inline/*static*/ void static_MakeVertex( GLUvertex *newVertex, 
            GLUhalfEdge *eOrig, GLUvertex *vNext )
{
  GLUhalfEdge *e;
  GLUvertex *vPrev;
  GLUvertex *vNew = newVertex;
 
  assert(vNew != NULL);
 
  /* insert in circular doubly-linked list before vNext */
  vPrev = vNext->prev;
  vNew->prev = vPrev;
  vPrev->next = vNew;
  vNew->next = vNext;
  vNext->prev = vNew;
 
  vNew->anEdge = eOrig;
  vNew->data = NULL;
  /* leave coords, s, t undefined */
 
  /* fix other edges on this vertex loop */
  e = eOrig;
  do {
    e->Org = vNew;
    e = e->Onext;
  } while( e != eOrig );
}
 
/* MakeFace( newFace, eOrig, fNext ) attaches a new face and makes it the left
 * face of all edges in the face loop to which eOrig belongs.  "fNext" gives
 * a place to insert the new face in the global face list.  We insert
 * the new face *before* fNext so that algorithms which walk the face
 * list will not see the newly created faces.
 */
inline/*static*/ void static_MakeFace( GLUface *newFace, GLUhalfEdge *eOrig, GLUface *fNext )
{
  GLUhalfEdge *e;
  GLUface *fPrev;
  GLUface *fNew = newFace;
 
  assert(fNew != NULL); 
 
  /* insert in circular doubly-linked list before fNext */
  fPrev = fNext->prev;
  fNew->prev = fPrev;
  fPrev->next = fNew;
  fNew->next = fNext;
  fNext->prev = fNew;
 
  fNew->anEdge = eOrig;
  fNew->data = NULL;
  fNew->trail = NULL;
  fNew->marked = TOOLS_GLU_FALSE;
 
  /* The new face is marked "inside" if the old one was.  This is a
   * convenience for the common case where a face has been split in two.
   */
  fNew->inside = fNext->inside;
 
  /* fix other edges on this face loop */
  e = eOrig;
  do {
    e->Lface = fNew;
    e = e->Lnext;
  } while( e != eOrig );
}
 
/* KillEdge( eDel ) destroys an edge (the half-edges eDel and eDel->Sym),
 * and removes from the global edge list.
 */
inline/*static*/ void static_KillEdge( GLUhalfEdge *eDel )
{
  GLUhalfEdge *ePrev, *eNext;
 
  /* Half-edges are allocated in pairs, see EdgePair above */
  if( eDel->Sym < eDel ) { eDel = eDel->Sym; }
 
  /* delete from circular doubly-linked list */
  eNext = eDel->next;
  ePrev = eDel->Sym->next;
  eNext->Sym->next = ePrev;
  ePrev->Sym->next = eNext;
 
  memFree( eDel );
}
 
 
/* KillVertex( vDel ) destroys a vertex and removes it from the global
 * vertex list.  It updates the vertex loop to point to a given new vertex.
 */
inline/*static*/ void static_KillVertex( GLUvertex *vDel, GLUvertex *newOrg )
{
  GLUhalfEdge *e, *eStart = vDel->anEdge;
  GLUvertex *vPrev, *vNext;
 
  /* change the origin of all affected edges */
  e = eStart;
  do {
    e->Org = newOrg;
    e = e->Onext;
  } while( e != eStart );
 
  /* delete from circular doubly-linked list */
  vPrev = vDel->prev;
  vNext = vDel->next;
  vNext->prev = vPrev;
  vPrev->next = vNext;
 
  memFree( vDel );
}
 
/* KillFace( fDel ) destroys a face and removes it from the global face
 * list.  It updates the face loop to point to a given new face.
 */
inline/*static*/ void static_KillFace( GLUface *fDel, GLUface *newLface )
{
  GLUhalfEdge *e, *eStart = fDel->anEdge;
  GLUface *fPrev, *fNext;
 
