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root/radiance/ray/src/common/bsdf_t.c

Comparing ray/src/common/bsdf_t.c (file contents):
Revision 3.4 by greg, Sat Feb 19 01:48:59 2011 UTC vs.
Revision 3.43 by greg, Sat Aug 1 23:27:04 2015 UTC

#	Line 10 | Line 10 | static const char RCSid[] = "$Id$";
10		*
11		*/
12
13	+	#define _USE_MATH_DEFINES
14		#include "rtio.h"
15		#include <stdlib.h>
16		#include <math.h>
#	Line 17 | Line 18 | static const char RCSid[] = "$Id$";
18		#include "ezxml.h"
19		#include "bsdf.h"
20		#include "bsdf_t.h"
21	+	#include "hilbert.h"
22
23	+	/* Callback function type for SDtraverseTre() */
24	+	typedef int     SDtreCallback(float val, const double *cmin, double csiz,
25	+	void *cptr);
26	+	/* reference width maximum (1.0) */
27	+	static const unsigned   iwbits = sizeof(unsigned)*4;
28	+	static const unsigned   iwmax = 1<<(sizeof(unsigned)*4);
29	+	/* maximum cumulative value */
30	+	static const unsigned   cumlmax = ~0;
31	+	/* constant z-vector */
32	+	static const FVECT      zvec = {.0, .0, 1.};
33	+	/* quantization value */
34	+	static double           quantum = 1./256.;
35	+	/* our RGB primaries */
36	+	static C_COLOR          tt_RGB_prim[3];
37	+	static float            tt_RGB_coef[3];
38	+
39	+	static const double     czero[SD_MAXDIM];
40	+
41	+	enum {tt_Y, tt_u, tt_v};                /* tree components (tt_Y==0) */
42	+
43	+	/* Struct used for our distribution-building callback */
44	+	typedef struct {
45	+	short           nic;            /* number of input coordinates */
46	+	short           rev;            /* reversing query */
47	+	unsigned        alen;           /* current array length */
48	+	unsigned        nall;           /* number of allocated entries */
49	+	unsigned        wmin;           /* minimum square size so far */
50	+	unsigned        wmax;           /* maximum square size */
51	+	struct outdir_s {
52	+	unsigned        hent;           /* entering Hilbert index */
53	+	int             wid;            /* this square size */
54	+	float           bsdf;           /* BSDF for this square */
55	+	}               *darr;          /* output direction array */
56	+	} SDdistScaffold;
57	+
58		/* Allocate a new scattering distribution node */
59		static SDNode *
60		SDnewNode(int nd, int lg)
#	Line 35 | Line 72 | SDnewNode(int nd, int lg)
72		}
73		if (lg < 0) {
74		st = (SDNode *)malloc(sizeof(SDNode) +
75	<	((1<<nd) - 1)*sizeof(st->u.t[0]));
76	<	if (st != NULL)
77	<	memset(st->u.t, 0, (1<<nd)*sizeof(st->u.t[0]));
78	<	} else
75	>	sizeof(st->u.t[0])*((1<<nd) - 1));
76	>	if (st == NULL) {
77	>	sprintf(SDerrorDetail,
78	>	"Cannot allocate %d branch BSDF tree", 1<<nd);
79	>	return NULL;
80	>	}
81	>	memset(st->u.t, 0, sizeof(st->u.t[0])<<nd);
82	>	} else {
83		st = (SDNode *)malloc(sizeof(SDNode) +
84	<	((1 << nd*lg) - 1)*sizeof(st->u.v[0]));
85	<
45	<	if (st == NULL) {
46	<	if (lg < 0)
84	>	sizeof(st->u.v[0])*((1 << nd*lg) - 1));
85	>	if (st == NULL) {
86		sprintf(SDerrorDetail,
48	–	"Cannot allocate %d branch BSDF tree", nd);
49	–	else
50	–	sprintf(SDerrorDetail,
87		"Cannot allocate %d BSDF leaves", 1 << nd*lg);
88	<	return NULL;
88	>	return NULL;
89	>	}
90		}
91		st->ndim = nd;
92		st->log2GR = lg;
#	Line 58 | Line 95 | SDnewNode(int nd, int lg)
95
96		/* Free an SD tree */
97		static void
98	<	SDfreeTree(void *p)
98	>	SDfreeTre(SDNode *st)
99		{
100	<	SDNode  *st = (SDNode *)p;
64	<	int     i;
100	>	int     n;
101
102		if (st == NULL)
103		return;
104	<	for (i = (st->log2GR < 0) << st->ndim; i--; )
105	<	SDfreeTree(st->u.t[i]);
106	<	free((void *)st);
104	>	for (n = (st->log2GR < 0) << st->ndim; n--; )
105	>	SDfreeTre(st->u.t[n]);
106	>	free(st);
107		}
108
109	+	/* Free a variable-resolution BSDF */
110	+	static void
111	+	SDFreeBTre(void *p)
112	+	{
113	+	SDTre   *sdt = (SDTre *)p;
114	+
115	+	if (sdt == NULL)
116	+	return;
117	+	SDfreeTre(sdt->stc[tt_Y]);
118	+	SDfreeTre(sdt->stc[tt_u]);
119	+	SDfreeTre(sdt->stc[tt_v]);
120	+	free(sdt);
121	+	}
122	+
123	+	/* Fill branch's worth of grid values from subtree */
124	+	static void
125	+	fill_grid_branch(float *dptr, const float *sptr, int nd, int shft)
126	+	{
127	+	unsigned        n = 1 << (shft-1);
128	+
129	+	if (!--nd) {                    /* end on the line */
130	+	memcpy(dptr, sptr, sizeof(*dptr)*n);
131	+	return;
132	+	}
133	+	while (n--)                     /* recurse on each slice */
134	+	fill_grid_branch(dptr + (n << shft*nd),
135	+	sptr + (n << (shft-1)*nd), nd, shft);
136	+	}
137	+
138	+	/* Get pointer at appropriate offset for the given branch */
139	+	static float *
140	+	grid_branch_start(SDNode *st, int n)
141	+	{
142	+	unsigned        skipsiz = 1 << (st->log2GR - 1);
143	+	float           *vptr = st->u.v;
144	+	int             i;
145	+
146	+	for (i = st->ndim; i--; skipsiz <<= st->log2GR)
147	+	if (1<<i & n)
148	+	vptr += skipsiz;
149	+	return vptr;
150	+	}
151	+
152	+	/* Simplify (consolidate) a tree by flattening uniform depth regions */
153	+	static SDNode *
154	+	SDsimplifyTre(SDNode *st)
155	+	{
156	+	int             match, n;
157	+
158	+	if (st == NULL)                 /* check for invalid tree */
159	+	return NULL;
160	+	if (st->log2GR >= 0)            /* grid just returns unaltered */
161	+	return st;
162	+	match = 1;                      /* check if grids below match */
163	+	for (n = 0; n < 1<<st->ndim; n++) {
164	+	if ((st->u.t[n] = SDsimplifyTre(st->u.t[n])) == NULL)
165	+	return NULL;    /* propogate error up call stack */
166	+	match &= (st->u.t[n]->log2GR == st->u.t[0]->log2GR);
167	+	}
168	+	if (match && (match = st->u.t[0]->log2GR) >= 0) {
169	+	SDNode  *stn = SDnewNode(st->ndim, match + 1);
170	+	if (stn == NULL)        /* out of memory? */
171	+	return st;
172	+	/* transfer values to new grid */
173	+	for (n = 1 << st->ndim; n--; )
174	+	fill_grid_branch(grid_branch_start(stn, n),
175	+	st->u.t[n]->u.v, stn->ndim, stn->log2GR);
176	+	SDfreeTre(st);          /* free old tree */
177	+	st = stn;               /* return new one */
178	+	}
179	+	return st;
180	+	}
181	+
182	+	/* Assign the given voxel in tree (produces no grid nodes) */
183	+	static SDNode *
184	+	SDsetVoxel(SDNode *sroot, int nd, const double *tmin, const double tsiz, float val)
185	+	{
186	+	double  ctrk[SD_MAXDIM];
187	+	double  csiz = 1.;
188	+	SDNode  *st;
189	+	int     i, n;
190	+	/* check arguments */
191	+	for (i = nd; i-- > 0; )
192	+	if ((tmin[i] < .0) | (tmin[i] >= 1.-FTINY))
193	+	break;
194	+	if ((i >= 0) | (nd <= 0) | (tsiz <= FTINY) | (tsiz > 1.+FTINY) |
195	+	(sroot != NULL && sroot->ndim != nd)) {
196	+	SDfreeTre(sroot);
197	+	return NULL;
198	+	}
199	+	if (tsiz >= 1.-FTINY) {         /* special case when tree is a leaf */
200	+	SDfreeTre(sroot);
201	+	if ((sroot = SDnewNode(nd, 0)) != NULL)
202	+	sroot->u.v[0] = val;
203	+	return sroot;
204	+	}
205	+	/* make sure we have branching root */
206	+	if (sroot != NULL && sroot->log2GR >= 0) {
207	+	SDfreeTre(sroot); sroot = NULL;
208	+	}
209	+	if (sroot == NULL && (sroot = SDnewNode(nd, -1)) == NULL)
210	+	return NULL;
211	+	st = sroot;                     /* climb/grow tree */
