# Kstars

mesh.h
1/*
2** Author: Eric Veach, July 1994.
3**
4*/
5
6#ifndef __mesh_h_
7#define __mesh_h_
8
9#include "glu.h"
10
11typedef struct GLUmesh GLUmesh;
12
13typedef struct GLUvertex GLUvertex;
14typedef struct GLUface GLUface;
15typedef struct GLUhalfEdge GLUhalfEdge;
16
17typedef struct ActiveRegion ActiveRegion; /* Internal data */
18
19/* The mesh structure is similar in spirit, notation, and operations
20 * to the "quad-edge" structure (see L. Guibas and J. Stolfi, Primitives
21 * for the manipulation of general subdivisions and the computation of
22 * Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985).
23 * For a simplified description, see the course notes for CS348a,
24 * "Mathematical Foundations of Computer Graphics", available at the
25 * Stanford bookstore (and taught during the fall quarter).
26 * The implementation also borrows a tiny subset of the graph-based approach
27 * use in Mantyla's Geometric Work Bench (see M. Mantyla, An Introduction
28 * to Sold Modeling, Computer Science Press, Rockville, Maryland, 1988).
29 *
30 * The fundamental data structure is the "half-edge". Two half-edges
31 * go together to make an edge, but they point in opposite directions.
32 * Each half-edge has a pointer to its mate (the "symmetric" half-edge Sym),
33 * its origin vertex (Org), the face on its left side (Lface), and the
34 * adjacent half-edges in the CCW direction around the origin vertex
35 * (Onext) and around the left face (Lnext). There is also a "next"
36 * pointer for the global edge list (see below).
37 *
38 * The notation used for mesh navigation:
39 * Sym = the mate of a half-edge (same edge, but opposite direction)
40 * Onext = edge CCW around origin vertex (keep same origin)
41 * Dnext = edge CCW around destination vertex (keep same dest)
42 * Lnext = edge CCW around left face (dest becomes new origin)
43 * Rnext = edge CCW around right face (origin becomes new dest)
44 *
45 * "prev" means to substitute CW for CCW in the definitions above.
46 *
47 * The mesh keeps global lists of all vertices, faces, and edges,
48 * stored as doubly-linked circular lists with a dummy header node.
50 *
51 * The circular edge list is special; since half-edges always occur
52 * in pairs (e and e->Sym), each half-edge stores a pointer in only
53 * one direction. Starting at eHead and following the e->next pointers
54 * will visit each *edge* once (ie. e or e->Sym, but not both).
55 * e->Sym stores a pointer in the opposite direction, thus it is
56 * always true that e->Sym->next->Sym->next == e.
57 *
58 * Each vertex has a pointer to next and previous vertices in the
59 * circular list, and a pointer to a half-edge with this vertex as
60 * the origin (NULL if this is the dummy header). There is also a
61 * field "data" for client data.
62 *
63 * Each face has a pointer to the next and previous faces in the
64 * circular list, and a pointer to a half-edge with this face as
65 * the left face (NULL if this is the dummy header). There is also
66 * a field "data" for client data.
67 *
68 * Note that what we call a "face" is really a loop; faces may consist
69 * of more than one loop (ie. not simply connected), but there is no
70 * record of this in the data structure. The mesh may consist of
71 * several disconnected regions, so it may not be possible to visit
72 * the entire mesh by starting at a half-edge and traversing the edge
73 * structure.
74 *
75 * The mesh does NOT support isolated vertices; a vertex is deleted along
76 * with its last edge. Similarly when two faces are merged, one of the
77 * faces is deleted (see __gl_meshDelete below). For mesh operations,
78 * all face (loop) and vertex pointers must not be NULL. However, once
79 * mesh manipulation is finished, __gl_MeshZapFace can be used to delete
80 * faces of the mesh, one at a time. All external faces can be "zapped"
81 * before the mesh is returned to the client; then a NULL face indicates
82 * a region which is not part of the output polygon.
83 */
84
85struct GLUvertex
86{
87 GLUvertex *next; /* next vertex (never NULL) */
88 GLUvertex *prev; /* previous vertex (never NULL) */
89 GLUhalfEdge *anEdge; /* a half-edge with this origin */
90 void *data; /* client's data */
91
92 /* Internal data (keep hidden) */
93 GLdouble coords[3]; /* vertex location in 3D */
94 GLdouble s, t; /* projection onto the sweep plane */
95 long pqHandle; /* to allow deletion from priority queue */
96};
97
98struct GLUface
99{
100 GLUface *next; /* next face (never NULL) */
101 GLUface *prev; /* previous face (never NULL) */
102 GLUhalfEdge *anEdge; /* a half edge with this left face */
103 void *data; /* room for client's data */
104
105 /* Internal data (keep hidden) */
106 GLUface *trail; /* "stack" for conversion to strips */
107 GLboolean marked; /* flag for conversion to strips */
108 GLboolean inside; /* this face is in the polygon interior */
109};
110
111struct GLUhalfEdge
112{
113 GLUhalfEdge *next; /* doubly-linked list (prev==Sym->next) */
114 GLUhalfEdge *Sym; /* same edge, opposite direction */
115 GLUhalfEdge *Onext; /* next edge CCW around origin */
116 GLUhalfEdge *Lnext; /* next edge CCW around left face */
117 GLUvertex *Org; /* origin vertex (Overtex too long) */
118 GLUface *Lface; /* left face */
119
120 /* Internal data (keep hidden) */
121 ActiveRegion *activeRegion; /* a region with this upper edge (sweep.c) */
122 int winding; /* change in winding number when crossing
123 from the right face to the left face */
124};
125
126#define Rface Sym->Lface
127#define Dst Sym->Org
128
129#define Oprev Sym->Lnext
130#define Lprev Onext->Sym
131#define Dprev Lnext->Sym
132#define Rprev Sym->Onext
133#define Dnext Rprev->Sym /* 3 pointers */
134#define Rnext Oprev->Sym /* 3 pointers */
135
136struct GLUmesh
137{
141 GLUhalfEdge eHeadSym; /* and its symmetric counterpart */
142};
143
144/* The mesh operations below have three motivations: completeness,
145 * convenience, and efficiency. The basic mesh operations are MakeEdge,
146 * Splice, and Delete. All the other edge operations can be implemented
147 * in terms of these. The other operations are provided for convenience
148 * and/or efficiency.
