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Comparing ray/src/rt/ambcomp.c (file contents):
Revision 1.9 by greg, Thu Jul 11 16:39:00 1991 UTC vs.
Revision 2.105 by greg, Thu Aug 21 20:38:41 2025 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	+	#ifndef MINADIV
25	+	#define MINADIV         7       /* minimum # divisions in each dimension */
26	+	#endif
27	+	#ifndef MINSDIST
28	+	#define MINSDIST        0.2     /* def. min. spacing = 1/5th division */
29	+	#endif
30	+
31		typedef struct {
32	<	short  t, p;            /* theta, phi indices */
33	<	COLOR  v;               /* value sum */
34	<	float  r;               /* 1/distance sum */
35	<	float  k;               /* variance for this division */
22	<	int  n;                 /* number of subsamples */
23	<	}  AMBSAMP;             /* ambient sample division */
32	>	FVECT   p;              /* intersection point */
33	>	float   d;              /* reciprocal distance */
34	>	SCOLOR  v;              /* hemisphere sample value */
35	>	} AMBSAMP;              /* sample value */
36
37		typedef struct {
38	<	FVECT  ux, uy, uz;      /* x, y and z axis directions */
39	<	short  nt, np;          /* number of theta and phi directions */
38	>	RAY     *rp;            /* originating ray sample */
39	>	int     ns;             /* number of samples per axis */
40	>	int     sampOK;         /* acquired full sample set? */
41	>	int     atyp;           /* RAMBIENT or TAMBIENT */
42	>	SCOLOR  acoef;          /* division contribution coefficient */
43	>	SCOLOR  acol;           /* accumulated color */
44	>	FVECT   onrm;           /* oriented unperturbed surface normal */
45	>	FVECT   ux, uy;         /* tangent axis unit vectors */
46	>	AMBSAMP sa[1];          /* sample array (extends struct) */
47		}  AMBHEMI;             /* ambient sample hemisphere */
48
49	<	extern double  sin(), cos(), sqrt();
49	>	#define AI(h,i,j)       ((i)*(h)->ns + (j))
50	>	#define ambsam(h,i,j)   (h)->sa[AI(h,i,j)]
51
52	+	typedef struct {
53	+	FVECT   r_i, r_i1, e_i, rcp, rI2_eJ2;
54	+	double  I1, I2;
55	+	} FFTRI;                /* vectors and coefficients for Hessian calculation */
56
57	+
58	+	#define XLOTSIZ         512             /* size of used car lot */
59	+	#define CFIRST          0               /* first corner */
60	+	#define COTHER          (CFIRST+4)      /* non-corner sample */
61	+	#define CMAXTARGET      (int)(XLOTSIZ*MINSDIST/(1-MINSDIST))
62	+
63		static int
64	<	ambcmp(d1, d2)                          /* decreasing order */
35	<	AMBSAMP  *d1, *d2;
64	>	psample_class(double ss[2])             /* classify patch sample */
65		{
66	<	if (d1->k < d2->k)
67	<	return(1);
68	<	if (d1->k > d2->k)
69	<	return(-1);
70	<	return(0);
66	>	if (ss[0] < MINSDIST) {
67	>	if (ss[1] < MINSDIST)
68	>	return(CFIRST);
69	>	if (ss[1] > 1.-MINSDIST)
70	>	return(CFIRST+2);
71	>	} else if (ss[0] > 1.-MINSDIST) {
72	>	if (ss[1] < MINSDIST)
73	>	return(CFIRST+1);
74	>	if (ss[1] > 1.-MINSDIST)
75	>	return(CFIRST+3);
76	>	}
77	>	return(COTHER);                 /* not in a corner */
78		}
79
80	+	static void
81	+	trade_patchsamp(double ss[2])           /* trade in problem patch position */
82	+	{
83	+	static float    tradelot[XLOTSIZ][2];
84	+	static int      gterm[COTHER+1];
85	+	double          repl[2];
86	+	int             sclass, rclass;
87	+	int             x;
88	+	re_initialize:                          /* initialize lot? */
89	+	while (gterm[COTHER] < XLOTSIZ) {
90	+	tradelot[gterm[COTHER]][0] = frandom();
91	+	tradelot[gterm[COTHER]][1] = frandom();
92	+	++gterm[COTHER];
93	+	}
94	+	/* get trade-in candidate... */
95	+	sclass = psample_class(ss);     /* submitted corner or not? */
96	+	switch (sclass) {
97	+	case COTHER:                    /* trade mid-edge with corner/any */
98	+	x = irandom( gterm[COTHER-1] > CMAXTARGET
99	+	? gterm[COTHER-1] : XLOTSIZ );
100	+	break;
101	+	case CFIRST:                    /* kick out of first corner */
102	+	x = gterm[CFIRST] + irandom(XLOTSIZ - gterm[CFIRST]);
103	+	break;
104	+	default:                        /* kick out of 2nd-4th corner */
105	+	x = irandom(XLOTSIZ - (gterm[sclass] - gterm[sclass-1]));
106	+	x += (x >= gterm[sclass-1])*(gterm[sclass] - gterm[sclass-1]);
107	+	break;
108	+	}
109	+	if (x >= XLOTSIZ) {             /* uh-oh... trapped in a corner! */
110	+	memset(gterm, 0, sizeof(gterm));
111	+	goto re_initialize;
112	+	}
113	+	repl[0] = tradelot[x][0];       /* save selected replacement (result) */
114	+	repl[1] = tradelot[x][1];
115	+	/* identify replacement class */
116	+	for (rclass = CFIRST; rclass < COTHER; rclass++)
117	+	if (x < gterm[rclass])
118	+	break;          /* repark to keep classes grouped */
119	+	while (rclass > sclass) {       /* replacement group after submitted? */
120	+	tradelot[x][0] = tradelot[gterm[rclass-1]][0];
121	+	tradelot[x][1] = tradelot[gterm[rclass-1]][1];
122	+	x = gterm[--rclass]++;
123	+	}
124	+	while (rclass < sclass) {       /* replacement group before submitted? */