212	+	memset(ctrk, 0, sizeof(ctrk));
213	+	for ( ; ; ) {
214	+	csiz *= .5;             /* find appropriate branch */
215	+	n = 0;
216	+	for (i = nd; i--; )
217	+	if (ctrk[i]+csiz <= tmin[i]+FTINY) {
218	+	ctrk[i] += csiz;
219	+	n |= 1 << i;
220	+	}
221	+	/* reached desired voxel? */
222	+	if (csiz <= tsiz+FTINY) {
223	+	SDfreeTre(st->u.t[n]);
224	+	st = st->u.t[n] = SDnewNode(nd, 0);
225	+	break;
226	+	}
227	+	/* else grow tree as needed */
228	+	if (st->u.t[n] != NULL && st->u.t[n]->log2GR >= 0) {
229	+	SDfreeTre(st->u.t[n]); st->u.t[n] = NULL;
230	+	}
231	+	if (st->u.t[n] == NULL)
232	+	st->u.t[n] = SDnewNode(nd, -1);
233	+	if ((st = st->u.t[n]) == NULL)
234	+	break;
235	+	}
236	+	if (st == NULL) {
237	+	SDfreeTre(sroot);
238	+	return NULL;
239	+	}
240	+	st->u.v[0] = val;               /* assign leaf and return root */
241	+	return sroot;
242	+	}
243	+
244	+	/* Find smallest leaf in tree */
245	+	static double
246	+	SDsmallestLeaf(const SDNode *st)
247	+	{
248	+	if (st->log2GR < 0) {           /* tree branches */
249	+	double  lmin = 1.;
250	+	int     n;
251	+	for (n = 1<<st->ndim; n--; ) {
252	+	double  lsiz = SDsmallestLeaf(st->u.t[n]);
253	+	if (lsiz < lmin)
254	+	lmin = lsiz;
255	+	}
256	+	return .5*lmin;
257	+	}
258	+	/* leaf grid width */
259	+	return 1. / (double)(1 << st->log2GR);
260	+	}
261	+
262		/* Add up N-dimensional hypercube array values over the given box */
263		static double
264	<	SDiterSum(const float *va, int nd, int siz, const int *imin, const int *imax)
264	>	SDiterSum(const float *va, int nd, int shft, const int *imin, const int *imax)
265		{
266	+	const unsigned  skipsiz = 1 << --nd*shft;
267		double          sum = .0;
78	–	unsigned        skipsiz = 1;
268		int             i;
269	<
270	<	for (i = nd; --i > 0; )
271	<	skipsiz *= siz;
269	>
270	>	va += *imin * skipsiz;
271	>
272		if (skipsiz == 1)
273		for (i = *imin; i < *imax; i++)
274	<	sum += va[i];
274	>	sum += *va++;
275		else
276	<	for (i = *imin; i < *imax; i++)
277	<	sum += SDiterSum(va + i*skipsiz,
89	<	nd-1, siz, imin+1, imax+1);
276	>	for (i = *imin; i < *imax; i++, va += skipsiz)
277	>	sum += SDiterSum(va, nd, shft, imin+1, imax+1);
278		return sum;
279		}
280
281		/* Average BSDF leaves over an orthotope defined by the unit hypercube */
282		static double
283	<	SDavgBox(const SDNode *st, const double *bmin, const double *bmax)
283	>	SDavgTreBox(const SDNode *st, const double *bmin, const double *bmax)
284		{
97	–	int             imin[SD_MAXDIM], imax[SD_MAXDIM];
285		unsigned        n;
286		int             i;
287
#	Line 104 | Line 291 | SDavgBox(const SDNode *st, const double *bmin, const d
291		for (i = st->ndim; i--; ) {
292		if (bmin[i] >= 1.)
293		return .0;
294	<	if (bmax[i] <= .0)
294	>	if (bmax[i] <= 0)
295		return .0;
296		if (bmin[i] >= bmax[i])
297		return .0;
#	Line 112 | Line 299 | SDavgBox(const SDNode *st, const double *bmin, const d
299		if (st->log2GR < 0) {           /* iterate on subtree */
300		double          sum = .0, wsum = 1e-20;
301		double          sbmin[SD_MAXDIM], sbmax[SD_MAXDIM], w;
115	–
302		for (n = 1 << st->ndim; n--; ) {
303		w = 1.;
304		for (i = st->ndim; i--; ) {
#	Line 124 | Line 310 | SDavgBox(const SDNode *st, const double *bmin, const d
310		}
311		if (sbmin[i] < .0) sbmin[i] = .0;
312		if (sbmax[i] > 1.) sbmax[i] = 1.;
313	+	if (sbmin[i] >= sbmax[i]) {
314	+	w = .0;
315	+	break;
316	+	}
317		w *= sbmax[i] - sbmin[i];
318		}
319		if (w > 1e-10) {
320	<	sum += w * SDavgBox(st->u.t[n], sbmin, sbmax);
320	>	sum += w * SDavgTreBox(st->u.t[n], sbmin, sbmax);
321		wsum += w;
322		}
323		}
324		return sum / wsum;
325	+	} else {                        /* iterate over leaves */
326	+	int             imin[SD_MAXDIM], imax[SD_MAXDIM];
327	+
328	+	n = 1;
329	+	for (i = st->ndim; i--; ) {
330	+	imin[i] = (bmin[i] <= 0) ? 0 :
331	+	(int)((1 << st->log2GR)*bmin[i]);
332	+	imax[i] = (bmax[i] >= 1.) ? (1 << st->log2GR) :
333	+	(int)((1 << st->log2GR)*bmax[i] + .999999);
334	+	n *= imax[i] - imin[i];
335	+	}
336	+	if (n)
337	+	return SDiterSum(st->u.v, st->ndim,
338	+	st->log2GR, imin, imax) / (double)n;
339		}
340	<	n = 1;                          /* iterate over leaves */
340	>	return .0;
341	>	}
342	>
343	>	/* Recursive call for SDtraverseTre() */
344	>	static int
345	>	SDdotravTre(const SDNode *st, const double *pos, int cmask,
346	>	SDtreCallback *cf, void *cptr,
347	>	const double *cmin, double csiz)
348	>	{
349	>	int     rv, rval = 0;
350	>	double  bmin[SD_MAXDIM];
351	>	int     i, n;
352	>	/* paranoia */
353	>	if (st == NULL)
354	>	return 0;
355	>	/* in branches? */
356	>	if (st->log2GR < 0) {
357	>	unsigned        skipmask = 0;
358	>	csiz *= .5;
359	>	for (i = st->ndim; i--; )
360	>	if (1<<i & cmask) {
361	>	if (pos[i] < cmin[i] + csiz)
362	>	for (n = 1 << st->ndim; n--; ) {
363	>	if (n & 1<<i)
364	>	skipmask |= 1<<n;
365	>	}
366	>	else
367	>	for (n = 1 << st->ndim; n--; ) {
368	>	if (!(n & 1<<i))
369	>	skipmask |= 1<<n;
370	>	}
371	>	}
372	>	for (n = 1 << st->ndim; n--; ) {
373	>	if (1<<n & skipmask)
374	>	continue;
375	>	for (i = st->ndim; i--; )
376	>	if (1<<i & n)
377	>	bmin[i] = cmin[i] + csiz;
378	>	else
379	>	bmin[i] = cmin[i];
380	>
381	>	rval += rv = SDdotravTre(st->u.t[n], pos, cmask,
382	>	cf, cptr, bmin, csiz);
383	>	if (rv < 0)
384	>	return rv;
385	>	}
386	>	} else {                        /* else traverse leaves */
387	>	int     clim[SD_MAXDIM][2];
388	>	int     cpos[SD_MAXDIM];
389	>
390	>	if (st->log2GR == 0)    /* short cut */
391	>	return (*cf)(st->u.v[0], cmin, csiz, cptr);
392	>
393	>	csiz /= (double)(1 << st->log2GR);
394	>	/* assign coord. ranges */
395	>	for (i = st->ndim; i--; )
396	>	if (1<<i & cmask) {
397	>	clim[i][0] = (pos[i] - cmin[i])/csiz;
398	>	/* check overflow from f.p. error */
399	>	clim[i][0] -= clim[i][0] >> st->log2GR;
400	>	clim[i][1] = clim[i][0] + 1;
401	>	} else {
402	>	clim[i][0] = 0;
403	>	clim[i][1] = 1 << st->log2GR;
404	>	}
405	>	#if (SD_MAXDIM == 4)
406	>	bmin[0] = cmin[0] + csiz*clim[0][0];
407	>	for (cpos[0] = clim[0][0]; cpos[0] < clim[0][1]; cpos[0]++) {
408	>	bmin[1] = cmin[1] + csiz*clim[1][0];
409	>	for (cpos[1] = clim[1][0]; cpos[1] < clim[1][1]; cpos[1]++) {
410	>	bmin[2] = cmin[2] + csiz*clim[2][0];
411	>	if (st->ndim == 3) {
412	>	cpos[2] = clim[2][0];
413	>	n = cpos[0];
414	>	for (i = 1; i < 3; i++)
415	>	n = (n << st->log2GR) + cpos[i];
416	>	for ( ; cpos[2] < clim[2][1]; cpos[2]++) {
417	>	rval += rv = (*cf)(st->u.v[n++], bmin, csiz, cptr);
418	>	if (rv < 0)
419	>	return rv;
420	>	bmin[2] += csiz;
421	>	}
422	>	} else {
423	>	for (cpos[2] = clim[2][0]; cpos[2] < clim[2][1]; cpos[2]++) {
424	>	bmin[3] = cmin[3] + csiz*(cpos[3] = clim[3][0]);
425	>	n = cpos[0];
426	>	for (i = 1; i < 4; i++)
427	>	n = (n << st->log2GR) + cpos[i];
428	>	for ( ; cpos[3] < clim[3][1]; cpos[3]++) {
429	>	rval += rv = (*cf)(st->u.v[n++], bmin, csiz, cptr);
430	>	if (rv < 0)
431	>	return rv;
432	>	bmin[3] += csiz;
433	>	}
434	>	bmin[2] += csiz;
435	>	}
436	>	}
437	>	bmin[1] += csiz;
438	>	}
439	>	bmin[0] += csiz;
440	>	}
441	>	#else
442	>	_!_ "broken code segment!"