  /* change the left face of all affected edges */
  e = eStart;
  do {
    e->Lface = newLface;
    e = e->Lnext;
  } while( e != eStart );
 
  /* delete from circular doubly-linked list */
  fPrev = fDel->prev;
  fNext = fDel->next;
  fNext->prev = fPrev;
  fPrev->next = fNext;
 
  memFree( fDel );
}
 
 
/****************** Basic Edge Operations **********************/
 
/* __gl_meshMakeEdge creates one edge, two vertices, and a loop (face).
 * The loop consists of the two new half-edges.
 */
inline GLUhalfEdge *__gl_meshMakeEdge( GLUmesh *mesh )
{
  GLUvertex *newVertex1= static_allocVertex();
  GLUvertex *newVertex2= static_allocVertex();
  GLUface *newFace= static_allocFace();
  GLUhalfEdge *e;
 
  /* if any one is null then all get freed */
  if (newVertex1 == NULL || newVertex2 == NULL || newFace == NULL) {
     if (newVertex1 != NULL) memFree(newVertex1);
     if (newVertex2 != NULL) memFree(newVertex2);
     if (newFace != NULL) memFree(newFace);     
     return NULL;
  } 
 
  e = static_MakeEdge( &mesh->eHead );
  if (e == NULL) {
     memFree(newVertex1);
     memFree(newVertex2);
     memFree(newFace);
     return NULL;
  }
 
  static_MakeVertex( newVertex1, e, &mesh->vHead );
  static_MakeVertex( newVertex2, e->Sym, &mesh->vHead );
  static_MakeFace( newFace, e, &mesh->fHead );
  return e;
}
  
 
/* __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
 * mesh connectivity and topology.  It changes the mesh so that
 *  eOrg->Onext <- OLD( eDst->Onext )
 *  eDst->Onext <- OLD( eOrg->Onext )
 * where OLD(...) means the value before the meshSplice operation.
 *
 * This can have two effects on the vertex structure:
 *  - if eOrg->Org != eDst->Org, the two vertices are merged together
 *  - if eOrg->Org == eDst->Org, the origin is split into two vertices
 * In both cases, eDst->Org is changed and eOrg->Org is untouched.
 *
 * Similarly (and independently) for the face structure,
 *  - if eOrg->Lface == eDst->Lface, one loop is split into two
 *  - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
 * In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
 *
 * Some special cases:
 * If eDst == eOrg, the operation has no effect.
 * If eDst == eOrg->Lnext, the new face will have a single edge.
 * If eDst == eOrg->Lprev, the old face will have a single edge.
 * If eDst == eOrg->Onext, the new vertex will have a single edge.
 * If eDst == eOrg->Oprev, the old vertex will have a single edge.
 */
inline int __gl_meshSplice( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
{
  int joiningLoops = TOOLS_GLU_FALSE;
  int joiningVertices = TOOLS_GLU_FALSE;
 
  if( eOrg == eDst ) return 1;
 
  if( eDst->Org != eOrg->Org ) {
    /* We are merging two disjoint vertices -- destroy eDst->Org */
    joiningVertices = TOOLS_GLU_TRUE;
    static_KillVertex( eDst->Org, eOrg->Org );
  }
  if( eDst->Lface != eOrg->Lface ) {
    /* We are connecting two disjoint loops -- destroy eDst->Lface */
    joiningLoops = TOOLS_GLU_TRUE;
    static_KillFace( eDst->Lface, eOrg->Lface );
  }
 
  /* Change the edge structure */
  static_Splice( eDst, eOrg );
 
  if( ! joiningVertices ) {
    GLUvertex *newVertex= static_allocVertex();
    if (newVertex == NULL) return 0;
 