125	+	tradelot[x][0] = tradelot[--gterm[rclass]][0];
126	+	tradelot[x][1] = tradelot[gterm[rclass]][1];
127	+	x = gterm[rclass++];
128	+	}
129	+	tradelot[x][0] = ss[0];         /* complete the trade-in */
130	+	tradelot[x][1] = ss[1];
131	+	ss[0] = repl[0];
132	+	ss[1] = repl[1];
133	+	}
134
135	+	#undef XLOTSIZ
136	+	#undef COTHER
137	+	#undef CFIRST
138	+
139	+
140		static int
141	<	ambnorm(d1, d2)                         /* standard order */
142	<	AMBSAMP  *d1, *d2;
141	>	ambcollision(                           /* proposed direction collides? */
142	>	AMBHEMI *hp,
143	>	int     i,
144	>	int     j,
145	>	RREAL   spt[2]
146	>	)
147		{
148	<	register int  c;
149	<
150	<	if (c = d1->t - d2->t)
151	<	return(c);
152	<	return(d1->p - d2->p);
148	>	int     ii, jj;
149	>	/* check existing neighbors */
150	>	for (ii = i-1; ii <= i+1; ii++) {
151	>	if (ii < 0) continue;
152	>	if (ii >= hp->ns) break;
153	>	for (jj = j-1; jj <= j+1; jj++) {
154	>	AMBSAMP *ap;
155	>	FVECT   avec;
156	>	double  dx, dy;
157	>	if (jj < 0) continue;
158	>	if (jj >= hp->ns) break;
159	>	if ((ii==i) & (jj==j)) continue;
160	>	ap = &ambsam(hp,ii,jj);
161	>	if (ap->d <= .5/FHUGE)
162	>	continue;       /* no one home */
163	>	VSUB(avec, ap->p, hp->rp->rop);
164	>	normalize(avec);        /* use diskworld distance */
165	>	dx = DOT(avec, hp->ux) - spt[0];
166	>	dy = DOT(avec, hp->uy) - spt[1];
167	>	if ((dx*dx + dy*dy)*(hp->ns*hp->ns) <
168	>	PI*MINSDIST*MINSDIST)
169	>	return(1);      /* too close */
170	>	}
171	>	}
172	>	return(0);                      /* nothing to worry about */
173		}
174
175
176	<	divsample(dp, h, r)                     /* sample a division */
177	<	register AMBSAMP  *dp;
178	<	AMBHEMI  *h;
179	<	RAY  *r;
176	>	static int
177	>	ambsample(                              /* initial ambient division sample */
178	>	AMBHEMI *hp,
179	>	int     i,
180	>	int     j,
181	>	int     n
182	>	)
183		{
184	<	RAY  ar;
185	<	int  hlist[4];
186	<	double  xd, yd, zd;
187	<	double  b2;
188	<	double  phi;
189	<	register int  i;
190	<
191	<	if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
192	<	return(-1);
193	<	hlist[0] = r->rno;
194	<	hlist[1] = dp->t;
195	<	hlist[2] = dp->p;
196	<	hlist[3] = 0;
197	<	zd = sqrt((dp->t+urand(urind(ilhash(hlist,4),dp->n)))/h->nt);
198	<	hlist[3] = 1;
199	<	phi = 2.0*PI * (dp->p+urand(urind(ilhash(hlist,4),dp->n)))/h->np;
200	<	xd = cos(phi) * zd;
201	<	yd = sin(phi) * zd;
202	<	zd = sqrt(1.0 - zd*zd);
203	<	for (i = 0; i < 3; i++)
204	<	ar.rdir[i] =    xd*h->ux[i] +
205	<	yd*h->uy[i] +
206	<	zd*h->uz[i];
207	<	dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
208	<	rayvalue(&ar);
209	<	ndims--;
210	<	addcolor(dp->v, ar.rcol);
211	<	if (ar.rt > FTINY && ar.rt < FHUGE)
212	<	dp->r += 1.0/ar.rt;
213	<	/* (re)initialize error */
214	<	if (dp->n++) {
215	<	b2 = bright(dp->v)/dp->n - bright(ar.rcol);
216	<	b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1));
217	<	dp->k = b2/(dp->n*dp->n);
218	<	} else
219	<	dp->k = 0.0;
220	<	return(0);
184	>	int     trade_ok = (!n & (hp->ns >= 4))*21;
185	>	AMBSAMP *ap = &ambsam(hp,i,j);
186	>	RAY     ar;
187	>	int     hlist[3], ii;
188	>	double  ss[2];
189	>	RREAL   spt[2];
190	>	double  zd;
191	>	/* generate hemispherical sample */
192	>	/* ambient coefficient for weight */
193	>	if (ambacc > FTINY)
194	>	setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
195	>	else
196	>	copyscolor(ar.rcoef, hp->acoef);
197	>	if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0)
198	>	return(0);
199	>	if (ambacc > FTINY) {
200	>	smultscolor(ar.rcoef, hp->acoef);
201	>	scalescolor(ar.rcoef, 1./AVGREFL);
202	>	}
203	>	hlist[0] = hp->rp->rno;
204	>	hlist[1] = AI(hp,i,j);
205	>	hlist[2] = samplendx;
206	>	multisamp(ss, 2, urand(ilhash(hlist,3)+n));
207	>	square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns);
208	>	/* avoid coincident samples? */
209	>	while (trade_ok-- && ambcollision(hp, i, j, spt)) {
210	>	if (trade_ok) {
211	>	trade_patchsamp(ss);
212	>	} else {                /* punting... */
213	>	ss[0] = MINSDIST + (1-2*MINSDIST)*frandom();
214	>	ss[1] = MINSDIST + (1-2*MINSDIST)*frandom();
215	>	}
216	>	square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns);
217	>	}
218	>	zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
219	>	for (ii = 3; ii--; )
220	>	ar.rdir[ii] =   spt[0]*hp->ux[ii] +
221	>	spt[1]*hp->uy[ii] +
222	>	zd*hp->onrm[ii];
223	>	checknorm(ar.rdir);
224	>	dimlist[ndims_inc()] = AI(hp,i,j) + 90171;
225	>	rayvalue(&ar);                  /* evaluate ray */
226	>	dec_ndims();
227	>	zd = raydistance(&ar);
228	>	if (zd <= FTINY)
229	>	return(0);              /* should never happen */
230	>	smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */
231	>	if (zd*ap->d < 1.0)             /* new/closer distance? */
232	>	ap->d = 1.0/zd;
233	>	if (!n) {                       /* record first vertex & value */
234	>	if (zd > 10.0*thescene.cusize + 1000.)