443	>	#endif
444	>	}
445	>	return rval;
446	>	}
447	>
448	>	/* Traverse a tree, visiting nodes in a slice that fits partial position */
449	>	static int
450	>	SDtraverseTre(const SDNode *st, const double *pos, int cmask,
451	>	SDtreCallback *cf, void *cptr)
452	>	{
453	>	int             i;
454	>	/* check arguments */
455	>	if ((st == NULL) | (cf == NULL))
456	>	return -1;
457	>	for (i = st->ndim; i--; )
458	>	if (1<<i & cmask && (pos[i] < 0) | (pos[i] >= 1.))
459	>	return -1;
460	>
461	>	return SDdotravTre(st, pos, cmask, cf, cptr, czero, 1.);
462	>	}
463	>
464	>	/* Look up tree value at the given grid position */
465	>	static float
466	>	SDlookupTre(const SDNode *st, const double *pos, double *hcube)
467	>	{
468	>	double  spos[SD_MAXDIM];
469	>	int     i, n, t;
470	>	/* initialize voxel return */
471	>	if (hcube) {
472	>	hcube[i = st->ndim] = 1.;
473	>	while (i--)
474	>	hcube[i] = .0;
475	>	}
476	>	/* climb the tree */
477	>	while (st != NULL && st->log2GR < 0) {
478	>	n = 0;                  /* move to appropriate branch */
479	>	if (hcube) hcube[st->ndim] *= .5;
480	>	for (i = st->ndim; i--; ) {
481	>	spos[i] = 2.*pos[i];
482	>	t = (spos[i] >= 1.);
483	>	n |= t<<i;
484	>	spos[i] -= (double)t;
485	>	if (hcube) hcube[i] += (double)t * hcube[st->ndim];
486	>	}
487	>	st = st->u.t[n];        /* avoids tail recursion */
488	>	pos = spos;
489	>	}
490	>	if (st == NULL)                 /* should never happen? */
491	>	return .0;
492	>	if (st->log2GR == 0)            /* short cut */
493	>	return st->u.v[0];
494	>	n = t = 0;                      /* find grid array index */
495		for (i = st->ndim; i--; ) {
496	<	imin[i] = (bmin[i] <= .0) ? 0
497	<	: (int)((1 << st->log2GR)*bmin[i]);
140	<	imax[i] = (bmax[i] >= 1.) ? (1 << st->log2GR)
141	<	: (int)((1 << st->log2GR)*bmax[i] + .999999);
142	<	n *= imax[i] - imin[i];
496	>	n += (int)((1<<st->log2GR)*pos[i]) << t;
497	>	t += st->log2GR;
498		}
499	<	if (!n)
499	>	if (hcube) {                    /* compute final hypercube */
500	>	hcube[st->ndim] /= (double)(1<<st->log2GR);
501	>	for (i = st->ndim; i--; )
502	>	hcube[i] += floor((1<<st->log2GR)*pos[i])*hcube[st->ndim];
503	>	}
504	>	return st->u.v[n];              /* no interpolation */
505	>	}
506	>
507	>	/* Convert CIE (Y,u',v') color to our RGB */
508	>	static void
509	>	SDyuv2rgb(double yval, double uprime, double vprime, float rgb[3])
510	>	{
511	>	const double    dfact = 1./(6.*uprime - 16.*vprime + 12.);
512	>	C_COLOR         cxy;
513	>
514	>	c_cset(&cxy, 9.*uprime*dfact, 4.*vprime*dfact);
515	>	c_toSharpRGB(&cxy, yval, rgb);
516	>	}
517	>
518	>	/* Query BSDF value and sample hypercube for the given vectors */
519	>	static int
520	>	SDqueryTre(const SDTre *sdt, float *coef,
521	>	const FVECT outVec, const FVECT inVec, double *hc)
522	>	{
523	>	const RREAL     *vtmp;
524	>	float           yval;
525	>	FVECT           rOutVec;
526	>	double          gridPos[4];
527	>
528	>	if (sdt->stc[tt_Y] == NULL)     /* paranoia, I hope */
529	>	return 0;
530	>
531	>	switch (sdt->sidef) {           /* whose side are you on? */
532	>	case SD_FREFL:
533	>	if ((outVec[2] < 0) | (inVec[2] < 0))
534	>	return 0;
535	>	break;
536	>	case SD_BREFL:
537	>	if ((outVec[2] > 0) | (inVec[2] > 0))
538	>	return 0;
539	>	break;
540	>	case SD_FXMIT:
541	>	if (outVec[2] > 0) {
542	>	if (inVec[2] > 0)
543	>	return 0;
544	>	vtmp = outVec; outVec = inVec; inVec = vtmp;
545	>	} else if (inVec[2] < 0)
546	>	return 0;
547	>	break;
548	>	case SD_BXMIT:
549	>	if (inVec[2] > 0) {
550	>	if (outVec[2] > 0)
551	>	return 0;
552	>	vtmp = outVec; outVec = inVec; inVec = vtmp;
553	>	} else if (outVec[2] < 0)
554	>	return 0;
555	>	break;
556	>	default:
557	>	return 0;
558	>	}
559	>	/* convert vector coordinates */
560	>	if (sdt->stc[tt_Y]->ndim == 3) {
561	>	spinvector(rOutVec, outVec, zvec, -atan2(-inVec[1],-inVec[0]));
562	>	gridPos[0] = (.5-FTINY) -
563	>	.5*sqrt(inVec[0]*inVec[0] + inVec[1]*inVec[1]);
564	>	SDdisk2square(gridPos+1, rOutVec[0], rOutVec[1]);
565	>	} else if (sdt->stc[tt_Y]->ndim == 4) {
566	>	SDdisk2square(gridPos, -inVec[0], -inVec[1]);
567	>	SDdisk2square(gridPos+2, outVec[0], outVec[1]);
568	>	} else
569	>	return 0;               /* should be internal error */
570	>	/* get BSDF value */
571	>	yval = SDlookupTre(sdt->stc[tt_Y], gridPos, hc);
572	>	if (coef == NULL)               /* just getting hypercube? */
573	>	return 1;
574	>	if (sdt->stc[tt_u] == NULL || sdt->stc[tt_v] == NULL) {
575	>	*coef = yval;
576	>	return 1;               /* no color */
577	>	}
578	>	/* else decode color */
579	>	SDyuv2rgb(yval, SDlookupTre(sdt->stc[tt_u], gridPos, NULL),
580	>	SDlookupTre(sdt->stc[tt_v], gridPos, NULL), coef);
581	>	coef[0] *= tt_RGB_coef[0];
582	>	coef[1] *= tt_RGB_coef[1];
583	>	coef[2] *= tt_RGB_coef[2];
584	>	return 3;
585	>	}
586	>
587	>	/* Compute non-diffuse component for variable-resolution BSDF */
588	>	static int
589	>	SDgetTreBSDF(float coef[SDmaxCh], const FVECT outVec,
590	>	const FVECT inVec, SDComponent *sdc)
591	>	{
592	>	/* check arguments */
593	>	if ((coef == NULL) | (outVec == NULL) | (inVec == NULL) | (sdc == NULL)
594	>	|| sdc->dist == NULL)
595	>	return 0;
596	>	/* get nearest BSDF value */
597	>	return SDqueryTre((SDTre *)sdc->dist, coef, outVec, inVec, NULL);
598	>	}
599	>
600	>	/* Callback to build cumulative distribution using SDtraverseTre() */
601	>	static int
602	>	build_scaffold(float val, const double *cmin, double csiz, void *cptr)
603	>	{
604	>	SDdistScaffold  *sp = (SDdistScaffold *)cptr;
605	>	int             wid = csiz*(double)iwmax + .5;
606	>	double          revcmin[2];
607	>	bitmask_t       bmin[2], bmax[2];
608	>
