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31 ** Author: Eric Veach, July 1994.
33 ** $Date: 2001/03/17 00:25:41 $ $Revision: 1.1 $
34 ** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libtess/mesh.h,v 1.1 2001/03/17 00:25:41 brianp Exp $
42 typedef struct GLUmesh GLUmesh
;
44 typedef struct GLUvertex GLUvertex
;
45 typedef struct GLUface GLUface
;
46 typedef struct GLUhalfEdge GLUhalfEdge
;
48 typedef struct ActiveRegion ActiveRegion
; /* Internal data */
50 /* The mesh structure is similar in spirit, notation, and operations
51 * to the "quad-edge" structure (see L. Guibas and J. Stolfi, Primitives
52 * for the manipulation of general subdivisions and the computation of
53 * Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985).
54 * For a simplified description, see the course notes for CS348a,
55 * "Mathematical Foundations of Computer Graphics", available at the
56 * Stanford bookstore (and taught during the fall quarter).
57 * The implementation also borrows a tiny subset of the graph-based approach
58 * use in Mantyla's Geometric Work Bench (see M. Mantyla, An Introduction
59 * to Sold Modeling, Computer Science Press, Rockville, Maryland, 1988).
61 * The fundamental data structure is the "half-edge". Two half-edges
62 * go together to make an edge, but they point in opposite directions.
63 * Each half-edge has a pointer to its mate (the "symmetric" half-edge Sym),
64 * its origin vertex (Org), the face on its left side (Lface), and the
65 * adjacent half-edges in the CCW direction around the origin vertex
66 * (Onext) and around the left face (Lnext). There is also a "next"
67 * pointer for the global edge list (see below).
69 * The notation used for mesh navigation:
70 * Sym = the mate of a half-edge (same edge, but opposite direction)
71 * Onext = edge CCW around origin vertex (keep same origin)
72 * Dnext = edge CCW around destination vertex (keep same dest)
73 * Lnext = edge CCW around left face (dest becomes new origin)
74 * Rnext = edge CCW around right face (origin becomes new dest)
76 * "prev" means to substitute CW for CCW in the definitions above.
78 * The mesh keeps global lists of all vertices, faces, and edges,
79 * stored as doubly-linked circular lists with a dummy header node.
80 * The mesh stores pointers to these dummy headers (vHead, fHead, eHead).
82 * The circular edge list is special; since half-edges always occur
83 * in pairs (e and e->Sym), each half-edge stores a pointer in only
84 * one direction. Starting at eHead and following the e->next pointers
85 * will visit each *edge* once (ie. e or e->Sym, but not both).
86 * e->Sym stores a pointer in the opposite direction, thus it is
87 * always true that e->Sym->next->Sym->next == e.
89 * Each vertex has a pointer to next and previous vertices in the
90 * circular list, and a pointer to a half-edge with this vertex as
91 * the origin (NULL if this is the dummy header). There is also a
92 * field "data" for client data.
94 * Each face has a pointer to the next and previous faces in the
95 * circular list, and a pointer to a half-edge with this face as
96 * the left face (NULL if this is the dummy header). There is also
97 * a field "data" for client data.
99 * Note that what we call a "face" is really a loop; faces may consist
100 * of more than one loop (ie. not simply connected), but there is no
101 * record of this in the data structure. The mesh may consist of
102 * several disconnected regions, so it may not be possible to visit
103 * the entire mesh by starting at a half-edge and traversing the edge
106 * The mesh does NOT support isolated vertices; a vertex is deleted along
107 * with its last edge. Similarly when two faces are merged, one of the
108 * faces is deleted (see __gl_meshDelete below). For mesh operations,
109 * all face (loop) and vertex pointers must not be NULL. However, once
110 * mesh manipulation is finished, __gl_MeshZapFace can be used to delete
111 * faces of the mesh, one at a time. All external faces can be "zapped"
112 * before the mesh is returned to the client; then a NULL face indicates
113 * a region which is not part of the output polygon.
