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root/radiance/ray/src/rt/ambcomp.c

Comparing ray/src/rt/ambcomp.c (file contents):
Revision 1.2 by greg, Fri Jun 7 13:43:05 1991 UTC vs.
Revision 2.46 by greg, Fri May 2 21:58:50 2014 UTC

#	Line 1 | Line 1
1	–	/* Copyright (c) 1991 Regents of the University of California */
2	–
1		#ifndef lint
2	<	static char SCCSid[] = "$SunId$ LBL";
2	>	static const char       RCSid[] = "$Id$";
3		#endif
6	–
4		/*
5		* Routines to compute "ambient" values using Monte Carlo
6	+	*
7	+	*  Hessian calculations based on "Practical Hessian-Based Error Control
8	+	*      for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz
9	+	*      from ACM SIGGRAPH Asia 2012 conference proceedings.
10	+	*
11	+	*  Added book-keeping optimization to avoid calculations that would
12	+	*      cancel due to traversal both directions on edges that are adjacent
13	+	*      to same-valued triangles.  This cuts about half of Hessian math.
14	+	*
15	+	*  Declarations of external symbols in ambient.h
16		*/
17
18	<	#include  "ray.h"
18	>	#include "copyright.h"
19
20	+	#include  "ray.h"
21		#include  "ambient.h"
14	–
22		#include  "random.h"
23
24	+	#ifdef NEWAMB
25	+
26	+	extern void             SDsquare2disk(double ds[2], double seedx, double seedy);
27	+
28	+	/* vertex direction bit positions */
29	+	#define VDB_xy  0
30	+	#define VDB_y   01
31	+	#define VDB_x   02
32	+	#define VDB_Xy  03
33	+	#define VDB_xY  04
34	+	#define VDB_X   05
35	+	#define VDB_Y   06
36	+	#define VDB_XY  07
37	+	/* get opposite vertex direction bit */
38	+	#define VDB_OPP(f)      (~(f) & 07)
39	+	/* adjacent triangle vertex flags */
40	+	static const int  adjacent_trifl[8] = {
41	+	0,                      /* forbidden diagonal */
42	+	1<<VDB_x|1<<VDB_y|1<<VDB_Xy,
43	+	1<<VDB_y|1<<VDB_x|1<<VDB_xY,
44	+	1<<VDB_y|1<<VDB_Xy|1<<VDB_X,
45	+	1<<VDB_x|1<<VDB_xY|1<<VDB_Y,
46	+	1<<VDB_Xy|1<<VDB_X|1<<VDB_Y,
47	+	1<<VDB_xY|1<<VDB_Y|1<<VDB_X,
48	+	0,                      /* forbidden diagonal */
49	+	};
50	+
51		typedef struct {
52	<	short  t, p;            /* theta, phi indices */
53	<	COLOR  v;               /* value sum */
54	<	float  r;               /* 1/distance sum */
21	<	float  k;               /* variance for this division */
22	<	int  n;                 /* number of subsamples */
23	<	}  AMBSAMP;             /* ambient sample division */
52	>	COLOR   v;              /* hemisphere sample value */
53	>	FVECT   p;              /* intersection point */
54	>	} AMBSAMP;              /* sample value */
55
56		typedef struct {
57	<	FVECT  ux, uy, uz;      /* x, y and z axis directions */
58	<	short  nt, np;          /* number of theta and phi directions */
57	>	RAY     *rp;            /* originating ray sample */
58	>	FVECT   ux, uy;         /* tangent axis unit vectors */
59	>	int     ns;             /* number of samples per axis */
60	>	COLOR   acoef;          /* division contribution coefficient */
61	>	AMBSAMP sa[1];          /* sample array (extends struct) */
62		}  AMBHEMI;             /* ambient sample hemisphere */
63
64	<	extern double  sin(), cos(), sqrt();
64	>	#define ambndx(h,i,j)   ((i)*(h)->ns + (j))
65	>	#define ambsam(h,i,j)   (h)->sa[ambndx(h,i,j)]
66
67	+	typedef struct {
68	+	FVECT   r_i, r_i1, e_i, rcp, rI2_eJ2;
69	+	double  I1, I2;
70	+	int     valid;
71	+	} FFTRI;                /* vectors and coefficients for Hessian calculation */
72
73	+
74	+	/* Get index for adjacent vertex */
75		static int
76	<	ambcmp(d1, d2)                          /* decreasing order */
35	<	AMBSAMP  *d1, *d2;
76	>	adjacent_verti(AMBHEMI *hp, int i, int j, int dbit)
77		{
78	<	if (d1->k < d2->k)
79	<	return(1);
80	<	if (d1->k > d2->k)
81	<	return(-1);
82	<	return(0);
78	>	int     i0 = i*hp->ns + j;
79	>
80	>	switch (dbit) {
81	>	case VDB_y:     return(i0 - hp->ns);
82	>	case VDB_x:     return(i0 - 1);
83	>	case VDB_Xy:    return(i0 - hp->ns + 1);
84	>	case VDB_xY:    return(i0 + hp->ns - 1);
85	>	case VDB_X:     return(i0 + 1);
86	>	case VDB_Y:     return(i0 + hp->ns);
87	>	/* the following should never occur */
88	>	case VDB_xy:    return(i0 - hp->ns - 1);
89	>	case VDB_XY:    return(i0 + hp->ns + 1);
90	>	}
91	>	return(-1);
92		}
93
94
95	+	/* Get vertex direction bit for the opposite edge to complete triangle */
96		static int
97	<	ambnorm(d1, d2)                         /* standard order */
47	<	AMBSAMP  *d1, *d2;
97	>	vdb_edge(int db1, int db2)
98		{
99	<	register int  c;
99	>	switch (db1) {
100	>	case VDB_x:     return(db2==VDB_y ? VDB_Xy : VDB_Y);
101	>	case VDB_y:     return(db2==VDB_x ? VDB_xY : VDB_X);
102	>	case VDB_X:     return(db2==VDB_Xy ? VDB_y : VDB_xY);
103	>	case VDB_Y:     return(db2==VDB_xY ? VDB_x : VDB_Xy);
104	>	case VDB_xY:    return(db2==VDB_x ? VDB_y : VDB_X);
105	>	case VDB_Xy:    return(db2==VDB_y ? VDB_x : VDB_Y);
106	>	}
107	>	error(INTERNAL, "forbidden diagonal in vdb_edge()");
108	>	return(-1);
109	>	}
110
111	<	if (c = d1->t - d2->t)
112	<	return(c);
113	<	return(d1->p - d2->p);
111	>
112	>	static AMBHEMI *
113	>	inithemi(                       /* initialize sampling hemisphere */
114	>	COLOR   ac,
115	>	RAY     *r,
116	>	double  wt
117	>	)
118	>	{
119	>	AMBHEMI *hp;
120	>	double  d;
121	>	int     n, i;
122	>	/* set number of divisions */
123	>	if (ambacc <= FTINY &&
124	>	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
125	>	wt = d;                 /* avoid ray termination */
126	>	n = sqrt(ambdiv * wt) + 0.5;
127	>	i = 1 + 5*(ambacc > FTINY);     /* minimum number of samples */
128	>	if (n < i)
129	>	n = i;
130	>	/* allocate sampling array */
131	>	hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