609	>	if (sp->rev) {                  /* need to reverse sense? */
610	>	revcmin[0] = 1. - cmin[0] - csiz;
611	>	revcmin[1] = 1. - cmin[1] - csiz;
612	>	cmin = revcmin;
613	>	} else {
614	>	cmin += sp->nic;        /* else skip to output coords */
615	>	}
616	>	if (wid < sp->wmin)             /* new minimum width? */
617	>	sp->wmin = wid;
618	>	if (wid > sp->wmax)             /* new maximum? */
619	>	sp->wmax = wid;
620	>	if (sp->alen >= sp->nall) {     /* need more space? */
621	>	struct outdir_s *ndarr;
622	>	sp->nall = (int)(1.5*sp->nall) + 256;
623	>	ndarr = (struct outdir_s *)realloc(sp->darr,
624	>	sizeof(struct outdir_s)*sp->nall);
625	>	if (ndarr == NULL) {
626	>	sprintf(SDerrorDetail,
627	>	"Cannot grow scaffold to %u entries", sp->nall);
628	>	return -1;      /* abort build */
629	>	}
630	>	sp->darr = ndarr;
631	>	}
632	>	/* find Hilbert entry index */
633	>	bmin[0] = cmin[0]*(double)iwmax + .5;
634	>	bmin[1] = cmin[1]*(double)iwmax + .5;
635	>	bmax[0] = bmin[0] + wid-1;
636	>	bmax[1] = bmin[1] + wid-1;
637	>	hilbert_box_vtx(2, sizeof(bitmask_t), iwbits, 1, bmin, bmax);
638	>	sp->darr[sp->alen].hent = hilbert_c2i(2, iwbits, bmin);
639	>	sp->darr[sp->alen].wid = wid;
640	>	sp->darr[sp->alen].bsdf = val;
641	>	sp->alen++;                     /* on to the next entry */
642	>	return 0;
643	>	}
644	>
645	>	/* Scaffold comparison function for qsort -- ascending Hilbert index */
646	>	static int
647	>	sscmp(const void *p1, const void *p2)
648	>	{
649	>	unsigned        h1 = (*(const struct outdir_s *)p1).hent;
650	>	unsigned        h2 = (*(const struct outdir_s *)p2).hent;
651	>
652	>	if (h1 > h2)
653	>	return 1;
654	>	if (h1 < h2)
655	>	return -1;
656	>	return 0;
657	>	}
658	>
659	>	/* Create a new cumulative distribution for the given input direction */
660	>	static SDTreCDst *
661	>	make_cdist(const SDTre *sdt, const double *invec, int rev)
662	>	{
663	>	SDdistScaffold  myScaffold;
664	>	double          pos[4];
665	>	int             cmask;
666	>	SDTreCDst       *cd;
667	>	struct outdir_s *sp;
668	>	double          scale, cursum;
669	>	int             i;
670	>	/* initialize scaffold */
671	>	myScaffold.wmin = iwmax;
672	>	myScaffold.wmax = 0;
673	>	myScaffold.nic = sdt->stc[tt_Y]->ndim - 2;
674	>	myScaffold.rev = rev;
675	>	myScaffold.alen = 0;
676	>	myScaffold.nall = 512;
677	>	myScaffold.darr = (struct outdir_s *)malloc(sizeof(struct outdir_s) *
678	>	myScaffold.nall);
679	>	if (myScaffold.darr == NULL)
680	>	return NULL;
681	>	/* set up traversal */
682	>	cmask = (1<<myScaffold.nic) - 1;
683	>	for (i = myScaffold.nic; i--; )
684	>	pos[i+2*rev] = invec[i];
685	>	cmask <<= 2*rev;
686	>	/* grow the distribution */
687	>	if (SDtraverseTre(sdt->stc[tt_Y], pos, cmask,
688	>	build_scaffold, &myScaffold) < 0) {
689	>	free(myScaffold.darr);
690	>	return NULL;
691	>	}
692	>	/* allocate result holder */
693	>	cd = (SDTreCDst *)malloc(sizeof(SDTreCDst) +
694	>	sizeof(cd->carr[0])*myScaffold.alen);
695	>	if (cd == NULL) {
696	>	sprintf(SDerrorDetail,
697	>	"Cannot allocate %u entry cumulative distribution",
698	>	myScaffold.alen);
699	>	free(myScaffold.darr);
700	>	return NULL;
701	>	}
702	>	cd->isodist = (myScaffold.nic == 1);
703	>	/* sort the distribution */
704	>	qsort(myScaffold.darr, cd->calen = myScaffold.alen,
705	>	sizeof(struct outdir_s), sscmp);
706	>
707	>	/* record input range */
708	>	scale = myScaffold.wmin / (double)iwmax;
709	>	for (i = myScaffold.nic; i--; ) {
710	>	cd->clim[i][0] = floor(pos[i+2*rev]/scale) * scale;
711	>	cd->clim[i][1] = cd->clim[i][0] + scale;
712	>	}
713	>	if (cd->isodist) {              /* avoid issue in SDqueryTreProjSA() */
714	>	cd->clim[1][0] = cd->clim[0][0];
715	>	cd->clim[1][1] = cd->clim[0][1];
716	>	}
717	>	cd->max_psa = myScaffold.wmax / (double)iwmax;
718	>	cd->max_psa *= cd->max_psa * M_PI;
719	>	if (rev)
720	>	cd->sidef = (sdt->sidef==SD_BXMIT) ? SD_FXMIT : SD_BXMIT;
721	>	else
722	>	cd->sidef = sdt->sidef;
723	>	cd->cTotal = 1e-20;             /* compute directional total */
724	>	sp = myScaffold.darr;
725	>	for (i = myScaffold.alen; i--; sp++)
726	>	cd->cTotal += sp->bsdf * (double)sp->wid * sp->wid;
727	>	cursum = .0;                    /* go back and get cumulative values */
728	>	scale = (double)cumlmax / cd->cTotal;
729	>	sp = myScaffold.darr;
730	>	for (i = 0; i < cd->calen; i++, sp++) {
731	>	cd->carr[i].hndx = sp->hent;
732	>	cd->carr[i].cuml = scale*cursum + .5;
733	>	cursum += sp->bsdf * (double)sp->wid * sp->wid;
734	>	}
735	>	cd->carr[i].hndx = ~0;          /* make final entry */
736	>	cd->carr[i].cuml = cumlmax;
737	>	cd->cTotal *= M_PI/(double)iwmax/iwmax;
738	>	/* all done, clean up and return */
739	>	free(myScaffold.darr);
740	>	return cd;
741	>	}
742	>
743	>	/* Find or allocate a cumulative distribution for the given incoming vector */
744	>	const SDCDst *
745	>	SDgetTreCDist(const FVECT inVec, SDComponent *sdc)
746	>	{
747	>	const SDTre     *sdt;
748	>	double          inCoord[2];
749	>	int             i;
750	>	int             mode;
751	>	SDTreCDst       *cd, *cdlast;
752	>	/* check arguments */
753	>	if ((inVec == NULL) | (sdc == NULL) ||
754	>	(sdt = (SDTre *)sdc->dist) == NULL)
755	>	return NULL;
756	>	switch (mode = sdt->sidef) {    /* check direction */
757	>	case SD_FREFL:
758	>	if (inVec[2] < 0)
759	>	return NULL;
760	>	break;
761	>	case SD_BREFL:
762	>	if (inVec[2] > 0)
763	>	return NULL;
764	>	break;
765	>	case SD_FXMIT:
766	>	if (inVec[2] < 0)
767	>	mode = SD_BXMIT;
768	>	break;
769	>	case SD_BXMIT:
770	>	if (inVec[2] > 0)
771	>	mode = SD_FXMIT;
772	>	break;
773	>	default:
774	>	return NULL;
775	>	}
776	>	if (sdt->stc[tt_Y]->ndim == 3) {        /* isotropic BSDF? */