235	>	zd = 10.0*thescene.cusize + 1000.;
236	>	VSUM(ap->p, ar.rorg, ar.rdir, zd);
237	>	copyscolor(ap->v, ar.rcol);
238	>	} else {                        /* else update recorded value */
239	>	sopscolor(hp->acol, -=, ap->v);
240	>	zd = 1.0/(double)(n+1);
241	>	scalescolor(ar.rcol, zd);
242	>	zd *= (double)n;
243	>	scalescolor(ap->v, zd);
244	>	saddscolor(ap->v, ar.rcol);
245	>	}
246	>	saddscolor(hp->acol, ap->v);    /* add to our sum */
247	>	return(1);
248		}
249
250
251	<	double
252	<	doambient(acol, r, pg, dg)              /* compute ambient component */
253	<	COLOR  acol;
105	<	RAY  *r;
106	<	FVECT  pg, dg;
251	>	/* Estimate variance based on ambient division differences */
252	>	static float *
253	>	getambdiffs(AMBHEMI *hp)
254		{
255	<	double  b, d;
256	<	AMBHEMI  hemi;
257	<	AMBSAMP  *div;
258	<	AMBSAMP  dnew;
259	<	register AMBSAMP  *dp;
260	<	double  arad;
261	<	int  ndivs, ns;
262	<	register int  i, j;
263	<	/* initialize color */
264	<	setcolor(acol, 0.0, 0.0, 0.0);
265	<	/* initialize hemisphere */
266	<	inithemi(&hemi, r);
267	<	ndivs = hemi.nt * hemi.np;
268	<	if (ndivs == 0)
269	<	return(0.0);
270	<	/* set number of super-samples */
271	<	ns = ambssamp * r->rweight + 0.5;
272	<	if (ns > 0 || pg != NULL || dg != NULL) {
273	<	div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
274	<	if (div == NULL)
275	<	error(SYSTEM, "out of memory in doambient");
129	<	} else
130	<	div = NULL;
131	<	/* sample the divisions */
132	<	arad = 0.0;
133	<	if ((dp = div) == NULL)
134	<	dp = &dnew;
135	<	for (i = 0; i < hemi.nt; i++)
136	<	for (j = 0; j < hemi.np; j++) {
137	<	dp->t = i; dp->p = j;
138	<	setcolor(dp->v, 0.0, 0.0, 0.0);
139	<	dp->r = 0.0;
140	<	dp->n = 0;
141	<	if (divsample(dp, &hemi, r) < 0)
142	<	goto oopsy;
143	<	if (div != NULL)
144	<	dp++;
145	<	else {
146	<	addcolor(acol, dp->v);
147	<	arad += dp->r;
148	<	}
255	>	const double    normf = 1./(pbright(hp->acoef) + FTINY);
256	>	float   *earr = (float *)calloc(2*hp->ns*hp->ns, sizeof(float));
257	>	float   *ep;
258	>	AMBSAMP *ap;
259	>	double  b, b1, d2;
260	>	int     i, j;
261	>
262	>	if (earr == NULL)               /* out of memory? */
263	>	return(NULL);
264	>	/* sum squared neighbor diffs */
265	>	ap = hp->sa;
266	>	ep = earr + hp->ns*hp->ns;      /* original estimates to scratch */
267	>	for (i = 0; i < hp->ns; i++)
268	>	for (j = 0; j < hp->ns; j++, ap++, ep++) {
269	>	b = pbright(ap[0].v);
270	>	if (i) {                /* from above */
271	>	b1 = pbright(ap[-hp->ns].v);
272	>	d2 = b - b1;
273	>	d2 *= d2*normf/(b + b1 + FTINY);
274	>	ep[0] += d2;
275	>	ep[-hp->ns] += d2;
276		}
277	<	if (ns > 0) {                   /* perform super-sampling */
278	<	comperrs(div, &hemi);                   /* compute errors */
279	<	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
280	<	/* super-sample */
281	<	for (i = ns; i > 0; i--) {
282	<	copystruct(&dnew, div);
283	<	if (divsample(&dnew, &hemi, r) < 0)
284	<	goto oopsy;
285	<	/* reinsert */
286	<	dp = div;
287	<	j = ndivs < i ? ndivs : i;
288	<	while (--j > 0 && dnew.k < dp[1].k) {
289	<	copystruct(dp, dp+1);
290	<	dp++;
291	<	}
292	<	copystruct(dp, &dnew);
293	<	}
294	<	if (pg != NULL || dg != NULL)   /* restore order */
295	<	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
277	>	if (!j) continue;
278	>	/* from behind */
279	>	b1 = pbright(ap[-1].v);
280	>	d2 = b - b1;
281	>	d2 *= d2*normf/(b + b1 + FTINY);
282	>	ep[0] += d2;
283	>	ep[-1] += d2;
284	>	if (!i) continue;
285	>	/* diagonal */
286	>	b1 = pbright(ap[-hp->ns-1].v);
287	>	d2 = b - b1;
288	>	d2 *= d2*normf/(b + b1 + FTINY);
289	>	ep[0] += d2;
290	>	ep[-hp->ns-1] += d2;
291	>	}
292	>	/* correct for number of neighbors */
293	>	ep = earr + hp->ns*hp->ns;
294	>	ep[0] *= 6./3.;
295	>	ep[hp->ns-1] *= 6./3.;
296	>	ep[(hp->ns-1)*hp->ns] *= 6./3.;
297	>	ep[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.;
298	>	for (i = 1; i < hp->ns-1; i++) {
299	>	ep[i*hp->ns] *= 6./5.;
300	>	ep[i*hp->ns + hp->ns-1] *= 6./5.;
301		}
302	<	/* compute returned values */
303	<	if (div != NULL) {
304	<	for (i = ndivs, dp = div; i-- > 0; dp++) {
173	<	arad += dp->r;
174	<	if (dp->n > 1) {
175	<	b = 1.0/dp->n;
176	<	scalecolor(dp->v, b);
177	<	dp->r *= b;
178	<	dp->n = 1;
179	<	}
180	<	addcolor(acol, dp->v);
181	<	}
182	<	b = bright(acol);
183	<	if (b > FTINY) {
184	<	b = ndivs/b;
185	<	if (pg != NULL) {
186	<	posgradient(pg, div, &hemi);
187	<	for (i = 0; i < 3; i++)
188	<	pg[i] *= b;
189	<	}
190	<	if (dg != NULL) {
191	<	dirgradient(dg, div, &hemi);
192	<	for (i = 0; i < 3; i++)
193	<	dg[i] *= b;
194	<	}
195	<	} else {
196	<	if (pg != NULL)
197	<	for (i = 0; i < 3; i++)
198	<	pg[i] = 0.0;
199	<	if (dg != NULL)
200	<	for (i = 0; i < 3; i++)
201	<	dg[i] = 0.0;
202	<	}
203	<	free((char *)div);
302	>	for (j = 1; j < hp->ns-1; j++) {
303	>	ep[j] *= 6./5.;
304	>	ep[(hp->ns-1)*hp->ns + j] *= 6./5.;
305		}
306	<	b = 1.0/ndivs;
307	<	scalecolor(acol, b);
308	<	if (arad <= FTINY)
309	<	arad = FHUGE;