    /* We split one vertex into two -- the new vertex is eDst->Org.
     * Make sure the old vertex points to a valid half-edge.
     */
    static_MakeVertex( newVertex, eDst, eOrg->Org );
    eOrg->Org->anEdge = eOrg;
  }
  if( ! joiningLoops ) {
    GLUface *newFace= static_allocFace();  
    if (newFace == NULL) return 0;
 
    /* We split one loop into two -- the new loop is eDst->Lface.
     * Make sure the old face points to a valid half-edge.
     */
    static_MakeFace( newFace, eDst, eOrg->Lface );
    eOrg->Lface->anEdge = eOrg;
  }
 
  return 1;
}
 
 
/* __gl_meshDelete( eDel ) removes the edge eDel.  There are several cases:
 * if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
 * eDel->Lface is deleted.  Otherwise, we are splitting one loop into two;
 * the newly created loop will contain eDel->Dst.  If the deletion of eDel
 * would create isolated vertices, those are deleted as well.
 *
 * This function could be implemented as two calls to __gl_meshSplice
 * plus a few calls to memFree, but this would allocate and delete
 * unnecessary vertices and faces.
 */
inline int __gl_meshDelete( GLUhalfEdge *eDel )
{
  GLUhalfEdge *eDelSym = eDel->Sym;
  int joiningLoops = TOOLS_GLU_FALSE;
 
  /* First step: disconnect the origin vertex eDel->Org.  We make all
   * changes to get a consistent mesh in this "intermediate" state.
   */
  if( eDel->Lface != eDel->Rface ) {
    /* We are joining two loops into one -- remove the left face */
    joiningLoops = TOOLS_GLU_TRUE;
    static_KillFace( eDel->Lface, eDel->Rface );
    /* G.Barrand : note : Coverity says that there is a problem using eDel->Lface->anEdge in the below,
       but it appears that at the out of the upper static_KillFace() call (then here), eDel->Lface before
       (the pointer freeed) is not the same than after (then here). */
  }
 
  if( eDel->Onext == eDel ) {
    static_KillVertex( eDel->Org, NULL );
  } else {
    /* Make sure that eDel->Org and eDel->Rface point to valid half-edges */
    eDel->Rface->anEdge = eDel->Oprev;
    eDel->Org->anEdge = eDel->Onext;
 
    static_Splice( eDel, eDel->Oprev );
    if( ! joiningLoops ) {
      GLUface *newFace= static_allocFace();
      if (newFace == NULL) return 0; 
 
      /* We are splitting one loop into two -- create a new loop for eDel. */
      static_MakeFace( newFace, eDel, eDel->Lface );
    }
  }
 
  /* Claim: the mesh is now in a consistent state, except that eDel->Org
   * may have been deleted.  Now we disconnect eDel->Dst.
   */
  if( eDelSym->Onext == eDelSym ) {
    static_KillVertex( eDelSym->Org, NULL );
    static_KillFace( eDelSym->Lface, NULL );
  } else {
    /* Make sure that eDel->Dst and eDel->Lface point to valid half-edges */
    eDel->Lface->anEdge = eDelSym->Oprev;
    eDelSym->Org->anEdge = eDelSym->Onext;
    static_Splice( eDelSym, eDelSym->Oprev );
  }
 
  /* Any isolated vertices or faces have already been freed. */
  static_KillEdge( eDel );
 
  return 1;
}
 
 
/******************** Other Edge Operations **********************/
 
/* All these routines can be implemented with the basic edge
 * operations above.  They are provided for convenience and efficiency.
 */
 
 
/* __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
 * eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
 * eOrg and eNew will have the same left face.
 */
inline GLUhalfEdge *__gl_meshAddEdgeVertex( GLUhalfEdge *eOrg )
{
  GLUhalfEdge *eNewSym;
  GLUhalfEdge *eNew = static_MakeEdge( eOrg );
  if (eNew == NULL) return NULL;
 
  eNewSym = eNew->Sym;
 
  /* Connect the new edge appropriately */
  static_Splice( eNew, eOrg->Lnext );
 
