1 /*
2 ** License Applicability. Except to the extent portions of this file are
3 ** made subject to an alternative license as permitted in the SGI Free
4 ** Software License B, Version 1.1 (the "License"), the contents of this
5 ** file are subject only to the provisions of the License. You may not use
6 ** this file except in compliance with the License. You may obtain a copy
7 ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
8 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
9 **
10 ** http://oss.sgi.com/projects/FreeB
11 **
12 ** Note that, as provided in the License, the Software is distributed on an
13 ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
14 ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
15 ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
16 ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
17 **
18 ** Original Code. The Original Code is: OpenGL Sample Implementation,
19 ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
20 ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
21 ** Copyright in any portions created by third parties is as indicated
22 ** elsewhere herein. All Rights Reserved.
23 **
24 ** Additional Notice Provisions: The application programming interfaces
25 ** established by SGI in conjunction with the Original Code are The
26 ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
27 ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
28 ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
29 ** Window System(R) (Version 1.3), released October 19, 1998. This software
30 ** was created using the OpenGL(R) version 1.2.1 Sample Implementation
31 ** published by SGI, but has not been independently verified as being
32 ** compliant with the OpenGL(R) version 1.2.1 Specification.
33 */
34 
35 /*
36  * patch.c++
37  *
38  */
39 
40 //#include <stdio.h>
41 //#include "glimports.h"
42 //#include "mystdio.h"
43 //#include "myassert.h"
44 #include "mymath.h"
45 //#include "mystring.h"
46 #include "patch.h"
47 #include "mapdesc.h"
48 #include "quilt.h"
49 //#include "nurbsconsts.h"
50 #include "simplemath.h" //for glu_abs function in ::singleStep();
51 
52 
53 /*--------------------------------------------------------------------------
54  * Patch - copy patch from quilt and transform control points
55  *--------------------------------------------------------------------------
56  */
57 
58 Patch::Patch( Quilt_ptr geo, REAL *pta, REAL *ptb, Patch *n )
59 {
60 /* pspec[i].range is uninit here */
61     mapdesc = geo->mapdesc;
62     cullval = mapdesc->isCulling() ? CULL_ACCEPT : CULL_TRIVIAL_ACCEPT;
63     notInBbox = mapdesc->isBboxSubdividing() ? 1 : 0;
64     needsSampling = mapdesc->isRangeSampling() ? 1 : 0;
65     pspec[0].order = geo->qspec[0].order;
66     pspec[1].order = geo->qspec[1].order;
67     pspec[0].stride = pspec[1].order * MAXCOORDS;
68     pspec[1].stride = MAXCOORDS;
69 
70     /* transform control points to sampling and culling spaces */
71     REAL *ps  = geo->cpts;
72     geo->select( pta, ptb );
73     ps += geo->qspec[0].offset;
74     ps += geo->qspec[1].offset;
75     ps += geo->qspec[0].index * geo->qspec[0].order * geo->qspec[0].stride;
76     ps += geo->qspec[1].index * geo->qspec[1].order * geo->qspec[1].stride;
77 
78     if( needsSampling ) {
79 	mapdesc->xformSampling( ps, geo->qspec[0].order, geo->qspec[0].stride,
80 				geo->qspec[1].order, geo->qspec[1].stride,
81 			        spts, pspec[0].stride, pspec[1].stride );
82     }
83 
84     if( cullval == CULL_ACCEPT  ) {
85 	mapdesc->xformCulling( ps, geo->qspec[0].order, geo->qspec[0].stride,
86 			       geo->qspec[1].order, geo->qspec[1].stride,
87 			       cpts, pspec[0].stride, pspec[1].stride );
88     }
89 
90     if( notInBbox ) {
91 	mapdesc->xformBounding( ps, geo->qspec[0].order, geo->qspec[0].stride,
92 			       geo->qspec[1].order, geo->qspec[1].stride,
93 			       bpts, pspec[0].stride, pspec[1].stride );
94     }
95 
96     /* set scale range */
97     pspec[0].range[0] = geo->qspec[0].breakpoints[geo->qspec[0].index];