310	<	else
311	<	arad = (ndivs+ns)/arad;
312	<	if (arad > maxarad)
313	<	arad = maxarad;
314	<	else if (arad < minarad)
315	<	arad = minarad;
215	<	arad /= sqrt(r->rweight);
216	<	if (pg != NULL) {               /* clip pos. gradient if too large */
217	<	d = 4.0*DOT(pg,pg)*arad*arad;
218	<	if (d > 1.0) {
219	<	d = 1.0/sqrt(d);
220	<	for (i = 0; i < 3; i++)
221	<	pg[i] *= d;
222	<	}
306	>	/* blur final map to reduce bias */
307	>	for (i = 0; i < hp->ns-1; i++) {
308	>	float  *ep2;
309	>	ep = earr + i*hp->ns;
310	>	ep2 = ep + hp->ns*hp->ns;
311	>	for (j = 0; j < hp->ns-1; j++, ep++, ep2++) {
312	>	ep[0] += .5*ep2[0] + .125*(ep2[1] + ep2[hp->ns]);
313	>	ep[1] += .125*ep2[0];
314	>	ep[hp->ns] += .125*ep2[0];
315	>	}
316		}
317	<	return(arad);
225	<	oopsy:
226	<	if (div != NULL)
227	<	free((char *)div);
228	<	return(0.0);
317	>	return(earr);
318		}
319
320
321	<	inithemi(hp, r)                 /* initialize sampling hemisphere */
322	<	register AMBHEMI  *hp;
323	<	RAY  *r;
321	>	/* Perform super-sampling on hemisphere (introduces bias) */
322	>	static void
323	>	ambsupersamp(AMBHEMI *hp, int cnt)
324		{
325	<	register int  i;
325	>	float   *earr = getambdiffs(hp);
326	>	double  e2rem = 0;
327	>	float   *ep;
328	>	int     i, j, n, nss;
329	>
330	>	if (earr == NULL)               /* just skip calc. if no memory */
331	>	return;
332	>	/* accumulate estimated variances */
333	>	for (ep = earr + hp->ns*hp->ns; ep > earr; )
334	>	e2rem += *--ep;
335	>	ep = earr;                      /* perform super-sampling */
336	>	for (i = 0; i < hp->ns; i++)
337	>	for (j = 0; j < hp->ns; j++) {
338	>	if (e2rem <= FTINY)
339	>	goto done;      /* nothing left to do */
340	>	nss = *ep/e2rem*cnt + frandom();
341	>	for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
342	>	if (!--cnt) goto done;
343	>	e2rem -= *ep++;         /* update remainder */
344	>	}
345	>	done:
346	>	free(earr);
347	>	}
348	>
349	>
350	>	static AMBHEMI *
351	>	samp_hemi(                              /* sample indirect hemisphere */
352	>	SCOLOR  rcol,
353	>	RAY     *r,
354	>	double  wt
355	>	)
356	>	{
357	>	int     backside = (wt < 0);
358	>	AMBHEMI *hp;
359	>	double  d;
360	>	int     n, i, j;
361	>	/* insignificance check */
362	>	d = sintens(rcol);
363	>	if (d <= FTINY)
364	>	return(NULL);
365		/* set number of divisions */
366	<	hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
367	<	hp->np = 2 * hp->nt;
368	<	/* make axes */
369	<	VCOPY(hp->uz, r->ron);
370	<	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
371	<	for (i = 0; i < 3; i++)
372	<	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
373	<	break;
374	<	if (i >= 3)
375	<	error(CONSISTENCY, "bad ray direction in inithemi");
376	<	hp->uy[i] = 1.0;
377	<	fcross(hp->ux, hp->uy, hp->uz);
378	<	normalize(hp->ux);
379	<	fcross(hp->uy, hp->uz, hp->ux);
366	>	if (backside) wt = -wt;
367	>	if (ambacc <= FTINY &&
368	>	wt > (d *= 0.8*r->rweight/(ambdiv*minweight + 1e-20)))
369	>	wt = d;                 /* avoid ray termination */
370	>	n = sqrt(ambdiv * wt) + 0.5;
371	>	i = 1 + (MINADIV-1)*(ambacc > FTINY);
372	>	if (n < i)                      /* use minimum number of samples? */
373	>	n = i;
374	>	/* allocate sampling array */
375	>	hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
376	>	if (hp == NULL)
377	>	error(SYSTEM, "out of memory in samp_hemi");
378	>
379	>	if (backside) {
380	>	hp->atyp = TAMBIENT;
381	>	hp->onrm[0] = -r->ron[0];
382	>	hp->onrm[1] = -r->ron[1];
383	>	hp->onrm[2] = -r->ron[2];
384	>	} else {
385	>	hp->atyp = RAMBIENT;
386	>	VCOPY(hp->onrm, r->ron);
387	>	}
388	>	hp->rp = r;
389	>	hp->ns = n;
390	>	scolorblack(hp->acol);
391	>	memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
392	>	hp->sampOK = 0;
393	>	/* assign coefficient */
394	>	copyscolor(hp->acoef, rcol);
395	>	d = 1.0/(n*n);
396	>	scalescolor(hp->acoef, d);
397	>	/* make tangent plane axes */
398	>	if (!getperpendicular(hp->ux, hp->onrm, 1))
399	>	error(CONSISTENCY, "bad ray direction in samp_hemi");
400	>	VCROSS(hp->uy, hp->onrm, hp->ux);
401	>	/* sample divisions */
402	>	for (i = hp->ns; i--; )
403	>	for (j = hp->ns; j--; )
404	>	hp->sampOK += ambsample(hp, i, j, 0);
405	>	copyscolor(rcol, hp->acol);
406	>	if (!hp->sampOK) {              /* utter failure? */
407	>	free(hp);
408	>	return(NULL);
409	>	}
410	>	if (hp->sampOK < hp->ns*hp->ns) {
411	>	hp->sampOK *= -1;       /* soft failure */
412	>	return(hp);
413	>	}
414	>	if (hp->sampOK <= MINADIV*MINADIV)
415	>	return(hp);             /* don't bother super-sampling */
416	>	n = ambssamp*wt + 0.5;
417	>	if (n >= 4*hp->ns) {            /* perform super-sampling? */
418	>	ambsupersamp(hp, n);
419	>	copyscolor(rcol, hp->acol);
420	>	}
421	>	return(hp);                     /* all is well */
422		}
423
424
425	<	comperrs(da, hp)                /* compute initial error estimates */
426	<	AMBSAMP  *da;           /* assumes standard ordering */
427	<	register AMBHEMI  *hp;