132	>	if (hp == NULL)
133	>	return(NULL);
134	>	hp->rp = r;
135	>	hp->ns = n;
136	>	/* assign coefficient */
137	>	copycolor(hp->acoef, ac);
138	>	d = 1.0/(n*n);
139	>	scalecolor(hp->acoef, d);
140	>	/* make tangent plane axes */
141	>	hp->uy[0] = 0.5 - frandom();
142	>	hp->uy[1] = 0.5 - frandom();
143	>	hp->uy[2] = 0.5 - frandom();
144	>	for (i = 3; i--; )
145	>	if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6))
146	>	break;
147	>	if (i < 0)
148	>	error(CONSISTENCY, "bad ray direction in inithemi");
149	>	hp->uy[i] = 1.0;
150	>	VCROSS(hp->ux, hp->uy, r->ron);
151	>	normalize(hp->ux);
152	>	VCROSS(hp->uy, r->ron, hp->ux);
153	>	/* we're ready to sample */
154	>	return(hp);
155		}
156
157
158	<	double
159	<	divsample(dp, h, r)                     /* sample a division */
160	<	register AMBSAMP  *dp;
60	<	AMBHEMI  *h;
61	<	RAY  *r;
158	>	/* Sample ambient division and apply weighting coefficient */
159	>	static int
160	>	getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n)
161		{
162	+	int     hlist[3], ii;
163	+	double  spt[2], zd;
164	+	/* ambient coefficient for weight */
165	+	if (ambacc > FTINY)
166	+	setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL);
167	+	else
168	+	copycolor(arp->rcoef, hp->acoef);
169	+	if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0)
170	+	return(0);
171	+	if (ambacc > FTINY) {
172	+	multcolor(arp->rcoef, hp->acoef);
173	+	scalecolor(arp->rcoef, 1./AVGREFL);
174	+	}
175	+	hlist[0] = hp->rp->rno;
176	+	hlist[1] = j;
177	+	hlist[2] = i;
178	+	multisamp(spt, 2, urand(ilhash(hlist,3)+n));
179	+	if (!n) {                       /* avoid border samples for n==0 */
180	+	if ((spt[0] < 0.1) | (spt[0] >= 0.9))
181	+	spt[0] = 0.1 + 0.8*frandom();
182	+	if ((spt[1] < 0.1) | (spt[1] >= 0.9))
183	+	spt[1] = 0.1 + 0.8*frandom();
184	+	}
185	+	SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
186	+	zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
187	+	for (ii = 3; ii--; )
188	+	arp->rdir[ii] = spt[0]*hp->ux[ii] +
189	+	spt[1]*hp->uy[ii] +
190	+	zd*hp->rp->ron[ii];
191	+	checknorm(arp->rdir);
192	+	dimlist[ndims++] = ambndx(hp,i,j) + 90171;
193	+	rayvalue(arp);                  /* evaluate ray */
194	+	ndims--;                        /* apply coefficient */
195	+	multcolor(arp->rcol, arp->rcoef);
196	+	return(1);
197	+	}
198	+
199	+
200	+	static AMBSAMP *
201	+	ambsample(                              /* initial ambient division sample */
202	+	AMBHEMI *hp,
203	+	int     i,
204	+	int     j
205	+	)
206	+	{
207	+	AMBSAMP *ap = &ambsam(hp,i,j);
208	+	RAY     ar;
209	+	/* generate hemispherical sample */
210	+	if (!getambsamp(&ar, hp, i, j, 0))
211	+	goto badsample;
212	+	/* limit vertex distance */
213	+	if (ar.rt > 10.0*thescene.cusize)
214	+	ar.rt = 10.0*thescene.cusize;
215	+	else if (ar.rt <= FTINY)        /* should never happen! */
216	+	goto badsample;
217	+	VSUM(ap->p, ar.rorg, ar.rdir, ar.rt);
218	+	copycolor(ap->v, ar.rcol);
219	+	return(ap);
220	+	badsample:
221	+	setcolor(ap->v, 0., 0., 0.);
222	+	VCOPY(ap->p, hp->rp->rop);
223	+	return(NULL);
224	+	}
225	+
226	+
227	+	/* Estimate errors based on ambient division differences */
228	+	static float *
229	+	getambdiffs(AMBHEMI *hp)
230	+	{
231	+	float   *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
232	+	float   *ep;
233	+	AMBSAMP *ap;
234	+	double  b, d2;
235	+	int     i, j;
236	+
237	+	if (earr == NULL)               /* out of memory? */
238	+	return(NULL);
239	+	/* compute squared neighbor diffs */
240	+	for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
241	+	for (j = 0; j < hp->ns; j++, ap++, ep++) {
242	+	b = bright(ap[0].v);
243	+	if (i) {                /* from above */
244	+	d2 = b - bright(ap[-hp->ns].v);
245	+	d2 *= d2;
246	+	ep[0] += d2;
247	+	ep[-hp->ns] += d2;
248	+	}
249	+	if (j) {                /* from behind */
250	+	d2 = b - bright(ap[-1].v);
251	+	d2 *= d2;
252	+	ep[0] += d2;
253	+	ep[-1] += d2;
254	+	}
255	+	}
256	+	/* correct for number of neighbors */
257	+	earr[0] *= 2.f;
258	+	earr[hp->ns-1] *= 2.f;
259	+	earr[(hp->ns-1)*hp->ns] *= 2.f;
260	+	earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f;
261	+	for (i = 1; i < hp->ns-1; i++) {
262	+	earr[i*hp->ns] *= 4./3.;
263	+	earr[i*hp->ns + hp->ns-1] *= 4./3.;
264	+	}
265	+	for (j = 1; j < hp->ns-1; j++) {
266	+	earr[j] *= 4./3.;
267	+	earr[(hp->ns-1)*hp->ns + j] *= 4./3.;
268	+	}
269	+	return(earr);
270	+	}
271	+
272	+
273	+	/* Perform super-sampling on hemisphere (introduces bias) */
274	+	static void
275	+	ambsupersamp(double acol[3], AMBHEMI *hp, int cnt)
276	+	{
277	+	float   *earr = getambdiffs(hp);
278	+	double  e2sum = 0;
279	+	AMBSAMP *ap;
280	+	RAY     ar;
281	+	COLOR   asum;
282	+	float   *ep;
283	+	int     i, j, n;
284	+
285	+	if (earr == NULL)               /* just skip calc. if no memory */
286	+	return;
287	+	/* add up estimated variances */
288	+	for (ep = earr + hp->ns*hp->ns; ep-- > earr; )
289	+	e2sum += *ep;
290	+	ep = earr;                      /* perform super-sampling */
291	+	for (ap = hp->sa, i = 0; i < hp->ns; i++)
292	+	for (j = 0; j < hp->ns; j++, ap++) {
293	+	int     nss = *ep/e2sum*cnt + frandom();
294	+	setcolor(asum, 0., 0., 0.);
295	+	for (n = 1; n <= nss; n++) {
296	+	if (!getambsamp(&ar, hp, i, j, n)) {
297	+	nss = n-1;
298	+	break;
299	+	}
300	+	addcolor(asum, ar.rcol);
301	+	}
302	+	if (nss) {              /* update returned ambient value */
303	+	const double    ssf = 1./(nss + 1);
304	+	for (n = 3; n--; )
305	+	acol[n] += ssf*colval(asum,n) +
306	+	(ssf - 1.)*colval(ap->v,n);
307	+	}
308	+	e2sum -= *ep++;         /* update remainders */