98     pspec[0].range[1] = geo->qspec[0].breakpoints[geo->qspec[0].index+1];
99     pspec[0].range[2] = pspec[0].range[1] - pspec[0].range[0];
100 
101     pspec[1].range[0] = geo->qspec[1].breakpoints[geo->qspec[1].index];
102     pspec[1].range[1] = geo->qspec[1].breakpoints[geo->qspec[1].index+1];
103     pspec[1].range[2] = pspec[1].range[1] - pspec[1].range[0];
104 
105     // may need to subdivide to match range of sub-patch
106     if( pspec[0].range[0] != pta[0] ) {
107 	assert( pspec[0].range[0] < pta[0] );
108 	Patch lower( *this, 0, pta[0], 0 );
109 	*this = lower;
110     }
111 
112     if( pspec[0].range[1] != ptb[0] ) {
113 	assert( pspec[0].range[1] > ptb[0] );
114 	Patch upper( *this, 0, ptb[0], 0 );
115     }
116 
117     if( pspec[1].range[0] != pta[1] ) {
118 	assert( pspec[1].range[0] < pta[1] );
119 	Patch lower( *this, 1, pta[1], 0 );
120 	*this = lower;
121     }
122 
123     if( pspec[1].range[1] != ptb[1] ) {
124 	assert( pspec[1].range[1] > ptb[1] );
125 	Patch upper( *this, 1, ptb[1], 0 );
126     }
127     checkBboxConstraint();
128     next = n;
129 }
130 
131 /*--------------------------------------------------------------------------
132  * Patch - subdivide a patch along an isoparametric line
133  *--------------------------------------------------------------------------
134  */
135 
136 Patch::Patch( Patch& upper, int param, REAL value, Patch *n )
137 {
138     Patch& lower = *this;
139 
140     lower.cullval = upper.cullval;
141     lower.mapdesc = upper.mapdesc;
142     lower.notInBbox = upper.notInBbox;
143     lower.needsSampling = upper.needsSampling;
144     lower.pspec[0].order = upper.pspec[0].order;
145     lower.pspec[1].order = upper.pspec[1].order;
146     lower.pspec[0].stride = upper.pspec[0].stride;
147     lower.pspec[1].stride = upper.pspec[1].stride;
148     lower.next = n;
149 
150     /* reset scale range */
151     switch( param ) {
152 	case 0: {
153     	    REAL d = (value-upper.pspec[0].range[0]) / upper.pspec[0].range[2];
154 	    if( needsSampling )
155                 mapdesc->subdivide( upper.spts, lower.spts, d, pspec[1].order,
156                         pspec[1].stride, pspec[0].order, pspec[0].stride );
157 
158     	    if( cullval == CULL_ACCEPT )
159 	        mapdesc->subdivide( upper.cpts, lower.cpts, d, pspec[1].order,
160                         pspec[1].stride, pspec[0].order, pspec[0].stride );
161 
162     	    if( notInBbox )
163 	        mapdesc->subdivide( upper.bpts, lower.bpts, d, pspec[1].order,
164                         pspec[1].stride, pspec[0].order, pspec[0].stride );
165 
166             lower.pspec[0].range[0] = upper.pspec[0].range[0];
167             lower.pspec[0].range[1] = value;
168     	    lower.pspec[0].range[2] = value - upper.pspec[0].range[0];
169             upper.pspec[0].range[0] = value;
170     	    upper.pspec[0].range[2] = upper.pspec[0].range[1] - value;
171 
172             lower.pspec[1].range[0] = upper.pspec[1].range[0];
173             lower.pspec[1].range[1] = upper.pspec[1].range[1];
174     	    lower.pspec[1].range[2] = upper.pspec[1].range[2];
175 	    break;
176 	}
177 	case 1: {
178     	    REAL d = (value-upper.pspec[1].range[0]) / upper.pspec[1].range[2];
179 	    if( needsSampling )
180 	        mapdesc->subdivide( upper.spts, lower.spts, d, pspec[0].order,
181                         pspec[0].stride, pspec[1].order, pspec[1].stride );
182     	    if( cullval == CULL_ACCEPT )
183 	        mapdesc->subdivide( upper.cpts, lower.cpts, d, pspec[0].order,
184                         pspec[0].stride, pspec[1].order, pspec[1].stride );
185     	    if( notInBbox )
186 	        mapdesc->subdivide( upper.bpts, lower.bpts, d, pspec[0].order,
187                         pspec[0].stride, pspec[1].order, pspec[1].stride );
188             lower.pspec[0].range[0] = upper.pspec[0].range[0];
189             lower.pspec[0].range[1] = upper.pspec[0].range[1];
190     	    lower.pspec[0].range[2] = upper.pspec[0].range[2];
191 