777	>	if (mode != sdt->sidef) /* XXX unhandled reciprocity */
778	>	return &SDemptyCD;
779	>	inCoord[0] = (.5-FTINY) -
780	>	.5*sqrt(inVec[0]*inVec[0] + inVec[1]*inVec[1]);
781	>	} else if (sdt->stc[tt_Y]->ndim == 4) {
782	>	if (mode != sdt->sidef) /* use reciprocity? */
783	>	SDdisk2square(inCoord, inVec[0], inVec[1]);
784	>	else
785	>	SDdisk2square(inCoord, -inVec[0], -inVec[1]);
786	>	} else
787	>	return NULL;            /* should be internal error */
788	>	/* quantize to avoid f.p. errors */
789	>	for (i = sdt->stc[tt_Y]->ndim - 2; i--; )
790	>	inCoord[i] = floor(inCoord[i]/quantum)*quantum + .5*quantum;
791	>	cdlast = NULL;                  /* check for direction in cache list */
792	>	for (cd = (SDTreCDst *)sdc->cdList; cd != NULL;
793	>	cdlast = cd, cd = cd->next) {
794	>	if (cd->sidef != mode)
795	>	continue;
796	>	for (i = sdt->stc[tt_Y]->ndim - 2; i--; )
797	>	if ((cd->clim[i][0] > inCoord[i]) |
798	>	(inCoord[i] >= cd->clim[i][1]))
799	>	break;
800	>	if (i < 0)
801	>	break;          /* means we have a match */
802	>	}
803	>	if (cd == NULL)                 /* need to create new entry? */
804	>	cdlast = cd = make_cdist(sdt, inCoord, mode != sdt->sidef);
805	>	if (cdlast != NULL) {           /* move entry to head of cache list */
806	>	cdlast->next = cd->next;
807	>	cd->next = (SDTreCDst *)sdc->cdList;
808	>	sdc->cdList = (SDCDst *)cd;
809	>	}
810	>	return (SDCDst *)cd;            /* ready to go */
811	>	}
812	>
813	>	/* Query solid angle for vector(s) */
814	>	static SDError
815	>	SDqueryTreProjSA(double *psa, const FVECT v1, const RREAL *v2,
816	>	int qflags, SDComponent *sdc)
817	>	{
818	>	double          myPSA[2];
819	>	/* check arguments */
820	>	if ((psa == NULL) | (v1 == NULL) | (sdc == NULL) ||
821	>	sdc->dist == NULL)
822	>	return SDEargument;
823	>	/* get projected solid angle(s) */
824	>	if (v2 != NULL) {
825	>	const SDTre     *sdt = (SDTre *)sdc->dist;
826	>	double          hcube[SD_MAXDIM+1];
827	>	if (!SDqueryTre(sdt, NULL, v1, v2, hcube)) {
828	>	strcpy(SDerrorDetail, "Bad call to SDqueryTreProjSA");
829	>	return SDEinternal;
830	>	}
831	>	myPSA[0] = hcube[sdt->stc[tt_Y]->ndim];
832	>	myPSA[1] = myPSA[0] *= myPSA[0] * M_PI;
833	>	} else {
834	>	const SDTreCDst *cd = (const SDTreCDst *)SDgetTreCDist(v1, sdc);
835	>	if (cd == NULL)
836	>	myPSA[0] = myPSA[1] = 0;
837	>	else {
838	>	myPSA[0] = M_PI * (cd->clim[0][1] - cd->clim[0][0]) *
839	>	(cd->clim[1][1] - cd->clim[1][0]);
840	>	myPSA[1] = cd->max_psa;
841	>	}
842	>	}
843	>	switch (qflags) {               /* record based on flag settings */
844	>	case SDqueryVal:
845	>	*psa = myPSA[0];
846	>	break;
847	>	case SDqueryMax:
848	>	if (myPSA[1] > *psa)
849	>	*psa = myPSA[1];
850	>	break;
851	>	case SDqueryMin+SDqueryMax:
852	>	if (myPSA[1] > psa[1])
853	>	psa[1] = myPSA[1];
854	>	/* fall through */
855	>	case SDqueryMin:
856	>	if ((myPSA[0] > 0) & (myPSA[0] < psa[0]))
857	>	psa[0] = myPSA[0];
858	>	break;
859	>	}
860	>	return SDEnone;
861	>	}
862	>
863	>	/* Sample cumulative distribution */
864	>	static SDError
865	>	SDsampTreCDist(FVECT ioVec, double randX, const SDCDst *cdp)
866	>	{
867	>	const unsigned  nBitsC = 4*sizeof(bitmask_t);
868	>	const unsigned  nExtraBits = 8*(sizeof(bitmask_t)-sizeof(unsigned));
869	>	const SDTreCDst *cd = (const SDTreCDst *)cdp;
870	>	const unsigned  target = randX*cumlmax;
871	>	bitmask_t       hndx, hcoord[2];
872	>	double          gpos[3], rotangle;
873	>	int             i, iupper, ilower;
874	>	/* check arguments */
875	>	if ((ioVec == NULL) | (cd == NULL))
876	>	return SDEargument;
877	>	if (!cd->sidef)
878	>	return SDEnone;         /* XXX should never happen */
879	>	if (ioVec[2] > 0) {
880	>	if ((cd->sidef != SD_FREFL) & (cd->sidef != SD_FXMIT))
881	>	return SDEargument;
882	>	} else if ((cd->sidef != SD_BREFL) & (cd->sidef != SD_BXMIT))
883	>	return SDEargument;
884	>	/* binary search to find position */
885	>	ilower = 0; iupper = cd->calen;
886	>	while ((i = (iupper + ilower) >> 1) != ilower)
887	>	if (target >= cd->carr[i].cuml)
888	>	ilower = i;
889	>	else
890	>	iupper = i;
891	>	/* localize random position */
892	>	randX = (randX*cumlmax - cd->carr[ilower].cuml) /
893	>	(double)(cd->carr[iupper].cuml - cd->carr[ilower].cuml);
894	>	/* index in longer Hilbert curve */
895	>	hndx = (randX*cd->carr[iupper].hndx + (1.-randX)*cd->carr[ilower].hndx)
896	>	* (double)((bitmask_t)1 << nExtraBits);
897	>	/* convert Hilbert index to vector */
898	>	hilbert_i2c(2, nBitsC, hndx, hcoord);
899	>	for (i = 2; i--; )
900	>	gpos[i] = ((double)hcoord[i] + rand()*(1./(RAND_MAX+.5))) /
901	>	(double)((bitmask_t)1 << nBitsC);
902	>	SDsquare2disk(gpos, gpos[0], gpos[1]);
903	>	/* compute Z-coordinate */
904	>	gpos[2] = 1. - gpos[0]*gpos[0] - gpos[1]*gpos[1];
905	>	gpos[2] = sqrt(gpos[2]*(gpos[2]>0));
906	>	/* emit from back? */
907	>	if ((cd->sidef == SD_BREFL) | (cd->sidef == SD_FXMIT))
908	>	gpos[2] = -gpos[2];
909	>	if (cd->isodist) {              /* rotate isotropic sample */
910	>	rotangle = atan2(-ioVec[1],-ioVec[0]);
911	>	spinvector(ioVec, gpos, zvec, rotangle);
912	>	} else
913	>	VCOPY(ioVec, gpos);
914	>	return SDEnone;
915	>	}
916	>
917	>	/* Advance pointer to the next non-white character in the string (or nul) */
918	>	static int
919	>	next_token(char **spp)
920	>	{
921	>	while (isspace(**spp))
922	>	++*spp;
923	>	return **spp;
924	>	}
925	>
926	>	/* Advance pointer past matching token (or any token if c==0) */
927	>	#define eat_token(spp,c)        ((next_token(spp)==(c)) ^ !(c) ? *(*(spp))++ : 0)
928	>
929	>	/* Count words from this point in string to '}' */
930	>	static int
931	>	count_values(char *cp)
932	>	{
933	>	int     n = 0;
