2 * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
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15 * shall be included in all copies or substantial portions of the Software.
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28 * Silicon Graphics, Inc.
31 ** Author: Eric Veach, July 1994.
44 /* This structure remembers the information we need about a primitive
45 * to be able to render it later, once we have determined which
46 * primitive is able to use the most triangles.
49 long size
; /* number of triangles used */
50 GLUhalfEdge
*eStart
; /* edge where this primitive starts */
51 void (*render
)(GLUtesselator
*, GLUhalfEdge
*, long);
52 /* routine to render this primitive */
55 static struct FaceCount
MaximumFan( GLUhalfEdge
*eOrig
);
56 static struct FaceCount
MaximumStrip( GLUhalfEdge
*eOrig
);
58 static void RenderFan( GLUtesselator
*tess
, GLUhalfEdge
*eStart
, long size
);
59 static void RenderStrip( GLUtesselator
*tess
, GLUhalfEdge
*eStart
, long size
);
60 static void RenderTriangle( GLUtesselator
*tess
, GLUhalfEdge
*eStart
,
63 static void RenderMaximumFaceGroup( GLUtesselator
*tess
, GLUface
*fOrig
);
64 static void RenderLonelyTriangles( GLUtesselator
*tess
, GLUface
*head
);
68 /************************ Strips and Fans decomposition ******************/
70 /* __gl_renderMesh( tess, mesh ) takes a mesh and breaks it into triangle
71 * fans, strips, and separate triangles. A substantial effort is made
72 * to use as few rendering primitives as possible (ie. to make the fans
73 * and strips as large as possible).
75 * The rendering output is provided as callbacks (see the api).
77 void __gl_renderMesh( GLUtesselator
*tess
, GLUmesh
*mesh
)
81 /* Make a list of separate triangles so we can render them all at once */
82 tess
->lonelyTriList
= NULL
;
84 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
87 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
89 /* We examine all faces in an arbitrary order. Whenever we find
90 * an unprocessed face F, we output a group of faces including F
91 * whose size is maximum.
93 if( f
->inside
&& ! f
->marked
) {
94 RenderMaximumFaceGroup( tess
, f
);
98 if( tess
->lonelyTriList
!= NULL
) {
99 RenderLonelyTriangles( tess
, tess
->lonelyTriList
);
100 tess
->lonelyTriList
= NULL
;
105 static void RenderMaximumFaceGroup( GLUtesselator
*tess
, GLUface
*fOrig
)
107 /* We want to find the largest triangle fan or strip of unmarked faces
108 * which includes the given face fOrig. There are 3 possible fans
109 * passing through fOrig (one centered at each vertex), and 3 possible
110 * strips (one for each CCW permutation of the vertices). Our strategy
111 * is to try all of these, and take the primitive which uses the most
112 * triangles (a greedy approach).
114 GLUhalfEdge
*e
= fOrig
->anEdge
;
115 struct FaceCount max
, newFace
;
119 max
.render
= &RenderTriangle
;
121 if( ! tess
->flagBoundary
) {
122 newFace
= MaximumFan( e
); if( newFace
.size
> max
.size
) { max
= newFace
; }
123 newFace
= MaximumFan( e
->Lnext
); if( newFace
.size
> max
.size
) { max
= newFace
; }
124 newFace
= MaximumFan( e
->Lprev
); if( newFace
.size
> max
.size
) { max
= newFace
; }
126 newFace
= MaximumStrip( e
); if( newFace
.size
> max
.size
) { max
= newFace
; }
127 newFace
= MaximumStrip( e
->Lnext
); if( newFace
.size
> max
.size
) { max
= newFace
; }
128 newFace
= MaximumStrip( e
->Lprev
); if( newFace
.size
> max
.size
) { max
= newFace
; }
130 (*(max
.render
))( tess
, max
.eStart
, max
.size
);
134 /* Macros which keep track of faces we have marked temporarily, and allow
135 * us to backtrack when necessary. With triangle fans, this is not
136 * really necessary, since the only awkward case is a loop of triangles
137 * around a single origin vertex. However with strips the situation is
138 * more complicated, and we need a general tracking method like the
141 #define Marked(f) (! (f)->inside || (f)->marked)
143 #define AddToTrail(f,t) ((f)->trail = (t), (t) = (f), (f)->marked = TRUE)
145 #define FreeTrail(t) do { \
146 while( (t) != NULL ) { \
147 (t)->marked = FALSE; t = (t)->trail; \
149 } while(0) /* absorb trailing semicolon */
153 static struct FaceCount
MaximumFan( GLUhalfEdge
*eOrig
)
155 /* eOrig->Lface is the face we want to render. We want to find the size
156 * of a maximal fan around eOrig->Org. To do this we just walk around
157 * the origin vertex as far as possible in both directions.
