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IABSD.fr/xenocara/lib/libGLU/src/libtess/mesh.c

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  • Author : jsg
    Date : 2013-09-01 03:51:12
    Hash : 729f7da4
    Message : Update to GLU 9.0.0, GLU was previously part of Mesa but is now seperate. tested in a ports bulk build by landry@, ok matthieu@

  • lib/libGLU/src/libtess/mesh.c
  • /*
     * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
     * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
     *
     * Permission is hereby granted, free of charge, to any person obtaining a
     * copy of this software and associated documentation files (the "Software"),
     * to deal in the Software without restriction, including without limitation
     * the rights to use, copy, modify, merge, publish, distribute, sublicense,
     * and/or sell copies of the Software, and to permit persons to whom the
     * Software is furnished to do so, subject to the following conditions:
     *
     * The above copyright notice including the dates of first publication and
     * either this permission notice or a reference to
     * http://oss.sgi.com/projects/FreeB/
     * shall be included in all copies or substantial portions of the Software.
     *
     * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
     * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
     * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
     * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
     * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
     * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
     * SOFTWARE.
     *
     * Except as contained in this notice, the name of Silicon Graphics, Inc.
     * shall not be used in advertising or otherwise to promote the sale, use or
     * other dealings in this Software without prior written authorization from
     * Silicon Graphics, Inc.
     */
    /*
    ** Author: Eric Veach, July 1994.
    **
    */
    
    #include "gluos.h"
    #include <stddef.h>
    #include <assert.h>
    #include "mesh.h"
    #include "memalloc.h"
    
    #ifndef TRUE
    #define TRUE 1
    #endif
    #ifndef FALSE
    #define FALSE 0
    #endif
    
    static GLUvertex *allocVertex()
    {
       return (GLUvertex *)memAlloc( sizeof( GLUvertex ));
    }
    
    static GLUface *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.
     */
    static GLUhalfEdge *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.
     */
    static void 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.
     */
    static void 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.
     */
    static void 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 = 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.
     */
    static void 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.
     */
    static void 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.
     */
    static void 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.
     */
    GLUhalfEdge *__gl_meshMakeEdge( GLUmesh *mesh )
    {
      GLUvertex *newVertex1= allocVertex();
      GLUvertex *newVertex2= allocVertex();
      GLUface *newFace= 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 = MakeEdge( &mesh->eHead );
      if (e == NULL) {
         memFree(newVertex1);
         memFree(newVertex2);
         memFree(newFace);
         return NULL;
      }
    
      MakeVertex( newVertex1, e, &mesh->vHead );
      MakeVertex( newVertex2, e->Sym, &mesh->vHead );
      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.
     */
    int __gl_meshSplice( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
    {
      int joiningLoops = FALSE;
      int joiningVertices = FALSE;
    
      if( eOrg == eDst ) return 1;
    
      if( eDst->Org != eOrg->Org ) {
        /* We are merging two disjoint vertices -- destroy eDst->Org */
        joiningVertices = TRUE;
        KillVertex( eDst->Org, eOrg->Org );
      }
      if( eDst->Lface != eOrg->Lface ) {
        /* We are connecting two disjoint loops -- destroy eDst->Lface */
        joiningLoops = TRUE;
        KillFace( eDst->Lface, eOrg->Lface );
      }
    
      /* Change the edge structure */
      Splice( eDst, eOrg );
    
      if( ! joiningVertices ) {
        GLUvertex *newVertex= 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.
         */
        MakeVertex( newVertex, eDst, eOrg->Org );
        eOrg->Org->anEdge = eOrg;
      }
      if( ! joiningLoops ) {
        GLUface *newFace= 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.
         */
        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.
     */
    int __gl_meshDelete( GLUhalfEdge *eDel )
    {
      GLUhalfEdge *eDelSym = eDel->Sym;
      int joiningLoops = 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 = TRUE;
        KillFace( eDel->Lface, eDel->Rface );
      }
    
      if( eDel->Onext == eDel ) {
        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;
    
        Splice( eDel, eDel->Oprev );
        if( ! joiningLoops ) {
          GLUface *newFace= allocFace();
          if (newFace == NULL) return 0; 
    
          /* We are splitting one loop into two -- create a new loop for eDel. */
          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 ) {
        KillVertex( eDelSym->Org, NULL );
        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;
        Splice( eDelSym, eDelSym->Oprev );
      }
    
      /* Any isolated vertices or faces have already been freed. */
      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.
     */
    GLUhalfEdge *__gl_meshAddEdgeVertex( GLUhalfEdge *eOrg )
    {
      GLUhalfEdge *eNewSym;
      GLUhalfEdge *eNew = MakeEdge( eOrg );
      if (eNew == NULL) return NULL;
    
      eNewSym = eNew->Sym;
    
      /* Connect the new edge appropriately */
      Splice( eNew, eOrg->Lnext );
    
      /* Set the vertex and face information */
      eNew->Org = eOrg->Dst;
      {
        GLUvertex *newVertex= allocVertex();
        if (newVertex == NULL) return NULL;
    
        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.
     */
    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 */
      Splice( eOrg->Sym, eOrg->Sym->Oprev );
      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.
     */
    GLUhalfEdge *__gl_meshConnect( GLUhalfEdge *eOrg, GLUhalfEdge *eDst )
    {
      GLUhalfEdge *eNewSym;
      int joiningLoops = FALSE;  
      GLUhalfEdge *eNew = 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 = TRUE;
        KillFace( eDst->Lface, eOrg->Lface );
      }
    
      /* Connect the new edge appropriately */
      Splice( eNew, eOrg->Lnext );
      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= allocFace();
        if (newFace == NULL) return NULL;
    
        /* We split one loop into two -- the new loop is eNew->Lface */
        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!
     */
    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 ) {
    	KillVertex( e->Org, NULL );
          } else {
    	/* Make sure that e->Org points to a valid half-edge */
    	e->Org->anEdge = e->Onext;
    	Splice( e, e->Oprev );
          }
          eSym = e->Sym;
          if( eSym->Onext == eSym ) {
    	KillVertex( eSym->Org, NULL );
          } else {
    	/* Make sure that eSym->Org points to a valid half-edge */
    	eSym->Org->anEdge = eSym->Onext;
    	Splice( eSym, eSym->Oprev );
          }
          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").
     */
    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 = FALSE;
      f->inside = 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).
     */
    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.
     */
    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.
     */
    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
    
    #ifndef NDEBUG
    
    /* __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
     */
    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