425	>	/* Return brightness of farthest ambient sample */
426	>	static double
427	>	back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
428		{
429	<	double  b, b2;
430	<	int  i, j;
431	<	register AMBSAMP  *dp;
432	<	/* sum differences from neighbors */
433	<	dp = da;
434	<	for (i = 0; i < hp->nt; i++)
435	<	for (j = 0; j < hp->np; j++) {
436	<	#ifdef  DEBUG
267	<	if (dp->t != i || dp->p != j)
268	<	error(CONSISTENCY,
269	<	"division order in comperrs");
270	<	#endif
271	<	b = bright(dp[0].v);
272	<	if (i > 0) {            /* from above */
273	<	b2 = bright(dp[-hp->np].v) - b;
274	<	b2 *= b2 * 0.25;
275	<	dp[0].k += b2;
276	<	dp[-hp->np].k += b2;
277	<	}
278	<	if (j > 0) {            /* from behind */
279	<	b2 = bright(dp[-1].v) - b;
280	<	b2 *= b2 * 0.25;
281	<	dp[0].k += b2;
282	<	dp[-1].k += b2;
283	<	} else {                /* around */
284	<	b2 = bright(dp[hp->np-1].v) - b;
285	<	b2 *= b2 * 0.25;
286	<	dp[0].k += b2;
287	<	dp[hp->np-1].k += b2;
288	<	}
289	<	dp++;
290	<	}
291	<	/* divide by number of neighbors */
292	<	dp = da;
293	<	for (j = 0; j < hp->np; j++)            /* top row */
294	<	(dp++)->k *= 1.0/3.0;
295	<	if (hp->nt < 2)
296	<	return;
297	<	for (i = 1; i < hp->nt-1; i++)          /* central region */
298	<	for (j = 0; j < hp->np; j++)
299	<	(dp++)->k *= 0.25;
300	<	for (j = 0; j < hp->np; j++)            /* bottom row */
301	<	(dp++)->k *= 1.0/3.0;
429	>	if (hp->sa[n1].d <= hp->sa[n2].d) {
430	>	if (hp->sa[n1].d <= hp->sa[n3].d)
431	>	return(hp->sa[n1].v[0]);
432	>	return(hp->sa[n3].v[0]);
433	>	}
434	>	if (hp->sa[n2].d <= hp->sa[n3].d)
435	>	return(hp->sa[n2].v[0]);
436	>	return(hp->sa[n3].v[0]);
437		}
438
439
440	<	posgradient(gv, da, hp)                         /* compute position gradient */
441	<	FVECT  gv;
442	<	AMBSAMP  *da;                   /* assumes standard ordering */
308	<	AMBHEMI  *hp;
440	>	/* Compute vectors and coefficients for Hessian/gradient calcs */
441	>	static void
442	>	comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
443		{
444	<	register int  i, j;
445	<	double  b, d;
312	<	double  mag0, mag1;
313	<	double  phi, cosp, sinp, xd, yd;
314	<	register AMBSAMP  *dp;
444	>	double  rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
445	>	int     ii;
446
447	<	xd = yd = 0.0;
448	<	for (j = 0; j < hp->np; j++) {
449	<	dp = da + j;
450	<	mag0 = mag1 = 0.0;
451	<	for (i = 0; i < hp->nt; i++) {
452	<	#ifdef  DEBUG
453	<	if (dp->t != i || dp->p != j)
454	<	error(CONSISTENCY,
455	<	"division order in posgradient");
456	<	#endif
457	<	b = bright(dp->v);
458	<	if (i > 0) {
459	<	d = dp[-hp->np].r;
460	<	if (dp[0].r > d) d = dp[0].r;
461	<	d *= 1.0 - sqrt((double)i/hp->nt);
462	<	mag0 += d*(b - bright(dp[-hp->np].v));
463	<	}
464	<	if (j > 0) {
465	<	d = dp[-1].r;
466	<	if (dp[0].r > d) d = dp[0].r;
467	<	mag1 += d*(b - bright(dp[-1].v));
468	<	} else {
469	<	d = dp[hp->np-1].r;
470	<	if (dp[0].r > d) d = dp[0].r;
471	<	mag1 += d*(b - bright(dp[hp->np-1].v));
472	<	}
473	<	dp += hp->np;
447	>	VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
448	>	VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
449	>	VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
450	>	VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
451	>	rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
452	>	dot_e = DOT(ftp->e_i,ftp->e_i);
453	>	dot_er = DOT(ftp->e_i, ftp->r_i);
454	>	rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
455	>	rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
456	>	ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
457	>	sqrt( rdot_cp );
458	>	ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
459	>	dot_e*ftp->I1 )*0.5*rdot_cp;
460	>	J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
461	>	for (ii = 3; ii--; )
462	>	ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
463	>	}
464	>
465	>
466	>	/* Compose 3x3 matrix from two vectors */
467	>	static void
468	>	compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
469	>	{
470	>	mat[0][0] = 2.0*va[0]*vb[0];
471	>	mat[1][1] = 2.0*va[1]*vb[1];
472	>	mat[2][2] = 2.0*va[2]*vb[2];
473	>	mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
474	>	mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
475	>	mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
476	>	}
477	>
478	>
479	>	/* Compute partial 3x3 Hessian matrix for edge */
480	>	static void
481	>	comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
482	>	{
483	>	FVECT   ncp;
484	>	FVECT   m1[3], m2[3], m3[3], m4[3];
485	>	double  d1, d2, d3, d4;
486	>	double  I3, J3, K3;
487	>	int     i, j;
488	>	/* compute intermediate coefficients */
489	>	d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
490	>	d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
491	>	d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
492	>	d4 = DOT(ftp->e_i, ftp->r_i);
493	>	I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
494	>	/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