117 GLUvertex
*next
; /* next vertex (never NULL) */
118 GLUvertex
*prev
; /* previous vertex (never NULL) */
119 GLUhalfEdge
*anEdge
; /* a half-edge with this origin */
120 void *data
; /* client's data */
122 /* Internal data (keep hidden) */
123 GLdouble coords
[3]; /* vertex location in 3D */
124 GLdouble s
, t
; /* projection onto the sweep plane */
125 long pqHandle
; /* to allow deletion from priority queue */
129 GLUface
*next
; /* next face (never NULL) */
130 GLUface
*prev
; /* previous face (never NULL) */
131 GLUhalfEdge
*anEdge
; /* a half edge with this left face */
132 void *data
; /* room for client's data */
134 /* Internal data (keep hidden) */
135 GLUface
*trail
; /* "stack" for conversion to strips */
136 GLboolean marked
; /* flag for conversion to strips */
137 GLboolean inside
; /* this face is in the polygon interior */
141 GLUhalfEdge
*next
; /* doubly-linked list (prev==Sym->next) */
142 GLUhalfEdge
*Sym
; /* same edge, opposite direction */
143 GLUhalfEdge
*Onext
; /* next edge CCW around origin */
144 GLUhalfEdge
*Lnext
; /* next edge CCW around left face */
145 GLUvertex
*Org
; /* origin vertex (Overtex too long) */
146 GLUface
*Lface
; /* left face */
148 /* Internal data (keep hidden) */
149 ActiveRegion
*activeRegion
; /* a region with this upper edge (sweep.c) */
150 int winding
; /* change in winding number when crossing
151 from the right face to the left face */
154 #define Rface Sym->Lface
157 #define Oprev Sym->Lnext
158 #define Lprev Onext->Sym
159 #define Dprev Lnext->Sym
160 #define Rprev Sym->Onext
161 #define Dnext Rprev->Sym /* 3 pointers */
162 #define Rnext Oprev->Sym /* 3 pointers */
166 GLUvertex vHead
; /* dummy header for vertex list */
167 GLUface fHead
; /* dummy header for face list */
168 GLUhalfEdge eHead
; /* dummy header for edge list */
169 GLUhalfEdge eHeadSym
; /* and its symmetric counterpart */
172 /* The mesh operations below have three motivations: completeness,
173 * convenience, and efficiency. The basic mesh operations are MakeEdge,
174 * Splice, and Delete. All the other edge operations can be implemented
175 * in terms of these. The other operations are provided for convenience
178 * When a face is split or a vertex is added, they are inserted into the
179 * global list *before* the existing vertex or face (ie. e->Org or e->Lface).
180 * This makes it easier to process all vertices or faces in the global lists
181 * without worrying about processing the same data twice. As a convenience,
182 * when a face is split, the "inside" flag is copied from the old face.
183 * Other internal data (v->data, v->activeRegion, f->data, f->marked,
184 * f->trail, e->winding) is set to zero.
186 * ********************** Basic Edge Operations **************************
188 * __gl_meshMakeEdge( mesh ) creates one edge, two vertices, and a loop.
189 * The loop (face) consists of the two new half-edges.
191 * __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
192 * mesh connectivity and topology. It changes the mesh so that
193 * eOrg->Onext <- OLD( eDst->Onext )
194 * eDst->Onext <- OLD( eOrg->Onext )
195 * where OLD(...) means the value before the meshSplice operation.
197 * This can have two effects on the vertex structure:
198 * - if eOrg->Org != eDst->Org, the two vertices are merged together
199 * - if eOrg->Org == eDst->Org, the origin is split into two vertices
200 * In both cases, eDst->Org is changed and eOrg->Org is untouched.
202 * Similarly (and independently) for the face structure,
203 * - if eOrg->Lface == eDst->Lface, one loop is split into two
204 * - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
205 * In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
207 * __gl_meshDelete( eDel ) removes the edge eDel. There are several cases:
208 * if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
209 * eDel->Lface is deleted. Otherwise, we are splitting one loop into two;
210 * the newly created loop will contain eDel->Dst. If the deletion of eDel
211 * would create isolated vertices, those are deleted as well.
213 * ********************** Other Edge Operations **************************
215 * __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
216 * eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
217 * eOrg and eNew will have the same left face.
219 * __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
220 * such that eNew == eOrg->Lnext. The new vertex is eOrg->Dst == eNew->Org.
221 * eOrg and eNew will have the same left face.
223 * __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
224 * to eDst->Org, and returns the corresponding half-edge eNew.
225 * If eOrg->Lface == eDst->Lface, this splits one loop into two,
226 * and the newly created loop is eNew->Lface. Otherwise, two disjoint
227 * loops are merged into one, and the loop eDst->Lface is destroyed.
229 * ************************ Other Operations *****************************
231 * __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
232 * and no loops (what we usually call a "face").
234 * __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
235 * both meshes, and returns the new mesh (the old meshes are destroyed).
237 * __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
239 * __gl_meshZapFace( fZap ) destroys a face and removes it from the
240 * global face list. All edges of fZap will have a NULL pointer as their
241 * left face. Any edges which also have a NULL pointer as their right face
242 * are deleted entirely (along with any isolated vertices this produces).
243 * An entire mesh can be deleted by zapping its faces, one at a time,
244 * in any order. Zapped faces cannot be used in further mesh operations!
246 * __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
249 GLUhalfEdge
*__gl_meshMakeEdge( GLUmesh
*mesh
);
250 int __gl_meshSplice( GLUhalfEdge
*eOrg
, GLUhalfEdge
*eDst
);
251 int __gl_meshDelete( GLUhalfEdge
*eDel
);
253 GLUhalfEdge
*__gl_meshAddEdgeVertex( GLUhalfEdge
*eOrg
);
254 GLUhalfEdge
*__gl_meshSplitEdge( GLUhalfEdge
*eOrg
);
255 GLUhalfEdge
*__gl_meshConnect( GLUhalfEdge
*eOrg
, GLUhalfEdge
*eDst
);
257 GLUmesh
*__gl_meshNewMesh( void );
258 GLUmesh
*__gl_meshUnion( GLUmesh
*mesh1
, GLUmesh
*mesh2
);
259 void __gl_meshDeleteMesh( GLUmesh
*mesh
);
260 void __gl_meshZapFace( GLUface
*fZap
);
263 #define __gl_meshCheckMesh( mesh )
265 void __gl_meshCheckMesh( GLUmesh
*mesh
);