  /* Set the vertex and face information */
  eNew->Org = eOrg->Dst;
  {
    GLUvertex *newVertex= static_allocVertex();
    if (newVertex == NULL) return NULL;
 
    static_MakeVertex( newVertex, eNewSym, eNew->Org );
  }
  eNew->Lface = eNewSym->Lface = eOrg->Lface;
 
  return eNew;
}
 
 
/* __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
 * such that eNew == eOrg->Lnext.  The new vertex is eOrg->Dst == eNew->Org.
 * eOrg and eNew will have the same left face.
 */
inline GLUhalfEdge *__gl_meshSplitEdge( GLUhalfEdge *eOrg )
{
  GLUhalfEdge *eNew;
  GLUhalfEdge *tempHalfEdge= __gl_meshAddEdgeVertex( eOrg );
  if (tempHalfEdge == NULL) return NULL;
 
  eNew = tempHalfEdge->Sym;
 
  /* Disconnect eOrg from eOrg->Dst and connect it to eNew->Org */
  static_Splice( eOrg->Sym, eOrg->Sym->Oprev );
  static_Splice( eOrg->Sym, eNew );
 
  /* Set the vertex and face information */
  eOrg->Dst = eNew->Org;
  eNew->Dst->anEdge = eNew->Sym;    /* may have pointed to eOrg->Sym */
  eNew->Rface = eOrg->Rface;
  eNew->winding = eOrg->winding;    /* copy old winding information */
  eNew->Sym->winding = eOrg->Sym->winding;
 
  return eNew;
}
 
 
/* __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
 * to eDst->Org, and returns the corresponding half-edge eNew.
 * If eOrg->Lface == eDst->Lface, this splits one loop into two,
 * and the newly created loop is eNew->Lface.  Otherwise, two disjoint
 * loops are merged into one, and the loop eDst->Lface is destroyed.
 *
 * If (eOrg == eDst), the new face will have only two edges.
 * If (eOrg->Lnext == eDst), the old face is reduced to a single edge.
 * If (eOrg->Lnext->Lnext == eDst), the old face is reduced to two edges.
 */
inline GLUhalfEdge *__gl_meshConnect( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
{
  GLUhalfEdge *eNewSym;
  int joiningLoops = TOOLS_GLU_FALSE;  
  GLUhalfEdge *eNew = static_MakeEdge( eOrg );
  if (eNew == NULL) return NULL;
 
  eNewSym = eNew->Sym;
 
  if( eDst->Lface != eOrg->Lface ) {
    /* We are connecting two disjoint loops -- destroy eDst->Lface */
    joiningLoops = TOOLS_GLU_TRUE;
    static_KillFace( eDst->Lface, eOrg->Lface );
  }
 
  /* Connect the new edge appropriately */
  static_Splice( eNew, eOrg->Lnext );
  static_Splice( eNewSym, eDst );
 
  /* Set the vertex and face information */
  eNew->Org = eOrg->Dst;
  eNewSym->Org = eDst->Org;
  eNew->Lface = eNewSym->Lface = eOrg->Lface;
 
  /* Make sure the old face points to a valid half-edge */
  eOrg->Lface->anEdge = eNewSym;
 
  if( ! joiningLoops ) {
    GLUface *newFace= static_allocFace();
    if (newFace == NULL) return NULL;
 
    /* We split one loop into two -- the new loop is eNew->Lface */
    static_MakeFace( newFace, eNew, eOrg->Lface );
  }
  return eNew;
}
 
 
/******************** Other Operations **********************/
 
/* __gl_meshZapFace( fZap ) destroys a face and removes it from the
 * global face list.  All edges of fZap will have a NULL pointer as their
 * left face.  Any edges which also have a NULL pointer as their right face
 * are deleted entirely (along with any isolated vertices this produces).
 * An entire mesh can be deleted by zapping its faces, one at a time,
 * in any order.  Zapped faces cannot be used in further mesh operations!
 */
inline void __gl_meshZapFace( GLUface *fZap )
{
  GLUhalfEdge *eStart = fZap->anEdge;
  GLUhalfEdge *e, *eNext, *eSym;
  GLUface *fPrev, *fNext;
 