309	+	cnt -= nss;
310	+	}
311	+	free(earr);
312	+	}
313	+
314	+
315	+	/* Compute vertex flags, indicating farthest in each direction */
316	+	static uby8 *
317	+	vertex_flags(AMBHEMI *hp)
318	+	{
319	+	uby8    *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8));
320	+	double  *dist2a = (double *)malloc(sizeof(double)*hp->ns);
321	+	uby8    *vf;
322	+	int     i, j;
323	+
324	+	if ((vflags == NULL) | (dist2a == NULL))
325	+	error(SYSTEM, "out of memory in vertex_flags()");
326	+	vf = vflags;            /* compute distances along first row */
327	+	for (j = 0; j < hp->ns; j++) {
328	+	dist2a[j] = dist2(ambsam(hp,0,j).p, hp->rp->rop);
329	+	++vf;
330	+	if (!j) continue;
331	+	if (dist2a[j] >= dist2a[j-1])
332	+	vf[0] |= 1<<VDB_x;
333	+	else
334	+	vf[-1] |= 1<<VDB_X;
335	+	}
336	+	/* flag subsequent rows */
337	+	for (i = 1; i < hp->ns; i++) {
338	+	double      d2n = dist2(ambsam(hp,i,0).p, hp->rp->rop);
339	+	for (j = 0; j < hp->ns-1; j++) {
340	+	double  d2 = d2n;
341	+	if (d2 >= dist2a[j])    /* row before */
342	+	vf[0] |= 1<<VDB_y;
343	+	else
344	+	vf[-hp->ns] |= 1<<VDB_Y;
345	+	dist2a[j] = d2n;
346	+	if (d2 >= dist2a[j+1])  /* diagonal we care about */
347	+	vf[0] |= 1<<VDB_Xy;
348	+	else
349	+	vf[1-hp->ns] |= 1<<VDB_xY;
350	+	d2n = dist2(ambsam(hp,i,j+1).p, hp->rp->rop);
351	+	if (d2 >= d2n)          /* column after */
352	+	vf[0] |= 1<<VDB_X;
353	+	else
354	+	vf[1] |= 1<<VDB_x;
355	+	++vf;
356	+	}
357	+	if (d2n >= dist2a[j])       /* final column edge */
358	+	vf[0] |= 1<<VDB_y;
359	+	else
360	+	vf[-hp->ns] |= 1<<VDB_Y;
361	+	dist2a[j] = d2n;
362	+	++vf;
363	+	}
364	+	free(dist2a);
365	+	return(vflags);
366	+	}
367	+
368	+
369	+	/* Return brightness of farthest ambient sample */
370	+	static double
371	+	back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags)
372	+	{
373	+	const int       v0 = ambndx(hp,i,j);
374	+	const int       tflags = (1<<dbit1 | 1<<dbit2);
375	+	int             v1, v2;
376	+
377	+	if ((vflags[v0] & tflags) == tflags)    /* is v0 the farthest? */
378	+	return(colval(hp->sa[v0].v,CIEY));
379	+	v1 = adjacent_verti(hp, i, j, dbit1);
380	+	if (vflags[v0] & 1<<dbit2)              /* v1 farthest if v0>v2 */
381	+	return(colval(hp->sa[v1].v,CIEY));
382	+	v2 = adjacent_verti(hp, i, j, dbit2);
383	+	if (vflags[v0] & 1<<dbit1)              /* v2 farthest if v0>v1 */
384	+	return(colval(hp->sa[v2].v,CIEY));
385	+	/* else check if v1>v2 */
386	+	if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2))
387	+	return(colval(hp->sa[v1].v,CIEY));
388	+	return(colval(hp->sa[v2].v,CIEY));
389	+	}
390	+
391	+
392	+	/* Compute vectors and coefficients for Hessian/gradient calcs */
393	+	static void
394	+	comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags)
395	+	{
396	+	const int       i0 = ambndx(hp,i,j);
397	+	double          rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
398	+	int             i1, ii;
399	+
400	+	ftp->valid = 0;                 /* check if we can skip this edge */
401	+	ii = adjacent_trifl[dbit];
402	+	if ((vflags[i0] & ii) == ii)    /* cancels if vertex used as value */
403	+	return;
404	+	i1 = adjacent_verti(hp, i, j, dbit);
405	+	ii = adjacent_trifl[VDB_OPP(dbit)];
406	+	if ((vflags[i1] & ii) == ii)    /* on either end (for both triangles) */
407	+	return;
408	+	/* else go ahead with calculation */
409	+	VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop);
410	+	VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop);
411	+	VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p);
412	+	VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
413	+	rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
414	+	dot_e = DOT(ftp->e_i,ftp->e_i);
415	+	dot_er = DOT(ftp->e_i, ftp->r_i);
416	+	rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
417	+	rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
418	+	ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
419	+	sqrt( rdot_cp );
420	+	ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
421	+	dot_e*ftp->I1 )*0.5*rdot_cp;
422	+	J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
423	+	for (ii = 3; ii--; )
424	+	ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
425	+	ftp->valid++;
426	+	}
427	+
428	+
429	+	/* Compose 3x3 matrix from two vectors */
430	+	static void
431	+	compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
432	+	{
433	+	mat[0][0] = 2.0*va[0]*vb[0];
434	+	mat[1][1] = 2.0*va[1]*vb[1];
435	+	mat[2][2] = 2.0*va[2]*vb[2];
436	+	mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
437	+	mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
438	+	mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
439	+	}
440	+
441	+
442	+	/* Compute partial 3x3 Hessian matrix for edge */
443	+	static void
444	+	comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
445	+	{
446	+	FVECT   ncp;
447	+	FVECT   m1[3], m2[3], m3[3], m4[3];
448	+	double  d1, d2, d3, d4;
449	+	double  I3, J3, K3;
450	+	int     i, j;
451	+
452	+	if (!ftp->valid) {              /* preemptive test */
453	+	memset(hess, 0, sizeof(FVECT)*3);
454	+	return;
455	+	}
456	+	/* compute intermediate coefficients */
457	+	d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
458	+	d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
459	+	d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
460	+	d4 = DOT(ftp->e_i, ftp->r_i);
461	+	I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
462	+	/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
463	+	J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
464	+	K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
465	+	/* intermediate matrices */
