2 * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
3 * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
5 * Permission is hereby granted, free of charge, to any person obtaining a
6 * copy of this software and associated documentation files (the "Software"),
7 * to deal in the Software without restriction, including without limitation
8 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
9 * and/or sell copies of the Software, and to permit persons to whom the
10 * Software is furnished to do so, subject to the following conditions:
12 * The above copyright notice including the dates of first publication and
13 * either this permission notice or a reference to
14 * http://oss.sgi.com/projects/FreeB/
15 * shall be included in all copies or substantial portions of the Software.
17 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
20 * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
21 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
22 * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
25 * Except as contained in this notice, the name of Silicon Graphics, Inc.
26 * shall not be used in advertising or otherwise to promote the sale, use or
27 * other dealings in this Software without prior written authorization from
28 * Silicon Graphics, Inc.
31 ** Author: Eric Veach, July 1994.
49 /* This structure remembers the information we need about a primitive
50 * to be able to render it later, once we have determined which
51 * primitive is able to use the most triangles.
54 long size
; /* number of triangles used */
55 GLUhalfEdge
*eStart
; /* edge where this primitive starts */
56 void (*render
)(GLUtesselator
*, GLUhalfEdge
*, long);
57 /* routine to render this primitive */
60 static struct FaceCount
MaximumFan( GLUhalfEdge
*eOrig
);
61 static struct FaceCount
MaximumStrip( GLUhalfEdge
*eOrig
);
63 static void RenderFan( GLUtesselator
*tess
, GLUhalfEdge
*eStart
, long size
);
64 static void RenderStrip( GLUtesselator
*tess
, GLUhalfEdge
*eStart
, long size
);
65 static void RenderTriangle( GLUtesselator
*tess
, GLUhalfEdge
*eStart
,
68 static void RenderMaximumFaceGroup( GLUtesselator
*tess
, GLUface
*fOrig
);
69 static void RenderLonelyTriangles( GLUtesselator
*tess
, GLUface
*head
);
73 /************************ Strips and Fans decomposition ******************/
75 /* __gl_renderMesh( tess, mesh ) takes a mesh and breaks it into triangle
76 * fans, strips, and separate triangles. A substantial effort is made
77 * to use as few rendering primitives as possible (ie. to make the fans
78 * and strips as large as possible).
80 * The rendering output is provided as callbacks (see the api).
82 void __gl_renderMesh( GLUtesselator
*tess
, GLUmesh
*mesh
)
86 /* Make a list of separate triangles so we can render them all at once */
87 tess
->lonelyTriList
= NULL
;
89 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
92 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
94 /* We examine all faces in an arbitrary order. Whenever we find
95 * an unprocessed face F, we output a group of faces including F
96 * whose size is maximum.
98 if( f
->inside
&& ! f
->marked
) {
99 RenderMaximumFaceGroup( tess
, f
);
103 if( tess
->lonelyTriList
!= NULL
) {
104 RenderLonelyTriangles( tess
, tess
->lonelyTriList
);
105 tess
->lonelyTriList
= NULL
;
110 static void RenderMaximumFaceGroup( GLUtesselator
*tess
, GLUface
*fOrig
)
112 /* We want to find the largest triangle fan or strip of unmarked faces
113 * which includes the given face fOrig. There are 3 possible fans
114 * passing through fOrig (one centered at each vertex), and 3 possible
115 * strips (one for each CCW permutation of the vertices). Our strategy
116 * is to try all of these, and take the primitive which uses the most
117 * triangles (a greedy approach).