192             lower.pspec[1].range[0] = upper.pspec[1].range[0];
193             lower.pspec[1].range[1] = value;
194     	    lower.pspec[1].range[2] = value - upper.pspec[1].range[0];
195             upper.pspec[1].range[0] = value;
196     	    upper.pspec[1].range[2] = upper.pspec[1].range[1] - value;
197 	    break;
198 	}
199     }
200 
201     // inherit bounding box
202     if( mapdesc->isBboxSubdividing() && ! notInBbox )
203 	memcpy( lower.bb, upper.bb, sizeof( bb ) );
204 
205     lower.checkBboxConstraint();
206     upper.checkBboxConstraint();
207 }
208 
209 /*--------------------------------------------------------------------------
210  * clamp - clamp the sampling rate to a given maximum
211  *--------------------------------------------------------------------------
212  */
213 
214 void
215 Patch::clamp( void )
216 {
217     if( mapdesc->clampfactor != N_NOCLAMPING ) {
218 	pspec[0].clamp( mapdesc->clampfactor );
219 	pspec[1].clamp( mapdesc->clampfactor );
220     }
221 }
222 
223 void
224 Patchspec::clamp( REAL clampfactor )
225 {
226     if( sidestep[0] < minstepsize )
227         sidestep[0] = clampfactor * minstepsize;
228     if( sidestep[1] < minstepsize )
229         sidestep[1] = clampfactor * minstepsize;
230     if( stepsize < minstepsize )
231         stepsize = clampfactor * minstepsize;
232 }
233 
234 void
235 Patch::checkBboxConstraint( void )
236 {
237     if( notInBbox &&
238 	mapdesc->bboxTooBig( bpts, pspec[0].stride, pspec[1].stride,
239 				   pspec[0].order, pspec[1].order, bb ) != 1 ) {
240 	notInBbox = 0;
241     }
242 }
243 
244 void
245 Patch::bbox( void )
246 {
247     if( mapdesc->isBboxSubdividing() )
248 	mapdesc->surfbbox( bb );
249 }
250 
251 /*--------------------------------------------------------------------------
252  * getstepsize - compute the sampling density across the patch
253  * 		and determine if patch needs to be subdivided
254  *--------------------------------------------------------------------------
255  */
256 
257 void
258 Patch::getstepsize( void )
259 {
260     pspec[0].minstepsize = pspec[1].minstepsize = 0;
261     pspec[0].needsSubdivision = pspec[1].needsSubdivision = 0;
262 
263     if( mapdesc->isConstantSampling() ) {
264 	// fixed number of samples per patch in each direction
265 	// maxsrate is number of s samples per patch
266 	// maxtrate is number of t samples per patch
267         pspec[0].getstepsize( mapdesc->maxsrate );
268         pspec[1].getstepsize( mapdesc->maxtrate );
269 
270     } else if( mapdesc->isDomainSampling() ) {
271 	// maxsrate is number of s samples per unit s length of domain
272 	// maxtrate is number of t samples per unit t length of domain
273         pspec[0].getstepsize( mapdesc->maxsrate * pspec[0].range[2] );
274         pspec[1].getstepsize( mapdesc->maxtrate * pspec[1].range[2] );
275 
276     } else if( ! needsSampling ) {
277 	pspec[0].singleStep();
278 	pspec[1].singleStep();
279     } else {
280 	// upper bound on path length between sample points
281         REAL tmp[MAXORDER][MAXORDER][MAXCOORDS];
282 	const int trstride = sizeof(tmp[0]) / sizeof(REAL);
283 	const int tcstride = sizeof(tmp[0][0]) / sizeof(REAL);
284 
285 	assert( pspec[0].order <= MAXORDER );
286 
287 	/* points have been transformed, therefore they are homogeneous */
288 
289 	int val = mapdesc->project( spts, pspec[0].stride, pspec[1].stride,
290 		 &tmp[0][0][0], trstride, tcstride,
291 		 pspec[0].order, pspec[1].order );
292         if( val == 0 ) {
293 	    // control points cross infinity, therefore partials are undefined
294             pspec[0].getstepsize( mapdesc->maxsrate );
295             pspec[1].getstepsize( mapdesc->maxtrate );
296         } else {
297             REAL t1 = mapdesc->getProperty( N_PIXEL_TOLERANCE );
298 //	    REAL t2 = mapdesc->getProperty( N_ERROR_TOLERANCE );
299 	    pspec[0].minstepsize = ( mapdesc->maxsrate > 0.0 ) ?
300 			(pspec[0].range[2] / mapdesc->maxsrate) : 0.0;
301 	    pspec[1].minstepsize = ( mapdesc->maxtrate > 0.0 ) ?