466	+	VCROSS(ncp, nrm, ftp->e_i);
467	+	compose_matrix(m1, ncp, ftp->rI2_eJ2);
468	+	compose_matrix(m2, ftp->r_i, ftp->r_i);
469	+	compose_matrix(m3, ftp->e_i, ftp->e_i);
470	+	compose_matrix(m4, ftp->r_i, ftp->e_i);
471	+	d1 = DOT(nrm, ftp->rcp);
472	+	d2 = -d1*ftp->I2;
473	+	d1 *= 2.0;
474	+	for (i = 3; i--; )              /* final matrix sum */
475	+	for (j = 3; j--; ) {
476	+	hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
477	+	2.0*J3*m4[i][j] );
478	+	hess[i][j] += d2*(i==j);
479	+	hess[i][j] *= -1.0/PI;
480	+	}
481	+	}
482	+
483	+
484	+	/* Reverse hessian calculation result for edge in other direction */
485	+	static void
486	+	rev_hessian(FVECT hess[3])
487	+	{
488	+	int     i;
489	+
490	+	for (i = 3; i--; ) {
491	+	hess[i][0] = -hess[i][0];
492	+	hess[i][1] = -hess[i][1];
493	+	hess[i][2] = -hess[i][2];
494	+	}
495	+	}
496	+
497	+
498	+	/* Add to radiometric Hessian from the given triangle */
499	+	static void
500	+	add2hessian(FVECT hess[3], FVECT ehess1[3],
501	+	FVECT ehess2[3], FVECT ehess3[3], double v)
502	+	{
503	+	int     i, j;
504	+
505	+	for (i = 3; i--; )
506	+	for (j = 3; j--; )
507	+	hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
508	+	}
509	+
510	+
511	+	/* Compute partial displacement form factor gradient for edge */
512	+	static void
513	+	comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
514	+	{
515	+	FVECT   ncp;
516	+	double  f1;
517	+	int     i;
518	+
519	+	if (!ftp->valid) {              /* preemptive test */
520	+	memset(grad, 0, sizeof(FVECT));
521	+	return;
522	+	}
523	+	f1 = 2.0*DOT(nrm, ftp->rcp);
524	+	VCROSS(ncp, nrm, ftp->e_i);
525	+	for (i = 3; i--; )
526	+	grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
527	+	}
528	+
529	+
530	+	/* Reverse gradient calculation result for edge in other direction */
531	+	static void
532	+	rev_gradient(FVECT grad)
533	+	{
534	+	grad[0] = -grad[0];
535	+	grad[1] = -grad[1];
536	+	grad[2] = -grad[2];
537	+	}
538	+
539	+
540	+	/* Add to displacement gradient from the given triangle */
541	+	static void
542	+	add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
543	+	{
544	+	int     i;
545	+
546	+	for (i = 3; i--; )
547	+	grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
548	+	}
549	+
550	+
551	+	/* Compute anisotropic radii and eigenvector directions */
552	+	static int
553	+	eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
554	+	{
555	+	double  hess2[2][2];
556	+	FVECT   a, b;
557	+	double  evalue[2], slope1, xmag1;
558	+	int     i;
559	+	/* project Hessian to sample plane */
560	+	for (i = 3; i--; ) {
561	+	a[i] = DOT(hessian[i], uv[0]);
562	+	b[i] = DOT(hessian[i], uv[1]);
563	+	}
564	+	hess2[0][0] = DOT(uv[0], a);
565	+	hess2[0][1] = DOT(uv[0], b);
566	+	hess2[1][0] = DOT(uv[1], a);
567	+	hess2[1][1] = DOT(uv[1], b);
568	+	/* compute eigenvalue(s) */
569	+	i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
570	+	hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
571	+	if (i == 1)                     /* double-root (circle) */
572	+	evalue[1] = evalue[0];
573	+	if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
574	+	((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) )
575	+	error(INTERNAL, "bad eigenvalue calculation");
576	+
577	+	if (evalue[0] > evalue[1]) {
578	+	ra[0] = sqrt(sqrt(4.0/evalue[0]));
579	+	ra[1] = sqrt(sqrt(4.0/evalue[1]));
580	+	slope1 = evalue[1];
581	+	} else {
582	+	ra[0] = sqrt(sqrt(4.0/evalue[1]));
583	+	ra[1] = sqrt(sqrt(4.0/evalue[0]));
584	+	slope1 = evalue[0];
585	+	}
586	+	/* compute unit eigenvectors */
587	+	if (fabs(hess2[0][1]) <= FTINY)
588	+	return;                 /* uv OK as is */
589	+	slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
590	+	xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
591	+	for (i = 3; i--; ) {
592	+	b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
593	+	a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
594	+	}
595	+	VCOPY(uv[0], a);
596	+	VCOPY(uv[1], b);
597	+	}
598	+
599	+
600	+	static void
601	+	ambHessian(                             /* anisotropic radii & pos. gradient */
602	+	AMBHEMI *hp,
603	+	FVECT   uv[2],                  /* returned */
604	+	float   ra[2],                  /* returned (optional) */
605	+	float   pg[2]                   /* returned (optional) */
606	+	)
607	+	{
608	+	static char     memerrmsg[] = "out of memory in ambHessian()";
609	+	FVECT           (*hessrow)[3] = NULL;
610	+	FVECT           *gradrow = NULL;
611	+	uby8            *vflags;
612	+	FVECT           hessian[3];
613	+	FVECT           gradient;
614	+	FFTRI           fftr;
615	+	int             i, j;
616	+	/* be sure to assign unit vectors */
617	+	VCOPY(uv[0], hp->ux);
618	+	VCOPY(uv[1], hp->uy);
619	+	/* clock-wise vertex traversal from sample POV */
620	+	if (ra != NULL) {               /* initialize Hessian row buffer */
621	+	hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
622	+	if (hessrow == NULL)
623	+	error(SYSTEM, memerrmsg);
624	+	memset(hessian, 0, sizeof(hessian));
625	+	} else if (pg == NULL)          /* bogus call? */
626	+	return;
627	+	if (pg != NULL) {               /* initialize form factor row buffer */
628	+	gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
629	+	if (gradrow == NULL)
630	+	error(SYSTEM, memerrmsg);
631	+	memset(gradient, 0, sizeof(gradient));
632	+	}
633	+	/* get vertex position flags */
634	+	vflags = vertex_flags(hp);
635	+	/* compute first row of edges */
636	+	for (j = 0; j < hp->ns-1; j++) {
637	+	comp_fftri(&fftr, hp, 0, j, VDB_X, vflags);
638	+	if (hessrow != NULL)
639	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