159 struct FaceCount newFace
= { 0, NULL
, &RenderFan
};
160 GLUface
*trail
= NULL
;
163 for( e
= eOrig
; ! Marked( e
->Lface
); e
= e
->Onext
) {
164 AddToTrail( e
->Lface
, trail
);
167 for( e
= eOrig
; ! Marked( e
->Rface
); e
= e
->Oprev
) {
168 AddToTrail( e
->Rface
, trail
);
178 #define IsEven(n) (((n) & 1) == 0)
180 static struct FaceCount
MaximumStrip( GLUhalfEdge
*eOrig
)
182 /* Here we are looking for a maximal strip that contains the vertices
183 * eOrig->Org, eOrig->Dst, eOrig->Lnext->Dst (in that order or the
184 * reverse, such that all triangles are oriented CCW).
186 * Again we walk forward and backward as far as possible. However for
187 * strips there is a twist: to get CCW orientations, there must be
188 * an *even* number of triangles in the strip on one side of eOrig.
189 * We walk the strip starting on a side with an even number of triangles;
190 * if both side have an odd number, we are forced to shorten one side.
192 struct FaceCount newFace
= { 0, NULL
, &RenderStrip
};
193 long headSize
= 0, tailSize
= 0;
194 GLUface
*trail
= NULL
;
195 GLUhalfEdge
*e
, *eTail
, *eHead
;
197 for( e
= eOrig
; ! Marked( e
->Lface
); ++tailSize
, e
= e
->Onext
) {
198 AddToTrail( e
->Lface
, trail
);
201 if( Marked( e
->Lface
)) break;
202 AddToTrail( e
->Lface
, trail
);
206 for( e
= eOrig
; ! Marked( e
->Rface
); ++headSize
, e
= e
->Dnext
) {
207 AddToTrail( e
->Rface
, trail
);
210 if( Marked( e
->Rface
)) break;
211 AddToTrail( e
->Rface
, trail
);
215 newFace
.size
= tailSize
+ headSize
;
216 if( IsEven( tailSize
)) {
217 newFace
.eStart
= eTail
->Sym
;
218 } else if( IsEven( headSize
)) {
219 newFace
.eStart
= eHead
;
221 /* Both sides have odd length, we must shorten one of them. In fact,
222 * we must start from eHead to guarantee inclusion of eOrig->Lface.
225 newFace
.eStart
= eHead
->Onext
;
233 static void RenderTriangle( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
235 /* Just add the triangle to a triangle list, so we can render all
236 * the separate triangles at once.
239 AddToTrail( e
->Lface
, tess
->lonelyTriList
);
243 static void RenderLonelyTriangles( GLUtesselator
*tess
, GLUface
*f
)
245 /* Now we render all the separate triangles which could not be
246 * grouped into a triangle fan or strip.
250 int edgeState
= -1; /* force edge state output for first vertex */
252 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLES
);
254 for( ; f
!= NULL
; f
= f
->trail
) {
255 /* Loop once for each edge (there will always be 3 edges) */
259 if( tess
->flagBoundary
) {
260 /* Set the "edge state" to TRUE just before we output the
261 * first vertex of each edge on the polygon boundary.
263 newState
= ! e
->Rface
->inside
;
264 if( edgeState
!= newState
) {
265 edgeState
= newState
;
266 CALL_EDGE_FLAG_OR_EDGE_FLAG_DATA( edgeState
);
269 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
272 } while( e
!= f
->anEdge
);
274 CALL_END_OR_END_DATA();
278 static void RenderFan( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
280 /* Render as many CCW triangles as possible in a fan starting from
281 * edge "e". The fan *should* contain exactly "size" triangles
282 * (otherwise we've goofed up somewhere).
284 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLE_FAN
);
285 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
286 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
288 while( ! Marked( e
->Lface
)) {
289 e
->Lface
->marked
= TRUE
;
292 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
296 CALL_END_OR_END_DATA();
300 static void RenderStrip( GLUtesselator
*tess
, GLUhalfEdge
*e
, long size
)
302 /* Render as many CCW triangles as possible in a strip starting from
303 * edge "e". The strip *should* contain exactly "size" triangles
304 * (otherwise we've goofed up somewhere).
306 CALL_BEGIN_OR_BEGIN_DATA( GL_TRIANGLE_STRIP
);
307 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
308 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
310 while( ! Marked( e
->Lface
)) {
311 e
->Lface
->marked
= TRUE
;
314 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
315 if( Marked( e
->Lface
)) break;
317 e
->Lface
->marked
= TRUE
;
320 CALL_VERTEX_OR_VERTEX_DATA( e
->Dst
->data
);
324 CALL_END_OR_END_DATA();
328 /************************ Boundary contour decomposition ******************/
330 /* __gl_renderBoundary( tess, mesh ) takes a mesh, and outputs one
331 * contour for each face marked "inside". The rendering output is
332 * provided as callbacks (see the api).
334 void __gl_renderBoundary( GLUtesselator
*tess
, GLUmesh
*mesh
)
339 for( f
= mesh
->fHead
.next
; f
!= &mesh
->fHead
; f
= f
->next
) {
341 CALL_BEGIN_OR_BEGIN_DATA( GL_LINE_LOOP
);
344 CALL_VERTEX_OR_VERTEX_DATA( e
->Org
->data
);
346 } while( e
!= f
->anEdge
);
347 CALL_END_OR_END_DATA();
353 /************************ Quick-and-dirty decomposition ******************/
355 #define SIGN_INCONSISTENT 2
357 static int ComputeNormal( GLUtesselator
*tess
, GLdouble norm
[3], int check
)
359 * If check==FALSE, we compute the polygon normal and place it in norm[].