302 			(pspec[1].range[2] / mapdesc->maxtrate) : 0.0;
303 	    if( mapdesc->isParametricDistanceSampling() ||
304                 mapdesc->isObjectSpaceParaSampling() ) {
305 
306                 REAL t2;
307                 t2 = mapdesc->getProperty( N_ERROR_TOLERANCE );
308 
309 		// t2 is upper bound on the distance between surface and tessellant
310 		REAL ssv[2], ttv[2];
311 		REAL ss = mapdesc->calcPartialVelocity( ssv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 2, 0, pspec[0].range[2], pspec[1].range[2], 0 );
312 		REAL st = mapdesc->calcPartialVelocity(   0, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 1, 1, pspec[0].range[2], pspec[1].range[2], -1 );
313 		REAL tt = mapdesc->calcPartialVelocity( ttv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 0, 2, pspec[0].range[2], pspec[1].range[2], 1 );
314 	        //make sure that ss st and tt are nonnegative:
315  	        if(ss <0) ss = -ss;
316 	        if(st <0) st = -st;
317                 if(tt <0) tt = -tt;
318 
319 		if( ss != 0.0 && tt != 0.0 ) {
320 		    /* printf( "ssv[0] %g ssv[1] %g ttv[0] %g ttv[1] %g\n",
321 			ssv[0], ssv[1], ttv[0], ttv[1] ); */
322 		    REAL ttq = sqrtf( (float) ss );
323 		    REAL ssq = sqrtf( (float) tt );
324 		    REAL ds = sqrtf( 4 * t2 * ttq / ( ss * ttq + st * ssq ) );
325 		    REAL dt = sqrtf( 4 * t2 * ssq / ( tt * ssq + st * ttq ) );
326 		    pspec[0].stepsize = ( ds < pspec[0].range[2] ) ? ds : pspec[0].range[2];
327 		    REAL scutoff = 2.0 * t2 / ( pspec[0].range[2] * pspec[0].range[2]);
328 		    pspec[0].sidestep[0] = (ssv[0] > scutoff) ? sqrtf( 2.0 * t2 / ssv[0] ) : pspec[0].range[2];
329 		    pspec[0].sidestep[1] = (ssv[1] > scutoff) ? sqrtf( 2.0 * t2 / ssv[1] ) : pspec[0].range[2];
330 
331 		    pspec[1].stepsize = ( dt < pspec[1].range[2] ) ? dt : pspec[1].range[2];
332 		    REAL tcutoff = 2.0 * t2 / ( pspec[1].range[2] * pspec[1].range[2]);
333 		    pspec[1].sidestep[0] = (ttv[0] > tcutoff) ? sqrtf( 2.0 * t2 / ttv[0] ) : pspec[1].range[2];
334 		    pspec[1].sidestep[1] = (ttv[1] > tcutoff) ? sqrtf( 2.0 * t2 / ttv[1] ) : pspec[1].range[2];
335 		} else if( ss != 0.0 ) {
336 		    REAL x = pspec[1].range[2] * st;
337 		    REAL ds = ( sqrtf( x * x + 8.0 * t2 * ss ) - x ) / ss;
338 		    pspec[0].stepsize = ( ds < pspec[0].range[2] ) ? ds : pspec[0].range[2];
339 		    REAL scutoff = 2.0 * t2 / ( pspec[0].range[2] * pspec[0].range[2]);
340 		    pspec[0].sidestep[0] = (ssv[0] > scutoff) ? sqrtf( 2.0 * t2 / ssv[0] ) : pspec[0].range[2];
341 		    pspec[0].sidestep[1] = (ssv[1] > scutoff) ? sqrtf( 2.0 * t2 / ssv[1] ) : pspec[0].range[2];
342 		    pspec[1].singleStep();
343 		} else if( tt != 0.0 ) {
344 		    REAL x = pspec[0].range[2] * st;
345 		    REAL dt = ( sqrtf( x * x + 8.0 * t2 * tt ) - x )  / tt;
346 		    pspec[0].singleStep();
347 		    REAL tcutoff = 2.0 * t2 / ( pspec[1].range[2] * pspec[1].range[2]);
348 		    pspec[1].stepsize = ( dt < pspec[1].range[2] ) ? dt : pspec[1].range[2];
349 		    pspec[1].sidestep[0] = (ttv[0] > tcutoff) ? sqrtf( 2.0 * t2 / ttv[0] ) : pspec[1].range[2];
350 		    pspec[1].sidestep[1] = (ttv[1] > tcutoff) ? sqrtf( 2.0 * t2 / ttv[1] ) : pspec[1].range[2];