640	+	if (gradrow != NULL)
641	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
642	+	}
643	+	/* sum each row of triangles */
644	+	for (i = 0; i < hp->ns-1; i++) {
645	+	FVECT       hesscol[3];     /* compute first vertical edge */
646	+	FVECT       gradcol;
647	+	comp_fftri(&fftr, hp, i, 0, VDB_Y, vflags);
648	+	if (hessrow != NULL)
649	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
650	+	if (gradrow != NULL)
651	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
652	+	for (j = 0; j < hp->ns-1; j++) {
653	+	FVECT   hessdia[3];     /* compute triangle contributions */
654	+	FVECT   graddia;
655	+	double  backg;
656	+	backg = back_ambval(hp, i, j, VDB_X, VDB_Y, vflags);
657	+	/* diagonal (inner) edge */
658	+	comp_fftri(&fftr, hp, i, j+1, VDB_xY, vflags);
659	+	if (hessrow != NULL) {
660	+	comp_hessian(hessdia, &fftr, hp->rp->ron);
661	+	rev_hessian(hesscol);
662	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
663	+	}
664	+	if (gradrow != NULL) {
665	+	comp_gradient(graddia, &fftr, hp->rp->ron);
666	+	rev_gradient(gradcol);
667	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
668	+	}
669	+	/* initialize edge in next row */
670	+	comp_fftri(&fftr, hp, i+1, j+1, VDB_x, vflags);
671	+	if (hessrow != NULL)
672	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
673	+	if (gradrow != NULL)
674	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
675	+	/* new column edge & paired triangle */
676	+	backg = back_ambval(hp, i+1, j+1, VDB_x, VDB_y, vflags);
677	+	comp_fftri(&fftr, hp, i, j+1, VDB_Y, vflags);
678	+	if (hessrow != NULL) {
679	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
680	+	rev_hessian(hessdia);
681	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
682	+	if (i < hp->ns-2)
683	+	rev_hessian(hessrow[j]);
684	+	}
685	+	if (gradrow != NULL) {
686	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
687	+	rev_gradient(graddia);
688	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
689	+	if (i < hp->ns-2)
690	+	rev_gradient(gradrow[j]);
691	+	}
692	+	}
693	+	}
694	+	/* release row buffers */
695	+	if (hessrow != NULL) free(hessrow);
696	+	if (gradrow != NULL) free(gradrow);
697	+	free(vflags);
698	+
699	+	if (ra != NULL)                 /* extract eigenvectors & radii */
700	+	eigenvectors(uv, ra, hessian);
701	+	if (pg != NULL) {               /* tangential position gradient */
702	+	pg[0] = DOT(gradient, uv[0]);
703	+	pg[1] = DOT(gradient, uv[1]);
704	+	}
705	+	}
706	+
707	+
708	+	/* Compute direction gradient from a hemispherical sampling */
709	+	static void
710	+	ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
711	+	{
712	+	AMBSAMP *ap;
713	+	double  dgsum[2];
714	+	int     n;
715	+	FVECT   vd;
716	+	double  gfact;
717	+
718	+	dgsum[0] = dgsum[1] = 0.0;      /* sum values times -tan(theta) */
719	+	for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
720	+	/* use vector for azimuth + 90deg */
721	+	VSUB(vd, ap->p, hp->rp->rop);
722	+	/* brightness over cosine factor */
723	+	gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
724	+	/* sine = proj_radius/vd_length */
725	+	dgsum[0] -= DOT(uv[1], vd) * gfact;
726	+	dgsum[1] += DOT(uv[0], vd) * gfact;
727	+	}
728	+	dg[0] = dgsum[0] / (hp->ns*hp->ns);
729	+	dg[1] = dgsum[1] / (hp->ns*hp->ns);
730	+	}
731	+
732	+
733	+	int
734	+	doambient(                              /* compute ambient component */
735	+	COLOR   rcol,                   /* input/output color */
736	+	RAY     *r,
737	+	double  wt,
738	+	FVECT   uv[2],                  /* returned (optional) */
739	+	float   ra[2],                  /* returned (optional) */
740	+	float   pg[2],                  /* returned (optional) */
741	+	float   dg[2]                   /* returned (optional) */
742	+	)
743	+	{
744	+	AMBHEMI *hp = inithemi(rcol, r, wt);
745	+	int     cnt;
746	+	FVECT   my_uv[2];
747	+	double  d, K, acol[3];
748	+	AMBSAMP *ap;
749	+	int     i, j;
750	+	/* check/initialize */
751	+	if (hp == NULL)
752	+	return(0);
753	+	if (uv != NULL)
754	+	memset(uv, 0, sizeof(FVECT)*2);
755	+	if (ra != NULL)
756	+	ra[0] = ra[1] = 0.0;
757	+	if (pg != NULL)
758	+	pg[0] = pg[1] = 0.0;
759	+	if (dg != NULL)
760	+	dg[0] = dg[1] = 0.0;
761	+	/* sample the hemisphere */
762	+	acol[0] = acol[1] = acol[2] = 0.0;
763	+	cnt = 0;
764	+	for (i = hp->ns; i--; )
765	+	for (j = hp->ns; j--; )
766	+	if ((ap = ambsample(hp, i, j)) != NULL) {
767	+	addcolor(acol, ap->v);
768	+	++cnt;
769	+	}
770	+	if (!cnt) {
771	+	setcolor(rcol, 0.0, 0.0, 0.0);
772	+	free(hp);
773	+	return(0);              /* no valid samples */
774	+	}
775	+	if (cnt < hp->ns*hp->ns) {      /* incomplete sampling? */
776	+	copycolor(rcol, acol);
777	+	free(hp);
778	+	return(-1);             /* return value w/o Hessian */
779	+	}
780	+	cnt = ambssamp*wt + 0.5;        /* perform super-sampling? */
781	+	if (cnt > 0)
782	+	ambsupersamp(acol, hp, cnt);
783	+	copycolor(rcol, acol);          /* final indirect irradiance/PI */
784	+	if ((ra == NULL) & (pg == NULL) & (dg == NULL)) {
785	+	free(hp);
786	+	return(-1);             /* no radius or gradient calc. */
787	+	}
788	+	if ((d = bright(acol)) > FTINY) {       /* normalize Y values */
789	+	d = 0.99*(hp->ns*hp->ns)/d;
790	+	K = 0.01;
791	+	} else {                        /* or fall back on geometric Hessian */
792	+	K = 1.0;
793	+	pg = NULL;
794	+	dg = NULL;
795	+	}
796	+	ap = hp->sa;                    /* relative Y channel from here on... */
797	+	for (i = hp->ns*hp->ns; i--; ap++)
798	+	colval(ap->v,CIEY) = bright(ap->v)*d + K;
799	+
800	+	if (uv == NULL)                 /* make sure we have axis pointers */
801	+	uv = my_uv;