495	>	J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
496	>	K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
497	>	/* intermediate matrices */
498	>	VCROSS(ncp, nrm, ftp->e_i);
499	>	compose_matrix(m1, ncp, ftp->rI2_eJ2);
500	>	compose_matrix(m2, ftp->r_i, ftp->r_i);
501	>	compose_matrix(m3, ftp->e_i, ftp->e_i);
502	>	compose_matrix(m4, ftp->r_i, ftp->e_i);
503	>	d1 = DOT(nrm, ftp->rcp);
504	>	d2 = -d1*ftp->I2;
505	>	d1 *= 2.0;
506	>	for (i = 3; i--; )              /* final matrix sum */
507	>	for (j = 3; j--; ) {
508	>	hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
509	>	2.0*J3*m4[i][j] );
510	>	hess[i][j] += d2*(i==j);
511	>	hess[i][j] *= -1.0/PI;
512	>	}
513	>	}
514	>
515	>
516	>	/* Reverse hessian calculation result for edge in other direction */
517	>	static void
518	>	rev_hessian(FVECT hess[3])
519	>	{
520	>	int     i;
521	>
522	>	for (i = 3; i--; ) {
523	>	hess[i][0] = -hess[i][0];
524	>	hess[i][1] = -hess[i][1];
525	>	hess[i][2] = -hess[i][2];
526	>	}
527	>	}
528	>
529	>
530	>	/* Add to radiometric Hessian from the given triangle */
531	>	static void
532	>	add2hessian(FVECT hess[3], FVECT ehess1[3],
533	>	FVECT ehess2[3], FVECT ehess3[3], double v)
534	>	{
535	>	int     i, j;
536	>
537	>	for (i = 3; i--; )
538	>	for (j = 3; j--; )
539	>	hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
540	>	}
541	>
542	>
543	>	/* Compute partial displacement form factor gradient for edge */
544	>	static void
545	>	comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
546	>	{
547	>	FVECT   ncp;
548	>	double  f1;
549	>	int     i;
550	>
551	>	f1 = 2.0*DOT(nrm, ftp->rcp);
552	>	VCROSS(ncp, nrm, ftp->e_i);
553	>	for (i = 3; i--; )
554	>	grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
555	>	}
556	>
557	>
558	>	/* Reverse gradient calculation result for edge in other direction */
559	>	static void
560	>	rev_gradient(FVECT grad)
561	>	{
562	>	grad[0] = -grad[0];
563	>	grad[1] = -grad[1];
564	>	grad[2] = -grad[2];
565	>	}
566	>
567	>
568	>	/* Add to displacement gradient from the given triangle */
569	>	static void
570	>	add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
571	>	{
572	>	int     i;
573	>
574	>	for (i = 3; i--; )
575	>	grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
576	>	}
577	>
578	>
579	>	/* Compute anisotropic radii and eigenvector directions */
580	>	static void
581	>	eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
582	>	{
583	>	double  hess2[2][2];
584	>	FVECT   a, b;
585	>	double  evalue[2], slope1, xmag1;
586	>	int     i;
587	>	/* project Hessian to sample plane */
588	>	for (i = 3; i--; ) {
589	>	a[i] = DOT(hessian[i], uv[0]);
590	>	b[i] = DOT(hessian[i], uv[1]);
591	>	}
592	>	hess2[0][0] = DOT(uv[0], a);
593	>	hess2[0][1] = DOT(uv[0], b);
594	>	hess2[1][0] = DOT(uv[1], a);
595	>	hess2[1][1] = DOT(uv[1], b);
596	>	/* compute eigenvalue(s) */
597	>	i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
598	>	hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
599	>	if (i == 1)                     /* double-root (circle) */
600	>	evalue[1] = evalue[0];
601	>	if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
602	>	((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
603	>	ra[0] = ra[1] = maxarad;
604	>	return;
605	>	}
606	>	if (evalue[0] > evalue[1]) {
607	>	ra[0] = sqrt(sqrt(4.0/evalue[0]));
608	>	ra[1] = sqrt(sqrt(4.0/evalue[1]));
609	>	slope1 = evalue[1];
610	>	} else {
611	>	ra[0] = sqrt(sqrt(4.0/evalue[1]));
612	>	ra[1] = sqrt(sqrt(4.0/evalue[0]));
613	>	slope1 = evalue[0];
614	>	}
615	>	/* compute unit eigenvectors */
616	>	if (fabs(hess2[0][1]) <= FTINY)
617	>	return;                 /* uv OK as is */
618	>	slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
619	>	xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
620	>	for (i = 3; i--; ) {
621	>	b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
622	>	a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
623	>	}
624	>	VCOPY(uv[0], a);
625	>	VCOPY(uv[1], b);
626	>	}
627	>
628	>
629	>	static void
630	>	ambHessian(                             /* anisotropic radii & pos. gradient */
631	>	AMBHEMI *hp,
632	>	FVECT   uv[2],                  /* returned */
633	>	float   ra[2],                  /* returned (optional) */
634	>	float   pg[2]                   /* returned (optional) */
635	>	)
636	>	{
637	>	static char     memerrmsg[] = "out of memory in ambHessian()";
638	>	FVECT           (*hessrow)[3] = NULL;
639	>	FVECT           *gradrow = NULL;
640	>	FVECT           hessian[3];
641	>	FVECT           gradient;
642	>	FFTRI           fftr;
643	>	int             i, j;
644	>	/* be sure to assign unit vectors */
645	>	VCOPY(uv[0], hp->ux);
646	>	VCOPY(uv[1], hp->uy);
647	>	/* clock-wise vertex traversal from sample POV */
648	>	if (ra != NULL) {               /* initialize Hessian row buffer */
649	>	hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
650	>	if (hessrow == NULL)
651	>	error(SYSTEM, memerrmsg);