  /* walk around face, deleting edges whose right face is also NULL */
  eNext = eStart->Lnext;
  do {
    e = eNext;
    eNext = e->Lnext;
 
    e->Lface = NULL;
    if( e->Rface == NULL ) {
      /* delete the edge -- see __gl_MeshDelete above */
 
      if( e->Onext == e ) {
    static_KillVertex( e->Org, NULL );
      } else {
    /* Make sure that e->Org points to a valid half-edge */
    e->Org->anEdge = e->Onext;
    static_Splice( e, e->Oprev );
      }
      eSym = e->Sym;
      if( eSym->Onext == eSym ) {
    static_KillVertex( eSym->Org, NULL );
      } else {
    /* Make sure that eSym->Org points to a valid half-edge */
    eSym->Org->anEdge = eSym->Onext;
    static_Splice( eSym, eSym->Oprev );
      }
      static_KillEdge( e );
    }
  } while( e != eStart );
 
  /* delete from circular doubly-linked list */
  fPrev = fZap->prev;
  fNext = fZap->next;
  fNext->prev = fPrev;
  fPrev->next = fNext;
 
  memFree( fZap );
}
 
 
/* __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
 * and no loops (what we usually call a "face").
 */
inline GLUmesh *__gl_meshNewMesh( void )
{
  GLUvertex *v;
  GLUface *f;
  GLUhalfEdge *e;
  GLUhalfEdge *eSym;
  GLUmesh *mesh = (GLUmesh *)memAlloc( sizeof( GLUmesh ));
  if (mesh == NULL) {
     return NULL;
  }
  
  v = &mesh->vHead;
  f = &mesh->fHead;
  e = &mesh->eHead;
  eSym = &mesh->eHeadSym;
 
  v->next = v->prev = v;
  v->anEdge = NULL;
  v->data = NULL;
 
  f->next = f->prev = f;
  f->anEdge = NULL;
  f->data = NULL;
  f->trail = NULL;
  f->marked = TOOLS_GLU_FALSE;
  f->inside = TOOLS_GLU_FALSE;
 
  e->next = e;
  e->Sym = eSym;
  e->Onext = NULL;
  e->Lnext = NULL;
  e->Org = NULL;
  e->Lface = NULL;
  e->winding = 0;
  e->activeRegion = NULL;
 
  eSym->next = eSym;
  eSym->Sym = e;
  eSym->Onext = NULL;
  eSym->Lnext = NULL;
  eSym->Org = NULL;
  eSym->Lface = NULL;
  eSym->winding = 0;
  eSym->activeRegion = NULL;
 
  return mesh;
}
 
 
/* __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
 * both meshes, and returns the new mesh (the old meshes are destroyed).
 */
inline GLUmesh *__gl_meshUnion( GLUmesh *mesh1, GLUmesh *mesh2 )
{
  GLUface *f1 = &mesh1->fHead;
  GLUvertex *v1 = &mesh1->vHead;
  GLUhalfEdge *e1 = &mesh1->eHead;
  GLUface *f2 = &mesh2->fHead;
  GLUvertex *v2 = &mesh2->vHead;
  GLUhalfEdge *e2 = &mesh2->eHead;
 