802	+	/* compute radii & pos. gradient */
803	+	ambHessian(hp, uv, ra, pg);
804	+
805	+	if (dg != NULL)                 /* compute direction gradient */
806	+	ambdirgrad(hp, uv, dg);
807	+
808	+	if (ra != NULL) {               /* scale/clamp radii */
809	+	if (pg != NULL) {
810	+	if (ra[0]*(d = fabs(pg[0])) > 1.0)
811	+	ra[0] = 1.0/d;
812	+	if (ra[1]*(d = fabs(pg[1])) > 1.0)
813	+	ra[1] = 1.0/d;
814	+	if (ra[0] > ra[1])
815	+	ra[0] = ra[1];
816	+	}
817	+	if (ra[0] < minarad) {
818	+	ra[0] = minarad;
819	+	if (ra[1] < minarad)
820	+	ra[1] = minarad;
821	+	}
822	+	ra[0] *= d = 1.0/sqrt(sqrt(wt));
823	+	if ((ra[1] *= d) > 2.0*ra[0])
824	+	ra[1] = 2.0*ra[0];
825	+	if (ra[1] > maxarad) {
826	+	ra[1] = maxarad;
827	+	if (ra[0] > maxarad)
828	+	ra[0] = maxarad;
829	+	}
830	+	if (pg != NULL) {       /* cap gradient if necessary */
831	+	d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
832	+	if (d > 1.0) {
833	+	d = 1.0/sqrt(d);
834	+	pg[0] *= d;
835	+	pg[1] *= d;
836	+	}
837	+	}
838	+	}
839	+	free(hp);                       /* clean up and return */
840	+	return(1);
841	+	}
842	+
843	+
844	+	#else /* ! NEWAMB */
845	+
846	+
847	+	void
848	+	inithemi(                       /* initialize sampling hemisphere */
849	+	AMBHEMI  *hp,
850	+	COLOR ac,
851	+	RAY  *r,
852	+	double  wt
853	+	)
854	+	{
855	+	double  d;
856	+	int  i;
857	+	/* set number of divisions */
858	+	if (ambacc <= FTINY &&
859	+	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
860	+	wt = d;                 /* avoid ray termination */
861	+	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
862	+	i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
863	+	if (hp->nt < i)
864	+	hp->nt = i;
865	+	hp->np = PI * hp->nt + 0.5;
866	+	/* set number of super-samples */
867	+	hp->ns = ambssamp * wt + 0.5;
868	+	/* assign coefficient */
869	+	copycolor(hp->acoef, ac);
870	+	d = 1.0/(hp->nt*hp->np);
871	+	scalecolor(hp->acoef, d);
872	+	/* make axes */
873	+	VCOPY(hp->uz, r->ron);
874	+	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
875	+	for (i = 0; i < 3; i++)
876	+	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
877	+	break;
878	+	if (i >= 3)
879	+	error(CONSISTENCY, "bad ray direction in inithemi");
880	+	hp->uy[i] = 1.0;
881	+	fcross(hp->ux, hp->uy, hp->uz);
882	+	normalize(hp->ux);
883	+	fcross(hp->uy, hp->uz, hp->ux);
884	+	}
885	+
886	+
887	+	int
888	+	divsample(                              /* sample a division */
889	+	AMBSAMP  *dp,
890	+	AMBHEMI  *h,
891	+	RAY  *r
892	+	)
893	+	{
894		RAY  ar;
895	<	int  hlist[4];
895	>	int  hlist[3];
896	>	double  spt[2];
897		double  xd, yd, zd;
898		double  b2;
899		double  phi;
900	<	register int  i;
901	<
902	<	if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
903	<	return(0.0);
900	>	int  i;
901	>	/* ambient coefficient for weight */
902	>	if (ambacc > FTINY)
903	>	setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
904	>	else
905	>	copycolor(ar.rcoef, h->acoef);
906	>	if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
907	>	return(-1);
908	>	if (ambacc > FTINY) {
909	>	multcolor(ar.rcoef, h->acoef);
910	>	scalecolor(ar.rcoef, 1./AVGREFL);
911	>	}
912		hlist[0] = r->rno;
913		hlist[1] = dp->t;
914		hlist[2] = dp->p;
915	<	hlist[3] = 0;
916	<	zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
917	<	hlist[3] = 1;
918	<	phi = 2.0*PI * (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
919	<	xd = cos(phi) * zd;
80	<	yd = sin(phi) * zd;
915	>	multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
916	>	zd = sqrt((dp->t + spt[0])/h->nt);
917	>	phi = 2.0*PI * (dp->p + spt[1])/h->np;
918	>	xd = tcos(phi) * zd;
919	>	yd = tsin(phi) * zd;
920		zd = sqrt(1.0 - zd*zd);
921		for (i = 0; i < 3; i++)
922		ar.rdir[i] =    xd*h->ux[i] +
923		yd*h->uy[i] +
924		zd*h->uz[i];
925	+	checknorm(ar.rdir);
926		dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
927		rayvalue(&ar);
928		ndims--;
929	+	multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
930		addcolor(dp->v, ar.rcol);
931	<	if (ar.rot < FHUGE)
932	<	dp->r += 1.0/ar.rot;
931	>	/* use rt to improve gradient calc */
932	>	if (ar.rt > FTINY && ar.rt < FHUGE)
933	>	dp->r += 1.0/ar.rt;
934		/* (re)initialize error */
935		if (dp->n++) {
936		b2 = bright(dp->v)/dp->n - bright(ar.rcol);
#	Line 96 | Line 938 | RAY  *r;
938		dp->k = b2/(dp->n*dp->n);
939		} else
940		dp->k = 0.0;
941	<	return(ar.rot);
941	>	return(0);
942		}
943
944
945	+	static int
946	+	ambcmp(                                 /* decreasing order */
947	+	const void *p1,
948	+	const void *p2
949	+	)
950	+	{
951	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
952	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
953	+
954	+	if (d1->k < d2->k)
955	+	return(1);
956	+	if (d1->k > d2->k)
957	+	return(-1);
958	+	return(0);
959	+	}
960	+
961	+
962	+	static int
963	+	ambnorm(                                /* standard order */
964	+	const void *p1,
965	+	const void *p2
966	+	)
967	+	{
968	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
969	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
970	+	int     c;
971	+
972	+	if ( (c = d1->t - d2->t) )
973	+	return(c);
974	+	return(d1->p - d2->p);
975	+	}
976	+
977	+
978		double
979	<	doambient(acol, r, pg, dg)              /* compute ambient component */
980	<	COLOR  acol;
981	<	RAY  *r;
982	<	FVECT  pg, dg;
979	>	doambient(                              /* compute ambient component */
980	>	COLOR  rcol,
981	>	RAY  *r,
982	>	double  wt,
983	>	FVECT  pg,
984	>	FVECT  dg
985	>	)
986		{
987	<	double  b, d;
987	>	double  b, d=0;
988		AMBHEMI  hemi;
989		AMBSAMP  *div;
990		AMBSAMP  dnew;
991	<	register AMBSAMP  *dp;