119 GLUhalfEdge
*e
= fOrig
->anEdge
;
120 struct FaceCount max
, newFace
;
124 max
.render
= &RenderTriangle
;
126 if( ! tess
->flagBoundary
) {
127 newFace
= MaximumFan( e
); if( newFace
.size
> max
.size
) { max
= newFace
; }
128 newFace
= MaximumFan( e
->Lnext
); if( newFace
.size
> max
.size
) { max
= newFace
; }
129 newFace
= MaximumFan( e
->Lprev
); if( newFace
.size
> max
.size
) { max
= newFace
; }
131 newFace
= MaximumStrip( e
); if( newFace
.size
> max
.size
) { max
= newFace
; }
132 newFace
= MaximumStrip( e
->Lnext
); if( newFace
.size
> max
.size
) { max
= newFace
; }
133 newFace
= MaximumStrip( e
->Lprev
); if( newFace
.size
> max
.size
) { max
= newFace
; }
135 (*(max
.render
))( tess
, max
.eStart
, max
.size
);
139 /* Macros which keep track of faces we have marked temporarily, and allow
140 * us to backtrack when necessary. With triangle fans, this is not
141 * really necessary, since the only awkward case is a loop of triangles
142 * around a single origin vertex. However with strips the situation is
143 * more complicated, and we need a general tracking method like the
146 #define Marked(f) (! (f)->inside || (f)->marked)
148 #define AddToTrail(f,t) ((f)->trail = (t), (t) = (f), (f)->marked = TRUE)
150 #define FreeTrail(t) do { \
151 while( (t) != NULL ) { \
152 (t)->marked = FALSE; t = (t)->trail; \
154 } while(0) /* absorb trailing semicolon */
158 static struct FaceCount
MaximumFan( GLUhalfEdge
*eOrig
)
160 /* eOrig->Lface is the face we want to render. We want to find the size
161 * of a maximal fan around eOrig->Org. To do this we just walk around
162 * the origin vertex as far as possible in both directions.
164 struct FaceCount newFace
= { 0, NULL
, &RenderFan
};
165 GLUface
*trail
= NULL
;
168 for( e
= eOrig
; ! Marked( e
->Lface
); e
= e
->Onext
) {
169 AddToTrail( e
->Lface
, trail
);
172 for( e
= eOrig
; ! Marked( e
->Rface
); e
= e
->Oprev
) {
173 AddToTrail( e
->Rface
, trail
);
183 #define IsEven(n) (((n) & 1) == 0)
185 static struct FaceCount
MaximumStrip( GLUhalfEdge
*eOrig
)
187 /* Here we are looking for a maximal strip that contains the vertices
188 * eOrig->Org, eOrig->Dst, eOrig->Lnext->Dst (in that order or the
189 * reverse, such that all triangles are oriented CCW).
191 * Again we walk forward and backward as far as possible. However for
192 * strips there is a twist: to get CCW orientations, there must be
193 * an *even* number of triangles in the strip on one side of eOrig.
194 * We walk the strip starting on a side with an even number of triangles;
195 * if both side have an odd number, we are forced to shorten one side.
197 struct FaceCount newFace
= { 0, NULL
, &RenderStrip
};
198 long headSize
= 0, tailSize
= 0;
199 GLUface
*trail
= NULL
;
200 GLUhalfEdge
*e
, *eTail
, *eHead
;
202 for( e
= eOrig
; ! Marked( e
->Lface
); ++tailSize
, e
= e
->Onext
) {
203 AddToTrail( e
->Lface
, trail
);
206 if( Marked( e
->Lface
)) break;
207 AddToTrail( e
->Lface
, trail
);
211 for( e
= eOrig
; ! Marked( e
->Rface
); ++headSize
, e
= e
->Dnext
) {
212 AddToTrail( e
->Rface
, trail
);
215 if( Marked( e
->Rface
)) break;
216 AddToTrail( e
->Rface
, trail
);
220 newFace
.size
= tailSize
+ headSize
;
221 if( IsEven( tailSize
)) {
222 newFace
.eStart
= eTail
->Sym
;
223 } else if( IsEven( headSize
)) {
224 newFace
.eStart
= eHead
;
226 /* Both sides have odd length, we must shorten one of them. In fact,
227 * we must start from eHead to guarantee inclusion of eOrig->Lface.