  /* Add the faces, vertices, and edges of mesh2 to those of mesh1 */
  if( f2->next != f2 ) {
    f1->prev->next = f2->next;
    f2->next->prev = f1->prev;
    f2->prev->next = f1;
    f1->prev = f2->prev;
  }
 
  if( v2->next != v2 ) {
    v1->prev->next = v2->next;
    v2->next->prev = v1->prev;
    v2->prev->next = v1;
    v1->prev = v2->prev;
  }
 
  if( e2->next != e2 ) {
    e1->Sym->next->Sym->next = e2->next;
    e2->next->Sym->next = e1->Sym->next;
    e2->Sym->next->Sym->next = e1;
    e1->Sym->next = e2->Sym->next;
  }
 
  memFree( mesh2 );
  return mesh1;
}
 
 
#ifdef DELETE_BY_ZAPPING
 
/* __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
 */
inline void __gl_meshDeleteMesh( GLUmesh *mesh )
{
  GLUface *fHead = &mesh->fHead;
 
  while( fHead->next != fHead ) {
    __gl_meshZapFace( fHead->next );
  }
  assert( mesh->vHead.next == &mesh->vHead );
 
  memFree( mesh );
}
 
#else
 
/* __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
 */
inline void __gl_meshDeleteMesh( GLUmesh *mesh )
{
  GLUface *f, *fNext;
  GLUvertex *v, *vNext;
  GLUhalfEdge *e, *eNext;
 
  for( f = mesh->fHead.next; f != &mesh->fHead; f = fNext ) {
    fNext = f->next;
    memFree( f );
  }
 
  for( v = mesh->vHead.next; v != &mesh->vHead; v = vNext ) {
    vNext = v->next;
    memFree( v );
  }
 
  for( e = mesh->eHead.next; e != &mesh->eHead; e = eNext ) {
    /* One call frees both e and e->Sym (see EdgePair above) */
    eNext = e->next;
    memFree( e );
  }
 
  memFree( mesh );
}
 
#endif
 
inline void __gl_meshCheckMesh( GLUmesh *mesh )
{
  GLUface *fHead = &mesh->fHead;
  GLUvertex *vHead = &mesh->vHead;
  GLUhalfEdge *eHead = &mesh->eHead;
  GLUface *f, *fPrev;
  GLUvertex *v, *vPrev;
  GLUhalfEdge *e, *ePrev;
 
  fPrev = fHead;
  for( fPrev = fHead ; (f = fPrev->next) != fHead; fPrev = f) {
    assert( f->prev == fPrev );
    e = f->anEdge;
    do {
      assert( e->Sym != e );
      assert( e->Sym->Sym == e );
      assert( e->Lnext->Onext->Sym == e );
      assert( e->Onext->Sym->Lnext == e );
      assert( e->Lface == f );
      e = e->Lnext;
    } while( e != f->anEdge );
  }
  assert( f->prev == fPrev && f->anEdge == NULL && f->data == NULL );
 
  vPrev = vHead;
  for( vPrev = vHead ; (v = vPrev->next) != vHead; vPrev = v) {
    assert( v->prev == vPrev );
    e = v->anEdge;
    do {
      assert( e->Sym != e );
      assert( e->Sym->Sym == e );
      assert( e->Lnext->Onext->Sym == e );
      assert( e->Onext->Sym->Lnext == e );
      assert( e->Org == v );
      e = e->Onext;
    } while( e != v->anEdge );
  }
  assert( v->prev == vPrev && v->anEdge == NULL && v->data == NULL );
 
  ePrev = eHead;
  for( ePrev = eHead ; (e = ePrev->next) != eHead; ePrev = e) {
    assert( e->Sym->next == ePrev->Sym );
    assert( e->Sym != e );
    assert( e->Sym->Sym == e );
    assert( e->Org != NULL );
    assert( e->Dst != NULL );
    assert( e->Lnext->Onext->Sym == e );
    assert( e->Onext->Sym->Lnext == e );
  }
  assert( e->Sym->next == ePrev->Sym
       && e->Sym == &mesh->eHeadSym
       && e->Sym->Sym == e
       && e->Org == NULL && e->Dst == NULL
       && e->Lface == NULL && e->Rface == NULL );
}
 
#endif