991	>	double  acol[3];
992	>	AMBSAMP  *dp;
993		double  arad;
994	<	int  ndivs, ns;
995	<	register int  i, j;
117	<	/* initialize color */
118	<	setcolor(acol, 0.0, 0.0, 0.0);
994	>	int  divcnt;
995	>	int  i, j;
996		/* initialize hemisphere */
997	<	inithemi(&hemi, r);
998	<	ndivs = hemi.nt * hemi.np;
999	<	if (ndivs == 0)
997	>	inithemi(&hemi, rcol, r, wt);
998	>	divcnt = hemi.nt * hemi.np;
999	>	/* initialize */
1000	>	if (pg != NULL)
1001	>	pg[0] = pg[1] = pg[2] = 0.0;
1002	>	if (dg != NULL)
1003	>	dg[0] = dg[1] = dg[2] = 0.0;
1004	>	setcolor(rcol, 0.0, 0.0, 0.0);
1005	>	if (divcnt == 0)
1006		return(0.0);
1007	<	/* set number of super-samples */
1008	<	ns = ambssamp * r->rweight + 0.5;
1009	<	if (ns > 0 || pg != NULL || dg != NULL) {
127	<	div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
1007	>	/* allocate super-samples */
1008	>	if (hemi.ns > 0 || pg != NULL || dg != NULL) {
1009	>	div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP));
1010		if (div == NULL)
1011		error(SYSTEM, "out of memory in doambient");
1012		} else
1013		div = NULL;
1014		/* sample the divisions */
1015		arad = 0.0;
1016	+	acol[0] = acol[1] = acol[2] = 0.0;
1017		if ((dp = div) == NULL)
1018		dp = &dnew;
1019	+	divcnt = 0;
1020		for (i = 0; i < hemi.nt; i++)
1021		for (j = 0; j < hemi.np; j++) {
1022		dp->t = i; dp->p = j;
1023		setcolor(dp->v, 0.0, 0.0, 0.0);
1024		dp->r = 0.0;
1025		dp->n = 0;
1026	<	if ((d = divsample(dp, &hemi, r)) == 0.0)
1027	<	goto oopsy;
1026	>	if (divsample(dp, &hemi, r) < 0) {
1027	>	if (div != NULL)
1028	>	dp++;
1029	>	continue;
1030	>	}
1031	>	arad += dp->r;
1032	>	divcnt++;
1033		if (div != NULL)
1034		dp++;
1035	<	else {
1035	>	else
1036		addcolor(acol, dp->v);
148	–	arad += dp->r;
149	–	}
1037		}
1038	<	if (ns > 0) {                   /* perform super-sampling */
1039	<	comperrs(div, hemi);                    /* compute errors */
1040	<	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
1041	<	dp = div + ndivs;                       /* skim excess */
1042	<	for (i = ndivs; i > ns; i--) {
1043	<	dp--;
1044	<	addcolor(acol, dp->v);
1045	<	arad += dp->r;
1046	<	}
1038	>	if (!divcnt) {
1039	>	if (div != NULL)
1040	>	free((void *)div);
1041	>	return(0.0);            /* no samples taken */
1042	>	}
1043	>	if (divcnt < hemi.nt*hemi.np) {
1044	>	pg = dg = NULL;         /* incomplete sampling */
1045	>	hemi.ns = 0;
1046	>	} else if (arad > FTINY && divcnt/arad < minarad) {
1047	>	hemi.ns = 0;            /* close enough */
1048	>	} else if (hemi.ns > 0) {       /* else perform super-sampling? */
1049	>	comperrs(div, &hemi);                   /* compute errors */
1050	>	qsort(div, divcnt, sizeof(AMBSAMP), ambcmp);    /* sort divs */
1051		/* super-sample */
1052	<	for (i = ns; i > 0; i--) {
1053	<	copystruct(&dnew, div);
1054	<	if ((d = divsample(&dnew, &hemi)) == 0.0)
1055	<	goto oopsy;
1056	<	if (d < FHUGE)
1057	<	arad += 1.0 / d;
1058	<	/* reinsert */
1059	<	dp = div;
169	<	j = ndivs < i ? ndivs : i;
1052	>	for (i = hemi.ns; i > 0; i--) {
1053	>	dnew = *div;
1054	>	if (divsample(&dnew, &hemi, r) < 0) {
1055	>	dp++;
1056	>	continue;
1057	>	}
1058	>	dp = div;               /* reinsert */
1059	>	j = divcnt < i ? divcnt : i;
1060		while (--j > 0 && dnew.k < dp[1].k) {
1061	<	copystruct(dp, dp+1);
1061	>	*dp = *(dp+1);
1062		dp++;
1063		}
1064	<	copystruct(dp, &dnew);
175	<	/* extract darkest */
176	<	if (i <= ndivs) {
177	<	dp = div + i-1;
178	<	arad += dp->r;
179	<	if (dp->n > 1) {
180	<	b = 1.0/dp->n;
181	<	scalecolor(dp->v, b);
182	<	dp->r *= b;
183	<	dp->n = 1;
184	<	}
185	<	addcolor(acol, dp->v);
186	<	}
1064	>	*dp = dnew;
1065		}
1066		if (pg != NULL || dg != NULL)   /* restore order */
1067	<	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
1067	>	qsort(div, divcnt, sizeof(AMBSAMP), ambnorm);
1068		}
1069		/* compute returned values */
1070	<	if (pg != NULL)
1071	<	posgradient(pg, div, &hemi);
1072	<	if (dg != NULL)
1073	<	dirgradient(dg, div, &hemi);
1074	<	if (div != NULL)
1075	<	free((char *)div);
1076	<	b = 1.0/ndivs;
1077	<	scalecolor(acol, b);
1070	>	if (div != NULL) {
1071	>	arad = 0.0;             /* note: divcnt may be < nt*np */
1072	>	for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) {
1073	>	arad += dp->r;
1074	>	if (dp->n > 1) {
1075	>	b = 1.0/dp->n;
1076	>	scalecolor(dp->v, b);
1077	>	dp->r *= b;
1078	>	dp->n = 1;
1079	>	}
1080	>	addcolor(acol, dp->v);
1081	>	}
1082	>	b = bright(acol);
1083	>	if (b > FTINY) {
1084	>	b = 1.0/b;      /* compute & normalize gradient(s) */
1085	>	if (pg != NULL) {
1086	>	posgradient(pg, div, &hemi);
1087	>	for (i = 0; i < 3; i++)
1088	>	pg[i] *= b;
1089	>	}
1090	>	if (dg != NULL) {
1091	>	dirgradient(dg, div, &hemi);
1092	>	for (i = 0; i < 3; i++)
1093	>	dg[i] *= b;
1094	>	}
1095	>	}
1096	>	free((void *)div);
1097	>	}
1098	>	copycolor(rcol, acol);
1099		if (arad <= FTINY)
201	–	arad = FHUGE;
202	–	else
203	–	arad = (ndivs+ns)/arad;
204	–	if (arad > maxarad)
1100		arad = maxarad;
1101	<	else if (arad < minarad)
1101	>	else
1102	>	arad = (divcnt+hemi.ns)/arad;
1103	>	if (pg != NULL) {               /* reduce radius if gradient large */
1104	>	d = DOT(pg,pg);
1105	>	if (d*arad*arad > 1.0)
1106	>	arad = 1.0/sqrt(d);
1107	>	}
1108	>	if (arad < minarad) {
1109		arad = minarad;
1110	<	arad /= sqrt(r->rweight);
1110	>	if (pg != NULL && d*arad*arad > 1.0) {  /* cap gradient */
1111	>	d = 1.0/arad/sqrt(d);
1112	>	for (i = 0; i < 3; i++)
1113	>	pg[i] *= d;
1114	>	}
1115	>	}
1116	>	if ((arad /= sqrt(wt)) > maxarad)
1117	>	arad = maxarad;
1118		return(arad);
210	–	oopsy:
211	–	if (div != NULL)
212	–	free((char *)div);