230 newFace
.eStart
= eHead
->Onext
;
238 static void RenderTriangle( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
240 /* Just add the triangle to a triangle list, so we can render all
241 * the separate triangles at once.
244 AddToTrail( e
->Lface
, tess
->lonelyTriList
);
248 static void RenderLonelyTriangles( GLUtesselator
*tess
, GLUface
*f
)
250 /* Now we render all the separate triangles which could not be
251 * grouped into a triangle fan or strip.
255 int edgeState
= -1; /* force edge state output for first vertex */
257 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLES
);
259 for( ; f
!= NULL
; f
= f
->trail
) {
260 /* Loop once for each edge (there will always be 3 edges) */
264 if( tess
->flagBoundary
) {
265 /* Set the "edge state" to TRUE just before we output the
266 * first vertex of each edge on the polygon boundary.
268 newState
= ! e
->Rface
->inside
;
269 if( edgeState
!= newState
) {
270 edgeState
= newState
;
271 CALL_EDGE_FLAG_OR_EDGE_FLAG_DATA( edgeState
);
274 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
277 } while( e
!= f
->anEdge
);
279 CALL_END_OR_END_DATA();
283 static void RenderFan( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
285 /* Render as many CCW triangles as possible in a fan starting from
286 * edge "e". The fan *should* contain exactly "size" triangles
287 * (otherwise we've goofed up somewhere).
289 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLE_FAN
);
290 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
291 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
293 while( ! Marked( e
->Lface
)) {
294 e
->Lface
->marked
= TRUE
;
297 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
301 CALL_END_OR_END_DATA();
305 static void RenderStrip( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
307 /* Render as many CCW triangles as possible in a strip starting from
308 * edge "e". The strip *should* contain exactly "size" triangles
309 * (otherwise we've goofed up somewhere).
311 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLE_STRIP
);
312 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
313 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
315 while( ! Marked( e
->Lface
)) {
316 e
->Lface
->marked
= TRUE
;
319 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
320 if( Marked( e
->Lface
)) break;
322 e
->Lface
->marked
= TRUE
;
325 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
329 CALL_END_OR_END_DATA();
333 /************************ Boundary contour decomposition ******************/
335 /* __gl_renderBoundary( tess, mesh ) takes a mesh, and outputs one
336 * contour for each face marked "inside". The rendering output is
337 * provided as callbacks (see the api).
339 void __gl_renderBoundary( GLUtesselator
*tess
, GLUmesh
*mesh
)
344 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
346 CALL_BEGIN_OR_BEGIN_DATA( GL_LINE_LOOP
);
349 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
351 } while( e
!= f
->anEdge
);
352 CALL_END_OR_END_DATA();
358 /************************ Quick-and-dirty decomposition ******************/
360 #define SIGN_INCONSISTENT 2
362 static int ComputeNormal( GLUtesselator
*tess
, GLdouble norm
[3], int check
)
364 * If check==FALSE, we compute the polygon normal and place it in norm[].
365 * If check==TRUE, we check that each triangle in the fan from v0 has a
366 * consistent orientation with respect to norm[]. If triangles are
367 * consistently oriented CCW, return 1; if CW, return -1; if all triangles
368 * are degenerate return 0; otherwise (no consistent orientation) return
372 CachedVertex
*v0
= tess
->cache
;
373 CachedVertex
*vn
= v0
+ tess
->cacheCount
;
375 GLdouble dot
, xc
, yc
, zc
, xp
, yp
, zp
, n
[3];
378 /* Find the polygon normal. It is important to get a reasonable
379 * normal even when the polygon is self-intersecting (eg. a bowtie).
380 * Otherwise, the computed normal could be very tiny, but perpendicular
381 * to the true plane of the polygon due to numerical noise. Then all
382 * the triangles would appear to be degenerate and we would incorrectly
383 * decompose the polygon as a fan (or simply not render it at all).