351 		} else {
352 		    if( 4.0 * t2  > st * pspec[0].range[2] * pspec[1].range[2] ) {
353 			pspec[0].singleStep();
354 			pspec[1].singleStep();
355 		    } else {
356 			REAL area = 4.0 * t2 / st;
357 			REAL ds = sqrtf( area * pspec[0].range[2] / pspec[1].range[2] );
358 			REAL dt = sqrtf( area * pspec[1].range[2] / pspec[0].range[2] );
359 			pspec[0].stepsize = ( ds < pspec[0].range[2] ) ? ds : pspec[0].range[2];
360 			pspec[0].sidestep[0] = pspec[0].range[2];
361 			pspec[0].sidestep[1] = pspec[0].range[2];
362 
363 			pspec[1].stepsize = ( dt < pspec[1].range[2] ) ? dt : pspec[1].range[2];
364 			pspec[1].sidestep[0] = pspec[1].range[2];
365 			pspec[1].sidestep[1] = pspec[1].range[2];
366 		    }
367 		}
368 	    } else if( mapdesc->isPathLengthSampling() ||
369 		      mapdesc->isObjectSpacePathSampling()) {
370 		// t1 is upper bound on path length
371 		REAL msv[2], mtv[2];
372 		REAL ms = mapdesc->calcPartialVelocity( msv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 1, 0, pspec[0].range[2], pspec[1].range[2], 0 );
373 		REAL mt = mapdesc->calcPartialVelocity( mtv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 0, 1, pspec[0].range[2], pspec[1].range[2], 1 );
374                 REAL side_scale = 1.0;
375 
376 		if( ms != 0.0 ) {
377 		    if( mt != 0.0 ) {
378 /*		    REAL d = t1 / ( ms * ms + mt * mt );*/
379 /*		    REAL ds = mt * d;*/
380 		    REAL ds = t1 / (2.0*ms);
381 /*		    REAL dt = ms * d;*/
382 		    REAL dt = t1 / (2.0*mt);
383 			pspec[0].stepsize = ( ds < pspec[0].range[2] ) ? ds : pspec[0].range[2];
384 			pspec[0].sidestep[0] = ( msv[0] * pspec[0].range[2] > t1 ) ? (side_scale* t1 / msv[0]) : pspec[0].range[2];
385 			pspec[0].sidestep[1] = ( msv[1] * pspec[0].range[2] > t1 ) ? (side_scale* t1 / msv[1]) : pspec[0].range[2];
386 
387 			pspec[1].stepsize = ( dt < pspec[1].range[2] ) ? dt : pspec[1].range[2];
388 			pspec[1].sidestep[0] = ( mtv[0] * pspec[1].range[2] > t1 ) ? (side_scale*t1 / mtv[0]) : pspec[1].range[2];
389 			pspec[1].sidestep[1] = ( mtv[1] * pspec[1].range[2] > t1 ) ? (side_scale*t1 / mtv[1]) : pspec[1].range[2];
390 		    } else {
391 			pspec[0].stepsize = ( t1 < ms * pspec[0].range[2] ) ? (t1 / ms) : pspec[0].range[2];
392 			pspec[0].sidestep[0] = ( msv[0] * pspec[0].range[2] > t1 ) ? (t1 / msv[0]) : pspec[0].range[2];
393 			pspec[0].sidestep[1] = ( msv[1] * pspec[0].range[2] > t1 ) ? (t1 / msv[1]) : pspec[0].range[2];
394 
395 			pspec[1].singleStep();
396 		    }
397 		} else {
398 		    if( mt != 0.0 ) {
399 			pspec[0].singleStep();
400 
401 			pspec[1].stepsize = ( t1 < mt * pspec[1].range[2] ) ? (t1 / mt) : pspec[1].range[2];
402 			pspec[1].sidestep[0] = ( mtv[0] * pspec[1].range[2] > t1 ) ? (t1 / mtv[0]) : pspec[1].range[2];
403 			pspec[1].sidestep[1] = ( mtv[1] * pspec[1].range[2] > t1 ) ? (t1 / mtv[1]) : pspec[1].range[2];
404 		    } else {
405 			pspec[0].singleStep();
406 			pspec[1].singleStep();
407 		    }
408 		}
409 	    } else if( mapdesc->isSurfaceAreaSampling() ) {
410 		// t is the square root of area
411 /*
412 		REAL msv[2], mtv[2];
413 		REAL ms = mapdesc->calcPartialVelocity( msv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 1, 0, pspec[0].range[2], pspec[1].range[2], 0 );