360 * If check==TRUE, we check that each triangle in the fan from v0 has a
361 * consistent orientation with respect to norm[]. If triangles are
362 * consistently oriented CCW, return 1; if CW, return -1; if all triangles
363 * are degenerate return 0; otherwise (no consistent orientation) return
367 CachedVertex
*v0
= tess
->cache
;
368 CachedVertex
*vn
= v0
+ tess
->cacheCount
;
370 GLdouble dot
, xc
, yc
, zc
, xp
, yp
, zp
, n
[3];
373 /* Find the polygon normal. It is important to get a reasonable
374 * normal even when the polygon is self-intersecting (eg. a bowtie).
375 * Otherwise, the computed normal could be very tiny, but perpendicular
376 * to the true plane of the polygon due to numerical noise. Then all
377 * the triangles would appear to be degenerate and we would incorrectly
378 * decompose the polygon as a fan (or simply not render it at all).
380 * We use a sum-of-triangles normal algorithm rather than the more
381 * efficient sum-of-trapezoids method (used in CheckOrientation()
382 * in normal.c). This lets us explicitly reverse the signed area
383 * of some triangles to get a reasonable normal in the self-intersecting
387 norm
[0] = norm
[1] = norm
[2] = 0.0;
391 xc
= vc
->coords
[0] - v0
->coords
[0];
392 yc
= vc
->coords
[1] - v0
->coords
[1];
393 zc
= vc
->coords
[2] - v0
->coords
[2];
395 xp
= xc
; yp
= yc
; zp
= zc
;
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 /* Compute (vp - v0) cross (vc - v0) */
401 n
[0] = yp
*zc
- zp
*yc
;
402 n
[1] = zp
*xc
- xp
*zc
;
403 n
[2] = xp
*yc
- yp
*xc
;
405 dot
= n
[0]*norm
[0] + n
[1]*norm
[1] + n
[2]*norm
[2];
407 /* Reverse the contribution of back-facing triangles to get
408 * a reasonable normal for self-intersecting polygons (see above)
411 norm
[0] += n
[0]; norm
[1] += n
[1]; norm
[2] += n
[2];
413 norm
[0] -= n
[0]; norm
[1] -= n
[1]; norm
[2] -= n
[2];
415 } else if( dot
!= 0 ) {
416 /* Check the new orientation for consistency with previous triangles */
418 if( sign
< 0 ) return SIGN_INCONSISTENT
;
421 if( sign
> 0 ) return SIGN_INCONSISTENT
;
429 /* __gl_renderCache( tess ) takes a single contour and tries to render it
430 * as a triangle fan. This handles convex polygons, as well as some
431 * non-convex polygons if we get lucky.
433 * Returns TRUE if the polygon was successfully rendered. The rendering
434 * output is provided as callbacks (see the api).
436 GLboolean
__gl_renderCache( GLUtesselator
*tess
)
438 CachedVertex
*v0
= tess
->cache
;
439 CachedVertex
*vn
= v0
+ tess
->cacheCount
;
444 if( tess
->cacheCount
< 3 ) {
445 /* Degenerate contour -- no output */
449 norm
[0] = tess
->normal
[0];
450 norm
[1] = tess
->normal
[1];
451 norm
[2] = tess
->normal
[2];
452 if( norm
[0] == 0 && norm
[1] == 0 && norm
[2] == 0 ) {
453 ComputeNormal( tess
, norm
, FALSE
);
456 sign
= ComputeNormal( tess
, norm
, TRUE
);
457 if( sign
== SIGN_INCONSISTENT
) {
458 /* Fan triangles did not have a consistent orientation */
462 /* All triangles were degenerate */
466 /* Make sure we do the right thing for each winding rule */
467 switch( tess
->windingRule
) {
468 case GLU_TESS_WINDING_ODD
:
469 case GLU_TESS_WINDING_NONZERO
:
471 case GLU_TESS_WINDING_POSITIVE
:
472 if( sign
< 0 ) return TRUE
;
474 case GLU_TESS_WINDING_NEGATIVE
:
475 if( sign
> 0 ) return TRUE
;
477 case GLU_TESS_WINDING_ABS_GEQ_TWO
:
481 CALL_BEGIN_OR_BEGIN_DATA( tess
->boundaryOnly
? GL_LINE_LOOP
482 : (tess
->cacheCount
> 3) ? GL_TRIANGLE_FAN
485 CALL_VERTEX_OR_VERTEX_DATA( v0
->data
);
487 for( vc
= v0
+1; vc
< vn
; ++vc
) {
488 CALL_VERTEX_OR_VERTEX_DATA( vc
->data
);
491 for( vc
= vn
-1; vc
> v0
; --vc
) {
492 CALL_VERTEX_OR_VERTEX_DATA( vc
->data
);
495 CALL_END_OR_END_DATA();