385 * We use a sum-of-triangles normal algorithm rather than the more
386 * efficient sum-of-trapezoids method (used in CheckOrientation()
387 * in normal.c). This lets us explicitly reverse the signed area
388 * of some triangles to get a reasonable normal in the self-intersecting
392 norm
[0] = norm
[1] = norm
[2] = 0.0;
396 xc
= vc
->coords
[0] - v0
->coords
[0];
397 yc
= vc
->coords
[1] - v0
->coords
[1];
398 zc
= vc
->coords
[2] - v0
->coords
[2];
400 xp
= xc
; yp
= yc
; zp
= zc
;
401 xc
= vc
->coords
[0] - v0
->coords
[0];
402 yc
= vc
->coords
[1] - v0
->coords
[1];
403 zc
= vc
->coords
[2] - v0
->coords
[2];
405 /* Compute (vp - v0) cross (vc - v0) */
406 n
[0] = yp
*zc
- zp
*yc
;
407 n
[1] = zp
*xc
- xp
*zc
;
408 n
[2] = xp
*yc
- yp
*xc
;
410 dot
= n
[0]*norm
[0] + n
[1]*norm
[1] + n
[2]*norm
[2];
412 /* Reverse the contribution of back-facing triangles to get
413 * a reasonable normal for self-intersecting polygons (see above)
416 norm
[0] += n
[0]; norm
[1] += n
[1]; norm
[2] += n
[2];
418 norm
[0] -= n
[0]; norm
[1] -= n
[1]; norm
[2] -= n
[2];
420 } else if( dot
!= 0 ) {
421 /* Check the new orientation for consistency with previous triangles */
423 if( sign
< 0 ) return SIGN_INCONSISTENT
;
426 if( sign
> 0 ) return SIGN_INCONSISTENT
;
434 /* __gl_renderCache( tess ) takes a single contour and tries to render it
435 * as a triangle fan. This handles convex polygons, as well as some
436 * non-convex polygons if we get lucky.
438 * Returns TRUE if the polygon was successfully rendered. The rendering
439 * output is provided as callbacks (see the api).
441 GLboolean
__gl_renderCache( GLUtesselator
*tess
)
443 CachedVertex
*v0
= tess
->cache
;
444 CachedVertex
*vn
= v0
+ tess
->cacheCount
;
449 if( tess
->cacheCount
< 3 ) {
450 /* Degenerate contour -- no output */
454 norm
[0] = tess
->normal
[0];
455 norm
[1] = tess
->normal
[1];
456 norm
[2] = tess
->normal
[2];
457 if( norm
[0] == 0 && norm
[1] == 0 && norm
[2] == 0 ) {
458 ComputeNormal( tess
, norm
, FALSE
);
461 sign
= ComputeNormal( tess
, norm
, TRUE
);
462 if( sign
== SIGN_INCONSISTENT
) {
463 /* Fan triangles did not have a consistent orientation */
467 /* All triangles were degenerate */
471 /* Make sure we do the right thing for each winding rule */
472 switch( tess
->windingRule
) {
473 case GLU_TESS_WINDING_ODD
:
474 case GLU_TESS_WINDING_NONZERO
:
476 case GLU_TESS_WINDING_POSITIVE
:
477 if( sign
< 0 ) return TRUE
;
479 case GLU_TESS_WINDING_NEGATIVE
:
480 if( sign
> 0 ) return TRUE
;
482 case GLU_TESS_WINDING_ABS_GEQ_TWO
:
486 CALL_BEGIN_OR_BEGIN_DATA( tess
->boundaryOnly
? GL_LINE_LOOP
487 : (tess
->cacheCount
> 3) ? GL_TRIANGLE_FAN
490 CALL_VERTEX_OR_VERTEX_DATA( v0
->data
);
492 for( vc
= v0
+1; vc
< vn
; ++vc
) {
493 CALL_VERTEX_OR_VERTEX_DATA( vc
->data
);
496 for( vc
= vn
-1; vc
> v0
; --vc
) {
497 CALL_VERTEX_OR_VERTEX_DATA( vc
->data
);
500 CALL_END_OR_END_DATA();