652	>	memset(hessian, 0, sizeof(hessian));
653	>	} else if (pg == NULL)          /* bogus call? */
654	>	return;
655	>	if (pg != NULL) {               /* initialize form factor row buffer */
656	>	gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
657	>	if (gradrow == NULL)
658	>	error(SYSTEM, memerrmsg);
659	>	memset(gradient, 0, sizeof(gradient));
660	>	}
661	>	/* compute first row of edges */
662	>	for (j = 0; j < hp->ns-1; j++) {
663	>	comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
664	>	if (hessrow != NULL)
665	>	comp_hessian(hessrow[j], &fftr, hp->onrm);
666	>	if (gradrow != NULL)
667	>	comp_gradient(gradrow[j], &fftr, hp->onrm);
668	>	}
669	>	/* sum each row of triangles */
670	>	for (i = 0; i < hp->ns-1; i++) {
671	>	FVECT       hesscol[3];     /* compute first vertical edge */
672	>	FVECT       gradcol;
673	>	comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
674	>	if (hessrow != NULL)
675	>	comp_hessian(hesscol, &fftr, hp->onrm);
676	>	if (gradrow != NULL)
677	>	comp_gradient(gradcol, &fftr, hp->onrm);
678	>	for (j = 0; j < hp->ns-1; j++) {
679	>	FVECT   hessdia[3];     /* compute triangle contributions */
680	>	FVECT   graddia;
681	>	double  backg;
682	>	backg = back_ambval(hp, AI(hp,i,j),
683	>	AI(hp,i,j+1), AI(hp,i+1,j));
684	>	/* diagonal (inner) edge */
685	>	comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
686	>	if (hessrow != NULL) {
687	>	comp_hessian(hessdia, &fftr, hp->onrm);
688	>	rev_hessian(hesscol);
689	>	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
690		}
691	<	if (hp->nt > 1) {
692	<	mag0 /= (double)hp->np;
693	<	mag1 /= (double)hp->nt;
691	>	if (gradrow != NULL) {
692	>	comp_gradient(graddia, &fftr, hp->onrm);
693	>	rev_gradient(gradcol);
694	>	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
695		}
696	<	phi = 2.0*PI * (double)j/hp->np;
697	<	cosp = cos(phi); sinp = sin(phi);
698	<	xd += mag0*cosp - mag1*sinp;
699	<	yd += mag0*sinp + mag1*cosp;
696	>	/* initialize edge in next row */
697	>	comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
698	>	if (hessrow != NULL)
699	>	comp_hessian(hessrow[j], &fftr, hp->onrm);
700	>	if (gradrow != NULL)
701	>	comp_gradient(gradrow[j], &fftr, hp->onrm);
702	>	/* new column edge & paired triangle */
703	>	backg = back_ambval(hp, AI(hp,i+1,j+1),
704	>	AI(hp,i+1,j), AI(hp,i,j+1));
705	>	comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
706	>	if (hessrow != NULL) {
707	>	comp_hessian(hesscol, &fftr, hp->onrm);
708	>	rev_hessian(hessdia);
709	>	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
710	>	if (i < hp->ns-2)
711	>	rev_hessian(hessrow[j]);
712	>	}
713	>	if (gradrow != NULL) {
714	>	comp_gradient(gradcol, &fftr, hp->onrm);
715	>	rev_gradient(graddia);
716	>	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
717	>	if (i < hp->ns-2)
718	>	rev_gradient(gradrow[j]);
719	>	}
720	>	}
721		}
722	<	for (i = 0; i < 3; i++)
723	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/PI;
722	>	/* release row buffers */
723	>	if (hessrow != NULL) free(hessrow);
724	>	if (gradrow != NULL) free(gradrow);
725	>
726	>	if (ra != NULL)                 /* extract eigenvectors & radii */
727	>	eigenvectors(uv, ra, hessian);
728	>	if (pg != NULL) {               /* tangential position gradient */
729	>	pg[0] = DOT(gradient, uv[0]);
730	>	pg[1] = DOT(gradient, uv[1]);
731	>	}
732		}
733
734
735	<	dirgradient(gv, da, hp)                         /* compute direction gradient */
736	<	FVECT  gv;
737	<	AMBSAMP  *da;                   /* assumes standard ordering */
361	<	AMBHEMI  *hp;
735	>	/* Compute direction gradient from a hemispherical sampling */
736	>	static void
737	>	ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
738		{
739	<	register int  i, j;
740	<	double  mag;
741	<	double  phi, xd, yd;
742	<	register AMBSAMP  *dp;
739	>	AMBSAMP *ap;
740	>	double  dgsum[2];
741	>	int     n;
742	>	FVECT   vd;
743	>	double  gfact;
744
745	<	xd = yd = 0.0;
746	<	for (j = 0; j < hp->np; j++) {
747	<	dp = da + j;
748	<	mag = 0.0;
749	<	for (i = 0; i < hp->nt; i++) {
750	<	#ifdef  DEBUG
751	<	if (dp->t != i || dp->p != j)
752	<	error(CONSISTENCY,
753	<	"division order in dirgradient");
754	<	#endif
755	<	mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
756	<	dp += hp->np;
745	>	dgsum[0] = dgsum[1] = 0.0;      /* sum values times -tan(theta) */
746	>	for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
747	>	/* use vector for azimuth + 90deg */
748	>	VSUB(vd, ap->p, hp->rp->rop);
749	>	/* brightness over cosine factor */
750	>	gfact = ap->v[0] / DOT(hp->onrm, vd);
751	>	/* sine = proj_radius/vd_length */
752	>	dgsum[0] -= DOT(uv[1], vd) * gfact;
753	>	dgsum[1] += DOT(uv[0], vd) * gfact;
754	>	}
755	>	dg[0] = dgsum[0] / (hp->ns*hp->ns);
756	>	dg[1] = dgsum[1] / (hp->ns*hp->ns);
757	>	}
758	>
759	>
760	>	/* Compute potential light leak direction flags for cache value */
761	>	static uint32
762	>	ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