213	–	return(0.0);
1119		}
1120
1121
1122	<	inithemi(hp, r)                 /* initialize sampling hemisphere */
1123	<	register AMBHEMI  *hp;
1124	<	RAY  *r;
1122	>	void
1123	>	comperrs(                       /* compute initial error estimates */
1124	>	AMBSAMP  *da,   /* assumes standard ordering */
1125	>	AMBHEMI  *hp
1126	>	)
1127		{
221	–	register int  i;
222	–	/* set number of divisions */
223	–	hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
224	–	hp->np = 2 * hp->nt;
225	–	/* make axes */
226	–	VCOPY(hp->uz, r->ron);
227	–	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
228	–	for (i = 0; i < 3; i++)
229	–	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
230	–	break;
231	–	if (i >= 3)
232	–	error(CONSISTENCY, "bad ray direction in inithemi");
233	–	hp->uy[i] = 1.0;
234	–	fcross(hp->ux, hp->uz, hp->uy);
235	–	normalize(hp->ux);
236	–	fcross(hp->uy, hp->ux, hp->uz);
237	–	}
238	–
239	–
240	–	comperrs(da, hp)                /* compute initial error estimates */
241	–	AMBSAMP  *da;           /* assumes standard ordering */
242	–	register AMBHEMI  *hp;
243	–	{
1128		double  b, b2;
1129		int  i, j;
1130	<	register AMBSAMP  *dp;
1130	>	AMBSAMP  *dp;
1131		/* sum differences from neighbors */
1132		dp = da;
1133		for (i = 0; i < hp->nt; i++)
1134		for (j = 0; j < hp->np; j++) {
1135	+	#ifdef  DEBUG
1136	+	if (dp->t != i || dp->p != j)
1137	+	error(CONSISTENCY,
1138	+	"division order in comperrs");
1139	+	#endif
1140		b = bright(dp[0].v);
1141		if (i > 0) {            /* from above */
1142		b2 = bright(dp[-hp->np].v) - b;
#	Line 260 | Line 1149 | register AMBHEMI  *hp;
1149		b2 *= b2 * 0.25;
1150		dp[0].k += b2;
1151		dp[-1].k += b2;
1152	<	}
1153	<	if (j == hp->np-1) {    /* around */
265	<	b2 = bright(dp[-(hp->np-1)].v) - b;
1152	>	} else {                /* around */
1153	>	b2 = bright(dp[hp->np-1].v) - b;
1154		b2 *= b2 * 0.25;
1155		dp[0].k += b2;
1156	<	dp[-(hp->np-1)].k += b2;
1156	>	dp[hp->np-1].k += b2;
1157		}
1158		dp++;
1159		}
#	Line 283 | Line 1171 | register AMBHEMI  *hp;
1171		}
1172
1173
1174	<	posgradient(gv, da, hp)                         /* compute position gradient */
1175	<	FVECT  gv;
1176	<	AMBSAMP  *da;                   /* assumes standard ordering */
1177	<	AMBHEMI  *hp;
1174	>	void
1175	>	posgradient(                                    /* compute position gradient */
1176	>	FVECT  gv,
1177	>	AMBSAMP  *da,                   /* assumes standard ordering */
1178	>	AMBHEMI  *hp
1179	>	)
1180		{
1181	<	register int  i, j;
1182	<	double  b, d;
1181	>	int  i, j;
1182	>	double  nextsine, lastsine, b, d;
1183		double  mag0, mag1;
1184		double  phi, cosp, sinp, xd, yd;
1185	<	register AMBSAMP  *dp;
1185	>	AMBSAMP  *dp;
1186
1187		xd = yd = 0.0;
1188		for (j = 0; j < hp->np; j++) {
1189		dp = da + j;
1190		mag0 = mag1 = 0.0;
1191	+	lastsine = 0.0;
1192		for (i = 0; i < hp->nt; i++) {
1193		#ifdef  DEBUG
1194		if (dp->t != i || dp->p != j)
#	Line 308 | Line 1199 | AMBHEMI  *hp;
1199		if (i > 0) {
1200		d = dp[-hp->np].r;
1201		if (dp[0].r > d) d = dp[0].r;
1202	<	d *= 1.0 - sqrt((double)i/hp->nt);
1202	>	/* sin(t)*cos(t)^2 */
1203	>	d *= lastsine * (1.0 - (double)i/hp->nt);
1204		mag0 += d*(b - bright(dp[-hp->np].v));
1205		}
1206	+	nextsine = sqrt((double)(i+1)/hp->nt);
1207		if (j > 0) {
1208		d = dp[-1].r;
1209		if (dp[0].r > d) d = dp[0].r;
1210	<	mag1 += d*(b - bright(dp[-1].v));
1210	>	mag1 += d * (nextsine - lastsine) *
1211	>	(b - bright(dp[-1].v));
1212		} else {
1213		d = dp[hp->np-1].r;
1214		if (dp[0].r > d) d = dp[0].r;
1215	<	mag1 += d*(b - bright(dp[hp->np-1].v));
1215	>	mag1 += d * (nextsine - lastsine) *
1216	>	(b - bright(dp[hp->np-1].v));
1217		}
1218		dp += hp->np;
1219	+	lastsine = nextsine;
1220		}
1221	<	if (hp->nt > 1) {
326	<	mag0 /= (double)(hp->nt-1);
327	<	mag1 /= (double)hp->nt;
328	<	}
1221	>	mag0 *= 2.0*PI / hp->np;
1222		phi = 2.0*PI * (double)j/hp->np;
1223	<	cosp = cos(phi); sinp = sin(phi);
1223	>	cosp = tcos(phi); sinp = tsin(phi);
1224		xd += mag0*cosp - mag1*sinp;
1225		yd += mag0*sinp + mag1*cosp;
1226		}
1227		for (i = 0; i < 3; i++)
1228	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/hp->np;
1228	>	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI;
1229		}
1230
1231
1232	<	dirgradient(gv, da, hp)                         /* compute direction gradient */
1233	<	FVECT  gv;
1234	<	AMBSAMP  *da;                   /* assumes standard ordering */
1235	<	AMBHEMI  *hp;
1232	>	void
1233	>	dirgradient(                                    /* compute direction gradient */
1234	>	FVECT  gv,
1235	>	AMBSAMP  *da,                   /* assumes standard ordering */
1236	>	AMBHEMI  *hp
1237	>	)
1238		{
1239	<	register int  i, j;
1239	>	int  i, j;
1240		double  mag;
1241		double  phi, xd, yd;
1242	<	register AMBSAMP  *dp;
1242	>	AMBSAMP  *dp;
1243
1244		xd = yd = 0.0;
1245		for (j = 0; j < hp->np; j++) {
#	Line 356 | Line 1251 | AMBHEMI  *hp;
1251		error(CONSISTENCY,
1252		"division order in dirgradient");
1253		#endif
1254	<	mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
1254	>	/* tan(t) */
1255	>	mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
1256		dp += hp->np;
1257		}
1258		phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
1259	<	xd += mag * cos(phi);
1260	<	yd += mag * sin(phi);
1259	>	xd += mag * tcos(phi);
1260	>	yd += mag * tsin(phi);
1261		}
1262		for (i = 0; i < 3; i++)
1263	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/(hp->nt*hp->np);
1263	>	gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
1264		}
1265	+
1266	+	#endif  /* ! NEWAMB */

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