414 		REAL mt = mapdesc->calcPartialVelocity( mtv, &tmp[0][0][0], trstride, tcstride, pspec[0].order, pspec[1].order, 0, 1, pspec[0].range[2], pspec[1].range[2], 1 );
415 		if( ms != 0.0 &&  mt != 0.0 ) {
416 			REAL d = 1.0 / (ms * mt);
417 			t *= M_SQRT2;
418 			REAL ds = t * sqrtf( d * pspec[0].range[2] / pspec[1].range[2] );
419 			REAL dt = t * sqrtf( d * pspec[1].range[2] / pspec[0].range[2] );
420 			pspec[0].stepsize = ( ds < pspec[0].range[2] ) ? ds : pspec[0].range[2];
421 			pspec[0].sidestep[0] = ( msv[0] * pspec[0].range[2] > t ) ? (t / msv[0]) : pspec[0].range[2];
422 			pspec[0].sidestep[1] = ( msv[1] * pspec[0].range[2] > t ) ? (t / msv[1]) : pspec[0].range[2];
423 
424 			pspec[1].stepsize = ( dt < pspec[1].range[2] ) ? dt : pspec[1].range[2];
425 			pspec[1].sidestep[0] = ( mtv[0] * pspec[1].range[2] > t ) ? (t / mtv[0]) : pspec[1].range[2];
426 			pspec[1].sidestep[1] = ( mtv[1] * pspec[1].range[2] > t ) ? (t / mtv[1]) : pspec[1].range[2];
427 		} else {
428 		    pspec[0].singleStep();
429 		    pspec[1].singleStep();
430 		}
431 */
432 	    } else {
433 		pspec[0].singleStep();
434 		pspec[1].singleStep();
435 	    }
436 	}
437     }
438 
439 #ifdef DEBUG
440     _glu_dprintf( "sidesteps %g %g %g %g, stepsize %g %g\n",
441 	pspec[0].sidestep[0], pspec[0].sidestep[1],
442 	pspec[1].sidestep[0], pspec[1].sidestep[1],
443 	pspec[0].stepsize, pspec[1].stepsize );
444 #endif
445 
446     if( mapdesc->minsavings != N_NOSAVINGSSUBDIVISION ) {
447 	REAL savings = 1./(pspec[0].stepsize * pspec[1].stepsize) ;
448 	savings-= (2./( pspec[0].sidestep[0] + pspec[0].sidestep[1] )) *
449 		  (2./( pspec[1].sidestep[0] + pspec[1].sidestep[1] ));
450 
451 	savings *= pspec[0].range[2] * pspec[1].range[2];
452 	if( savings > mapdesc->minsavings ) {
453 	    pspec[0].needsSubdivision = pspec[1].needsSubdivision = 1;
454 	}
455     }
456 
457     if( pspec[0].stepsize < pspec[0].minstepsize )  pspec[0].needsSubdivision =  1;
458     if( pspec[1].stepsize < pspec[1].minstepsize )  pspec[1].needsSubdivision =  1;
459     needsSampling = (needsSampling ? needsSamplingSubdivision() : 0);
460 }
461 
462 void
463 Patchspec::singleStep()
464 {
465     stepsize =  sidestep[0] =  sidestep[1] = glu_abs(range[2]);
466 }
467 
468 void
469 Patchspec::getstepsize( REAL max ) // max is number of samples for entire patch
470 {
471     stepsize = ( max >= 1.0 ) ? range[2] / max : range[2];
472     if (stepsize < 0.0) {
473        stepsize = -stepsize;
474     }
475     sidestep[0]	=  sidestep[1] = minstepsize = stepsize;
476 }
477 
478 int
479 Patch::needsSamplingSubdivision( void )
480 {
481     return (pspec[0].needsSubdivision || pspec[1].needsSubdivision) ? 1 : 0;
482 }
483 
484 int
485 Patch::needsNonSamplingSubdivision( void )
486 {
487     return notInBbox;
488 }
489 
490 int
491 Patch::needsSubdivision( int param )
492 {
493     return pspec[param].needsSubdivision;
494 }
495 
496 int
497 Patch::cullCheck( void )
498 {
499     if( cullval == CULL_ACCEPT )
500 	cullval = mapdesc->cullCheck( cpts, pspec[0].order,  pspec[0].stride,
501 					    pspec[1].order,  pspec[1].stride );
502     return cullval;
503 }
504 
505