763	>	{
764	>	const double    max_d = 1.0/(minarad*ambacc + 0.001);
765	>	const double    ang_res = 0.5*PI/hp->ns;
766	>	const double    ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
767	>	double          avg_d = 0;
768	>	uint32          flgs = 0;
769	>	FVECT           vec;
770	>	double          u, v;
771	>	double          ang, a1;
772	>	int             i, j;
773	>	/* don't bother for a few samples */
774	>	if (hp->ns < 8)
775	>	return(0);
776	>	/* check distances overhead */
777	>	for (i = hp->ns*3/4; i-- > hp->ns>>2; )
778	>	for (j = hp->ns*3/4; j-- > hp->ns>>2; )
779	>	avg_d += ambsam(hp,i,j).d;
780	>	avg_d *= 4.0/(hp->ns*hp->ns);
781	>	if (avg_d*r0 >= 1.0)            /* ceiling too low for corral? */
782	>	return(0);
783	>	if (avg_d >= max_d)             /* insurance */
784	>	return(0);
785	>	/* else circle around perimeter */
786	>	for (i = 0; i < hp->ns; i++)
787	>	for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
788	>	AMBSAMP *ap = &ambsam(hp,i,j);
789	>	if ((ap->d <= FTINY) | (ap->d >= max_d))
790	>	continue;       /* too far or too near */
791	>	VSUB(vec, ap->p, hp->rp->rop);
792	>	u = DOT(vec, uv[0]);
793	>	v = DOT(vec, uv[1]);
794	>	if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
795	>	continue;       /* occluder outside ellipse */
796	>	ang = atan2a(v, u);     /* else set direction flags */
797	>	for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
798	>	flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
799	>	}
800	>	return(flgs);
801	>	}
802	>
803	>
804	>	int
805	>	doambient(                              /* compute ambient component */
806	>	SCOLOR  rcol,                   /* input/output color */
807	>	RAY     *r,
808	>	double  wt,                     /* negative for back side */
809	>	FVECT   uv[2],                  /* returned (optional) */
810	>	float   ra[2],                  /* returned (optional) */
811	>	float   pg[2],                  /* returned (optional) */
812	>	float   dg[2],                  /* returned (optional) */
813	>	uint32  *crlp                   /* returned (optional) */
814	>	)
815	>	{
816	>	AMBHEMI *hp = samp_hemi(rcol, r, wt);
817	>	FVECT   my_uv[2];
818	>	double  d, K;
819	>	AMBSAMP *ap;
820	>	int     i;
821	>	/* clear return values */
822	>	if (uv != NULL)
823	>	memset(uv, 0, sizeof(FVECT)*2);
824	>	if (ra != NULL)
825	>	ra[0] = ra[1] = 0.0;
826	>	if (pg != NULL)
827	>	pg[0] = pg[1] = 0.0;
828	>	if (dg != NULL)
829	>	dg[0] = dg[1] = 0.0;
830	>	if (crlp != NULL)
831	>	*crlp = 0;
832	>	if (hp == NULL)                 /* sampling falure? */
833	>	return(0);
834	>
835	>	if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
836	>	(hp->sampOK < 0) | (hp->ns < MINADIV)) {
837	>	free(hp);               /* Hessian not requested/possible */
838	>	return(-1);             /* value-only return value */
839	>	}
840	>	if ((d = scolor_mean(rcol)) > FTINY) {
841	>	d = 0.99*(hp->ns*hp->ns)/d;     /* normalize avg. values */
842	>	K = 0.01;
843	>	} else {                        /* or fall back on geometric Hessian */
844	>	K = 1.0;
845	>	pg = NULL;
846	>	dg = NULL;
847	>	crlp = NULL;
848	>	}
849	>	ap = hp->sa;                    /* single channel from here on... */
850	>	for (i = hp->ns*hp->ns; i--; ap++)
851	>	ap->v[0] = scolor_mean(ap->v)*d + K;
852	>
853	>	if (uv == NULL)                 /* make sure we have axis pointers */
854	>	uv = my_uv;
855	>	/* compute radii & pos. gradient */
856	>	ambHessian(hp, uv, ra, pg);
857	>
858	>	if (dg != NULL)                 /* compute direction gradient */
859	>	ambdirgrad(hp, uv, dg);
860	>
861	>	if (ra != NULL) {               /* scale/clamp radii */
862	>	if (pg != NULL) {
863	>	if (ra[0]*(d = fabs(pg[0])) > 1.0)
864	>	ra[0] = 1.0/d;
865	>	if (ra[1]*(d = fabs(pg[1])) > 1.0)
866	>	ra[1] = 1.0/d;
867	>	if (ra[0] > ra[1])
868	>	ra[0] = ra[1];
869		}
870	<	phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
871	<	xd += mag * cos(phi);
872	<	yd += mag * sin(phi);
870	>	if (ra[0] < minarad) {
871	>	ra[0] = minarad;
872	>	if (ra[1] < minarad)
873	>	ra[1] = minarad;
874	>	}
875	>	ra[0] *= d = 1.0/sqrt(fabs(wt));
876	>	if ((ra[1] *= d) > 2.0*ra[0])
877	>	ra[1] = 2.0*ra[0];
878	>	if (ra[1] > maxarad) {
879	>	ra[1] = maxarad;
880	>	if (ra[0] > maxarad)
881	>	ra[0] = maxarad;
882	>	}
883	>	/* flag encroached directions */
884	>	if (crlp != NULL)       /* XXX doesn't update with changes to ambacc */
885	>	*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
886	>	if (pg != NULL) {       /* cap gradient if necessary */
887	>	d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
888	>	if (d > 1.0) {
889	>	d = 1.0/sqrt(d);
890	>	pg[0] *= d;
891	>	pg[1] *= d;
892	>	}
893	>	}
894		}
895	<	for (i = 0; i < 3; i++)
896	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*PI/(hp->nt*hp->np);
895	>	free(hp);                       /* clean up and return */
896	>	return(1);
897		}

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