934	>
935	>	while (next_token(&cp) != '}' && *cp) {
936	>	while (!isspace(*cp) & (*cp != ',') & (*cp != '}'))
937	>	if (!*++cp)
938	>	break;
939	>	++n;
940	>	eat_token(&cp, ',');
941	>	}
942	>	return n;
943	>	}
944	>
945	>	/* Load an array of real numbers, returning total */
946	>	static int
947	>	load_values(char **spp, float *va, int n)
948	>	{
949	>	float   *v = va;
950	>	char    *svnext;
951	>
952	>	while (n-- > 0 && (svnext = fskip(*spp)) != NULL) {
953	>	if ((*v++ = atof(*spp)) < 0)
954	>	v[-1] = 0;
955	>	*spp = svnext;
956	>	eat_token(spp, ',');
957	>	}
958	>	return v - va;
959	>	}
960	>
961	>	/* Load BSDF tree data */
962	>	static SDNode *
963	>	load_tree_data(char **spp, int nd)
964	>	{
965	>	SDNode  *st;
966	>	int     n;
967	>
968	>	if (!eat_token(spp, '{')) {
969	>	strcpy(SDerrorDetail, "Missing '{' in tensor tree");
970	>	return NULL;
971	>	}
972	>	if (next_token(spp) == '{') {   /* tree branches */
973	>	st = SDnewNode(nd, -1);
974	>	if (st == NULL)
975	>	return NULL;
976	>	for (n = 0; n < 1<<nd; n++)
977	>	if ((st->u.t[n] = load_tree_data(spp, nd)) == NULL) {
978	>	SDfreeTre(st);
979	>	return NULL;
980	>	}
981	>	} else {                        /* else load value grid */
982	>	int     bsiz;
983	>	n = count_values(*spp); /* see how big the grid is */
984	>	for (bsiz = 0; bsiz < 8*sizeof(size_t); bsiz += nd)
985	>	if (1<<bsiz == n)
986	>	break;
987	>	if (bsiz >= 8*sizeof(size_t)) {
988	>	strcpy(SDerrorDetail, "Illegal value count in tensor tree");
989	>	return NULL;
990	>	}
991	>	st = SDnewNode(nd, bsiz/nd);
992	>	if (st == NULL)
993	>	return NULL;
994	>	if (load_values(spp, st->u.v, n) != n) {
995	>	strcpy(SDerrorDetail, "Real format error in tensor tree");
996	>	SDfreeTre(st);
997	>	return NULL;
998	>	}
999	>	}
1000	>	if (!eat_token(spp, '}')) {
1001	>	strcpy(SDerrorDetail, "Missing '}' in tensor tree");
1002	>	SDfreeTre(st);
1003	>	return NULL;
1004	>	}
1005	>	eat_token(spp, ',');
1006	>	return st;
1007	>	}
1008	>
1009	>	/* Compute min. proj. solid angle and max. direct hemispherical scattering */
1010	>	static SDError
1011	>	get_extrema(SDSpectralDF *df)
1012	>	{
1013	>	SDNode  *st = (*(SDTre *)df->comp[0].dist).stc[tt_Y];
1014	>	double  stepWidth, dhemi, bmin[4], bmax[4];
1015	>
1016	>	stepWidth = SDsmallestLeaf(st);
1017	>	if (quantum > stepWidth)        /* adjust quantization factor */
1018	>	quantum = stepWidth;
1019	>	df->minProjSA = M_PI*stepWidth*stepWidth;
1020	>	if (stepWidth < .03125)
1021	>	stepWidth = .03125;     /* 1/32 resolution good enough */
1022	>	df->maxHemi = .0;
1023	>	if (st->ndim == 3) {            /* isotropic BSDF */
1024	>	bmin[1] = bmin[2] = .0;
1025	>	bmax[1] = bmax[2] = 1.;
1026	>	for (bmin[0] = .0; bmin[0] < .5-FTINY; bmin[0] += stepWidth) {
1027	>	bmax[0] = bmin[0] + stepWidth;
1028	>	dhemi = SDavgTreBox(st, bmin, bmax);
1029	>	if (dhemi > df->maxHemi)
1030	>	df->maxHemi = dhemi;
1031	>	}
1032	>	} else if (st->ndim == 4) {     /* anisotropic BSDF */
1033	>	bmin[2] = bmin[3] = .0;
1034	>	bmax[2] = bmax[3] = 1.;
1035	>	for (bmin[0] = .0; bmin[0] < 1.-FTINY; bmin[0] += stepWidth) {
1036	>	bmax[0] = bmin[0] + stepWidth;
1037	>	for (bmin[1] = .0; bmin[1] < 1.-FTINY; bmin[1] += stepWidth) {
1038	>	bmax[1] = bmin[1] + stepWidth;
1039	>	dhemi = SDavgTreBox(st, bmin, bmax);
1040	>	if (dhemi > df->maxHemi)
1041	>	df->maxHemi = dhemi;
1042	>	}
1043	>	}
1044	>	} else
1045	>	return SDEinternal;
1046	>	/* correct hemispherical value */
1047	>	df->maxHemi *= M_PI;
1048	>	return SDEnone;
1049	>	}
1050	>
1051	>	/* Load BSDF distribution for this wavelength */
1052	>	static SDError
1053	>	load_bsdf_data(SDData *sd, ezxml_t wdb, int ct, int ndim)
1054	>	{
1055	>	SDSpectralDF    *df;
1056	>	SDTre           *sdt;
1057	>	char            *sdata;
1058	>	/* allocate BSDF component */
1059	>	sdata = ezxml_txt(ezxml_child(wdb, "WavelengthDataDirection"));
1060	>	if (!sdata)
1061	>	return SDEnone;
1062	>	/*
1063	>	* Remember that front and back are reversed from WINDOW 6 orientations
1064	>	*/
1065	>	if (!strcasecmp(sdata, "Transmission Front")) {
1066	>	if (sd->tb == NULL && (sd->tb = SDnewSpectralDF(1)) == NULL)
1067	>	return SDEmemory;
1068	>	df = sd->tb;
1069	>	} else if (!strcasecmp(sdata, "Transmission Back")) {
1070	>	if (sd->tf == NULL && (sd->tf = SDnewSpectralDF(1)) == NULL)
1071	>	return SDEmemory;
1072	>	df = sd->tf;
1073	>	} else if (!strcasecmp(sdata, "Reflection Front")) {
1074	>	if (sd->rb == NULL && (sd->rb = SDnewSpectralDF(1)) == NULL)
1075	>	return SDEmemory;
1076	>	df = sd->rb;
1077	>	} else if (!strcasecmp(sdata, "Reflection Back")) {
1078	>	if (sd->rf == NULL && (sd->rf = SDnewSpectralDF(1)) == NULL)
1079	>	return SDEmemory;
1080	>	df = sd->rf;
1081	>	} else
1082	>	return SDEnone;
1083	>	/* get angle bases */
1084	>	sdata = ezxml_txt(ezxml_child(wdb,"AngleBasis"));
1085	>	if (!sdata || strcasecmp(sdata, "LBNL/Shirley-Chiu")) {
1086	>	sprintf(SDerrorDetail, "%s angle basis for BSDF '%s'",
1087	>	!sdata ? "Missing" : "Unsupported", sd->name);
1088	>	return !sdata ? SDEformat : SDEsupport;
1089	>	}
1090	>	if (df->comp[0].dist == NULL) { /* need to allocate BSDF tree? */
1091	>	sdt = (SDTre *)malloc(sizeof(SDTre));
1092	>	if (sdt == NULL)
1093	>	return SDEmemory;
1094	>	if (df == sd->rf)
1095	>	sdt->sidef = SD_FREFL;
1096	>	else if (df == sd->rb)
1097	>	sdt->sidef = SD_BREFL;
1098	>	else if (df == sd->tf)
1099	>	sdt->sidef = SD_FXMIT;
1100	>	else /* df == sd->tb */
1101	>	sdt->sidef = SD_BXMIT;
1102	>	sdt->stc[tt_Y] = sdt->stc[tt_u] = sdt->stc[tt_v] = NULL;
1103	>	df->comp[0].dist = sdt;
1104	>	df->comp[0].func = &SDhandleTre;
1105	>	} else {
1106	>	sdt = (SDTre *)df->comp[0].dist;