149 *
150 * When a face is split or a vertex is added, they are inserted into the
151 * global list *before* the existing vertex or face (ie. e->Org or e->Lface).
152 * This makes it easier to process all vertices or faces in the global lists
153 * without worrying about processing the same data twice. As a convenience,
154 * when a face is split, the "inside" flag is copied from the old face.
155 * Other internal data (v->data, v->activeRegion, f->data, f->marked,
156 * f->trail, e->winding) is set to zero.
157 *
158 * ********************** Basic Edge Operations **************************
159 *
160 * __gl_meshMakeEdge( mesh ) creates one edge, two vertices, and a loop.
161 * The loop (face) consists of the two new half-edges.
162 *
163 * __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
164 * mesh connectivity and topology. It changes the mesh so that
165 * eOrg->Onext <- OLD( eDst->Onext )
166 * eDst->Onext <- OLD( eOrg->Onext )
167 * where OLD(...) means the value before the meshSplice operation.
168 *
169 * This can have two effects on the vertex structure:
170 * - if eOrg->Org != eDst->Org, the two vertices are merged together
171 * - if eOrg->Org == eDst->Org, the origin is split into two vertices
172 * In both cases, eDst->Org is changed and eOrg->Org is untouched.
173 *
174 * Similarly (and independently) for the face structure,
175 * - if eOrg->Lface == eDst->Lface, one loop is split into two
176 * - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
177 * In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
178 *
179 * __gl_meshDelete( eDel ) removes the edge eDel. There are several cases:
180 * if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
181 * eDel->Lface is deleted. Otherwise, we are splitting one loop into two;
182 * the newly created loop will contain eDel->Dst. If the deletion of eDel
183 * would create isolated vertices, those are deleted as well.
184 *
185 * ********************** Other Edge Operations **************************
186 *
187 * __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
188 * eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
189 * eOrg and eNew will have the same left face.
190 *
191 * __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
192 * such that eNew == eOrg->Lnext. The new vertex is eOrg->Dst == eNew->Org.
193 * eOrg and eNew will have the same left face.
194 *
195 * __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
196 * to eDst->Org, and returns the corresponding half-edge eNew.
197 * If eOrg->Lface == eDst->Lface, this splits one loop into two,
198 * and the newly created loop is eNew->Lface. Otherwise, two disjoint
199 * loops are merged into one, and the loop eDst->Lface is destroyed.
200 *
201 * ************************ Other Operations *****************************
202 *
203 * __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
204 * and no loops (what we usually call a "face").
205 *
206 * __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
207 * both meshes, and returns the new mesh (the old meshes are destroyed).
208 *
209 * __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
210 *
211 * __gl_meshZapFace( fZap ) destroys a face and removes it from the
212 * global face list. All edges of fZap will have a NULL pointer as their
213 * left face. Any edges which also have a NULL pointer as their right face
214 * are deleted entirely (along with any isolated vertices this produces).
215 * An entire mesh can be deleted by zapping its faces, one at a time,
216 * in any order. Zapped faces cannot be used in further mesh operations!
217 *
218 * __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
219 */
220
221GLUhalfEdge *__gl_meshMakeEdge(GLUmesh *mesh);
222int __gl_meshSplice(GLUhalfEdge *eOrg, GLUhalfEdge *eDst);
223int __gl_meshDelete(GLUhalfEdge *eDel);
224
226GLUhalfEdge *__gl_meshSplitEdge(GLUhalfEdge *eOrg);
227GLUhalfEdge *__gl_meshConnect(GLUhalfEdge *eOrg, GLUhalfEdge *eDst);
228
229GLUmesh *__gl_meshNewMesh(void);
230GLUmesh *__gl_meshUnion(GLUmesh *mesh1, GLUmesh *mesh2);
231void __gl_meshDeleteMesh(GLUmesh *mesh);
232void __gl_meshZapFace(GLUface *fZap);
233
234#ifdef NDEBUG
235#define __gl_meshCheckMesh(mesh)
236#else
237void __gl_meshCheckMesh(GLUmesh *mesh);
238#endif
239
240#endif
This file is part of the KDE documentation.