1107	>	if (sdt->stc[ct] != NULL) {
1108	>	SDfreeTre(sdt->stc[ct]);
1109	>	sdt->stc[ct] = NULL;
1110	>	}
1111	>	}
1112	>	/* read BSDF data */
1113	>	sdata = ezxml_txt(ezxml_child(wdb, "ScatteringData"));
1114	>	if (!sdata || !next_token(&sdata)) {
1115	>	sprintf(SDerrorDetail, "Missing BSDF ScatteringData in '%s'",
1116	>	sd->name);
1117	>	return SDEformat;
1118	>	}
1119	>	sdt->stc[ct] = load_tree_data(&sdata, ndim);
1120	>	if (sdt->stc[ct] == NULL)
1121	>	return SDEformat;
1122	>	if (next_token(&sdata)) {       /* check for unconsumed characters */
1123	>	sprintf(SDerrorDetail,
1124	>	"Extra characters at end of ScatteringData in '%s'",
1125	>	sd->name);
1126	>	return SDEformat;
1127	>	}
1128	>	/* flatten branches where possible */
1129	>	sdt->stc[ct] = SDsimplifyTre(sdt->stc[ct]);
1130	>	if (sdt->stc[ct] == NULL)
1131	>	return SDEinternal;
1132	>	/* compute global quantities for Y */
1133	>	return (ct == tt_Y) ? get_extrema(df) : SDEnone;
1134	>	}
1135	>
1136	>	/* Find minimum value in tree */
1137	>	static float
1138	>	SDgetTreMin(const SDNode *st)
1139	>	{
1140	>	float   vmin = FHUGE;
1141	>	int     n;
1142	>
1143	>	if (st->log2GR < 0) {
1144	>	for (n = 1<<st->ndim; n--; ) {
1145	>	float   v = SDgetTreMin(st->u.t[n]);
1146	>	if (v < vmin)
1147	>	vmin = v;
1148	>	}
1149	>	} else {
1150	>	for (n = 1<<(st->ndim*st->log2GR); n--; )
1151	>	if (st->u.v[n] < vmin)
1152	>	vmin = st->u.v[n];
1153	>	}
1154	>	return vmin;
1155	>	}
1156	>
1157	>	/* Subtract the given value from all tree nodes */
1158	>	static void
1159	>	SDsubtractTreVal(SDNode *st, float val)
1160	>	{
1161	>	int     n;
1162	>
1163	>	if (st->log2GR < 0) {
1164	>	for (n = 1<<st->ndim; n--; )
1165	>	SDsubtractTreVal(st->u.t[n], val);
1166	>	} else {
1167	>	for (n = 1<<(st->ndim*st->log2GR); n--; )
1168	>	if ((st->u.v[n] -= val) < 0)
1169	>	st->u.v[n] = .0f;
1170	>	}
1171	>	}
1172	>
1173	>	/* Subtract minimum Y value from BSDF */
1174	>	static double
1175	>	subtract_min_Y(SDNode *st)
1176	>	{
1177	>	float   vmin;
1178	>	/* be sure to skip unused portion */
1179	>	if (st->ndim == 3) {
1180	>	int     n;
1181	>	vmin = 1./M_PI;
1182	>	if (st->log2GR < 0) {
1183	>	for (n = 0; n < 8; n += 2) {
1184	>	float   v = SDgetTreMin(st->u.t[n]);
1185	>	if (v < vmin)
1186	>	vmin = v;
1187	>	}
1188	>	} else if (st->log2GR) {
1189	>	for (n = 1 << (3*st->log2GR - 1); n--; )
1190	>	if (st->u.v[n] < vmin)
1191	>	vmin = st->u.v[n];
1192	>	} else
1193	>	vmin = st->u.v[0];
1194	>	} else                          /* anisotropic covers entire tree */
1195	>	vmin = SDgetTreMin(st);
1196	>
1197	>	if (vmin <= .01/M_PI)
1198	>	return .0;              /* not worth bothering about */
1199	>
1200	>	SDsubtractTreVal(st, vmin);
1201	>
1202	>	return M_PI * vmin;             /* return hemispherical value */
1203	>	}
1204	>
1205	>	/* Struct used in callback to find RGB extrema */
1206	>	typedef struct {
1207	>	SDNode  **stc;                  /* original Y, u' & v' trees */
1208	>	float   rgb[3];                 /* RGB value */
1209	>	SDNode  *new_stu, *new_stv;     /* replacement u' & v' trees */
1210	>	} SDextRGBs;
1211	>
1212	>	/* Callback to find minimum RGB from Y value plus CIE (u',v') trees */
1213	>	static int
1214	>	get_min_RGB(float yval, const double *cmin, double csiz, void *cptr)
1215	>	{
1216	>	SDextRGBs       *mp = (SDextRGBs *)cptr;
1217	>	double          cmax[SD_MAXDIM];
1218	>	float           rgb[3];
1219	>
1220	>	if (mp->stc[tt_Y]->ndim == 3) {
1221	>	if (cmin[0] + .5*csiz >= .5)
1222	>	return 0;       /* ignore dead half of isotropic */
1223	>	} else
1224	>	cmax[3] = cmin[3] + csiz;
1225	>	cmax[0] = cmin[0] + csiz;
1226	>	cmax[1] = cmin[1] + csiz;
1227	>	cmax[2] = cmin[2] + csiz;
1228	>	/* average RGB color over voxel */
1229	>	SDyuv2rgb(yval, SDavgTreBox(mp->stc[tt_u], cmin, cmax),
1230	>	SDavgTreBox(mp->stc[tt_v], cmin, cmax), rgb);
1231	>	/* track smallest components */
1232	>	if (rgb[0] < mp->rgb[0]) mp->rgb[0] = rgb[0];
1233	>	if (rgb[1] < mp->rgb[1]) mp->rgb[1] = rgb[1];
1234	>	if (rgb[2] < mp->rgb[2]) mp->rgb[2] = rgb[2];
1235	>	return 0;
1236	>	}
1237	>
1238	>	/* Callback to build adjusted u' tree */
1239	>	static int
1240	>	adjust_utree(float uprime, const double *cmin, double csiz, void *cptr)
1241	>	{
1242	>	SDextRGBs       *mp = (SDextRGBs *)cptr;
1243	>	double          cmax[SD_MAXDIM];
1244	>	double          yval;
1245	>	float           rgb[3];
1246	>	C_COLOR         clr;
1247	>
1248	>	if (mp->stc[tt_Y]->ndim == 3) {
1249	>	if (cmin[0] + .5*csiz >= .5)
1250	>	return 0;       /* ignore dead half of isotropic */
1251	>	} else
1252	>	cmax[3] = cmin[3] + csiz;
1253	>	cmax[0] = cmin[0] + csiz;
1254	>	cmax[1] = cmin[1] + csiz;
1255	>	cmax[2] = cmin[2] + csiz;
1256	>	/* average RGB color over voxel */
1257	>	SDyuv2rgb(yval=SDavgTreBox(mp->stc[tt_Y], cmin, cmax), uprime,
1258	>	SDavgTreBox(mp->stc[tt_v], cmin, cmax), rgb);
1259	>	/* subtract minimum (& clamp) */
1260	>	if ((rgb[0] -= mp->rgb[0]) < 1e-5*yval) rgb[0] = 1e-5*yval;
1261	>	if ((rgb[1] -= mp->rgb[1]) < 1e-5*yval) rgb[1] = 1e-5*yval;
1262	>	if ((rgb[2] -= mp->rgb[2]) < 1e-5*yval) rgb[2] = 1e-5*yval;
1263	>	c_fromSharpRGB(rgb, &clr);      /* compute new u' for adj. RGB */
1264	>	uprime = 4.*clr.cx/(-2.*clr.cx + 12.*clr.cy + 3.);
1265	>	/* assign in new u' tree */
1266	>	mp->new_stu = SDsetVoxel(mp->new_stu, mp->stc[tt_Y]->ndim,
1267	>	cmin, csiz, uprime);
1268	>	return -(mp->new_stu == NULL);
1269	>	}
1270	>
1271	>	/* Callback to build adjusted v' tree */
1272	>	static int
1273	>	adjust_vtree(float vprime, const double *cmin, double csiz, void *cptr)
1274	>	{
1275	>	SDextRGBs       *mp = (SDextRGBs *)cptr;
1276	>	double          cmax[SD_MAXDIM];
1277	>	double          yval;
1278	>	float           rgb[3];
1279	>	C_COLOR         clr;
1280	>
1281	>	if (mp->stc[tt_Y]->ndim == 3) {
1282	>	if (cmin[0] + .5*csiz >= .5)
1283	>	return 0;       /* ignore dead half of isotropic */
1284	>	} else
1285	>	cmax[3] = cmin[3] + csiz;
1286	>	cmax[0] = cmin[0] + csiz;
1287	>	cmax[1] = cmin[1] + csiz;
1288	>	cmax[2] = cmin[2] + csiz;
1289	>	/* average RGB color over voxel */
1290	>	SDyuv2rgb(yval=SDavgTreBox(mp->stc[tt_Y], cmin, cmax),
1291	>	SDavgTreBox(mp->stc[tt_u], cmin, cmax),
1292	>	vprime, rgb);
1293	>	/* subtract minimum (& clamp) */
1294	>	if ((rgb[0] -= mp->rgb[0]) < 1e-5*yval) rgb[0] = 1e-5*yval;
1295	>	if ((rgb[1] -= mp->rgb[1]) < 1e-5*yval) rgb[1] = 1e-5*yval;
1296	>	if ((rgb[2] -= mp->rgb[2]) < 1e-5*yval) rgb[2] = 1e-5*yval;
1297	>	c_fromSharpRGB(rgb, &clr);      /* compute new v' for adj. RGB */
1298	>	vprime = 9.*clr.cy/(-2.*clr.cx + 12.*clr.cy + 3.);
1299	>	/* assign in new v' tree */
1300	>	mp->new_stv = SDsetVoxel(mp->new_stv, mp->stc[tt_Y]->ndim,
1301	>	cmin, csiz, vprime);
1302	>	return -(mp->new_stv == NULL);
1303	>	}
1304	>
1305	>	/* Subtract minimum (diffuse) color and return luminance & CIE (x,y) */
1306	>	static double
1307	>	subtract_min_RGB(C_COLOR *cs, SDNode *stc[])
1308	>	{
1309	>	SDextRGBs       my_min;
1310	>	double          ymin;
1311	>
1312	>	my_min.stc = stc;
1313	>	my_min.rgb[0] = my_min.rgb[1] = my_min.rgb[2] = FHUGE;
1314	>	my_min.new_stu = my_min.new_stv = NULL;
1315	>	/* get minimum RGB value */
1316	>	SDtraverseTre(stc[tt_Y], NULL, 0, get_min_RGB, &my_min);
1317	>	/* convert to C_COLOR */
1318	>	ymin =  c_fromSharpRGB(my_min.rgb, cs);
1319	>	if (ymin <= .01/M_PI)           /* not worth bothering about? */
1320		return .0;
1321	<
1322	<	return SDiterSum(st->u.v, st->ndim, 1 << st->log2GR, imin, imax) /
1323	<	(double)n;
1321	>	/* adjust u' & v' trees */
1322	>	SDtraverseTre(stc[tt_u], NULL, 0, adjust_utree, &my_min);
1323	>	SDtraverseTre(stc[tt_v], NULL, 0, adjust_vtree, &my_min);
1324	>	SDfreeTre(stc[tt_u]); SDfreeTre(stc[tt_v]);
1325	>	stc[tt_u] = SDsimplifyTre(my_min.new_stu);
1326	>	stc[tt_v] = SDsimplifyTre(my_min.new_stv);
1327	>	/* subtract Y & return hemispherical */
1328	>	SDsubtractTreVal(stc[tt_Y], ymin);
1329	>
1330	>	return M_PI * ymin;
1331		}
1332
1333	+	/* Extract and separate diffuse portion of BSDF */
1334	+	static void
1335	+	extract_diffuse(SDValue *dv, SDSpectralDF *df)
1336	+	{
1337	+	int     n;
1338	+	SDTre   *sdt;
1339	+
1340	+	if (df == NULL || df->ncomp <= 0) {
1341	+	dv->spec = c_dfcolor;
1342	+	dv->cieY = .0;
1343	+	return;
1344	+	}
1345	+	sdt = (SDTre *)df->comp[0].dist;
1346	+	/* subtract minimum color/grayscale */
1347	+	if (sdt->stc[tt_u] != NULL && sdt->stc[tt_v] != NULL) {
1348	+	int     i = 3*(tt_RGB_coef[1] < .001);
1349	+	while (i--) {           /* initialize on first call */
1350	+	float   rgb[3];
1351	+	rgb[0] = rgb[1] = rgb[2] = .0f; rgb[i] = 1.f;
1352	+	tt_RGB_coef[i] = c_fromSharpRGB(rgb, &tt_RGB_prim[i]);
1353	+	}
1354	+	memcpy(df->comp[0].cspec, tt_RGB_prim, sizeof(tt_RGB_prim));
1355	+	dv->cieY = subtract_min_RGB(&dv->spec, sdt->stc);
1356	+	} else {
1357	+	df->comp[0].cspec[0] = dv->spec = c_dfcolor;
1358	+	dv->cieY = subtract_min_Y(sdt->stc[tt_Y]);
1359	+	}
1360	+	df->maxHemi -= dv->cieY;        /* adjust maximum hemispherical */
1361	+	/* make sure everything is set */
1362	+	c_ccvt(&dv->spec, C_CSXY+C_CSSPEC);
1363	+	}
1364	+
1365		/* Load a variable-resolution BSDF tree from an open XML file */
1366		SDError
1367		SDloadTre(SDData *sd, ezxml_t wtl)
1368		{
1369	<	return SDEsupport;
1369	>	SDError         ec;
1370	>	ezxml_t         wld, wdb;
1371	>	int             rank;
1372	>	char            *txt;
1373	>	/* basic checks and tensor rank */
1374	>	txt = ezxml_txt(ezxml_child(ezxml_child(wtl,
1375	>	"DataDefinition"), "IncidentDataStructure"));
1376	>	if (txt == NULL || !*txt) {
1377	>	sprintf(SDerrorDetail,
1378	>	"BSDF \"%s\": missing IncidentDataStructure",
1379	>	sd->name);
1380	>	return SDEformat;
1381	>	}
1382	>	if (!strcasecmp(txt, "TensorTree3"))
1383	>	rank = 3;
1384	>	else if (!strcasecmp(txt, "TensorTree4"))
1385	>	rank = 4;
1386	>	else {
1387	>	sprintf(SDerrorDetail,
1388	>	"BSDF \"%s\": unsupported IncidentDataStructure",
1389	>	sd->name);
1390	>	return SDEsupport;
1391	>	}
1392	>	/* load BSDF components */
1393	>	for (wld = ezxml_child(wtl, "WavelengthData");
1394	>	wld != NULL; wld = wld->next) {
1395	>	const char      *cnm = ezxml_txt(ezxml_child(wld,"Wavelength"));
1396	>	int             ct = -1;
1397	>	if (!strcasecmp(cnm, "Visible"))
1398	>	ct = tt_Y;
1399	>	else if (!strcasecmp(cnm, "CIE-u"))
1400	>	ct = tt_u;
1401	>	else if (!strcasecmp(cnm, "CIE-v"))
1402	>	ct = tt_v;
1403	>	else
1404	>	continue;
1405	>	for (wdb = ezxml_child(wld, "WavelengthDataBlock");
1406	>	wdb != NULL; wdb = wdb->next)
1407	>	if ((ec = load_bsdf_data(sd, wdb, ct, rank)) != SDEnone)
1408	>	return ec;
1409	>	}
1410	>	/* separate diffuse components */
1411	>	extract_diffuse(&sd->rLambFront, sd->rf);
1412	>	extract_diffuse(&sd->rLambBack, sd->rb);
1413	>	if (sd->tf != NULL)
1414	>	extract_diffuse(&sd->tLamb, sd->tf);
1415	>	if (sd->tb != NULL)
1416	>	extract_diffuse(&sd->tLamb, sd->tb);
1417	>	/* return success */
1418	>	return SDEnone;
1419		}
1420
1421		/* Variable resolution BSDF methods */
1422	<	const SDFunc SDhandleTre = {
1423	<	NULL,
1424	<	NULL,
1425	<	NULL,
1426	<	NULL,
1427	<	&SDfreeTree,
1422	>	SDFunc SDhandleTre = {
1423	>	&SDgetTreBSDF,
1424	>	&SDqueryTreProjSA,
1425	>	&SDgetTreCDist,
1426	>	&SDsampTreCDist,
1427	>	&SDFreeBTre,
1428		};

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