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

Comparing ray/src/rt/ambcomp.c (file contents):
Revision 1.16 by greg, Mon Nov 4 11:14:46 1991 UTC vs.
Revision 2.54 by greg, Fri May 9 04:55:19 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 */
55	<	float  k;               /* variance for this division */
22	<	int  n;                 /* number of subsamples */
23	<	}  AMBSAMP;             /* ambient sample division */
52	>	COLOR   v;              /* hemisphere sample value */
53	>	float   d;              /* reciprocal distance (1/rt) */
54	>	FVECT   p;              /* intersection point */
55	>	} AMBSAMP;              /* sample value */
56
57		typedef struct {
58	<	FVECT  ux, uy, uz;      /* x, y and z axis directions */
59	<	short  nt, np;          /* number of theta and phi directions */
58	>	RAY     *rp;            /* originating ray sample */
59	>	FVECT   ux, uy;         /* tangent axis unit vectors */
60	>	int     ns;             /* number of samples per axis */
61	>	COLOR   acoef;          /* division contribution coefficient */
62	>	AMBSAMP sa[1];          /* sample array (extends struct) */
63		}  AMBHEMI;             /* ambient sample hemisphere */
64
65	<	extern double  sin(), cos(), sqrt();
65	>	#define ambndx(h,i,j)   ((i)*(h)->ns + (j))
66	>	#define ambsam(h,i,j)   (h)->sa[ambndx(h,i,j)]
67
68	+	typedef struct {
69	+	FVECT   r_i, r_i1, e_i, rcp, rI2_eJ2;
70	+	double  I1, I2;
71	+	int     valid;
72	+	} FFTRI;                /* vectors and coefficients for Hessian calculation */
73
74	+
75	+	/* Get index for adjacent vertex */
76		static int
77	<	ambcmp(d1, d2)                          /* decreasing order */
35	<	AMBSAMP  *d1, *d2;
77	>	adjacent_verti(AMBHEMI *hp, int i, int j, int dbit)
78		{
79	<	if (d1->k < d2->k)
80	<	return(1);
81	<	if (d1->k > d2->k)
82	<	return(-1);
83	<	return(0);
79	>	int     i0 = i*hp->ns + j;
80	>
81	>	switch (dbit) {
82	>	case VDB_y:     return(i0 - hp->ns);
83	>	case VDB_x:     return(i0 - 1);
84	>	case VDB_Xy:    return(i0 - hp->ns + 1);
85	>	case VDB_xY:    return(i0 + hp->ns - 1);
86	>	case VDB_X:     return(i0 + 1);
87	>	case VDB_Y:     return(i0 + hp->ns);
88	>	/* the following should never occur */
89	>	case VDB_xy:    return(i0 - hp->ns - 1);
90	>	case VDB_XY:    return(i0 + hp->ns + 1);
91	>	}
92	>	return(-1);
93		}
94
95
96	+	/* Get vertex direction bit for the opposite edge to complete triangle */
97		static int
98	<	ambnorm(d1, d2)                         /* standard order */
47	<	AMBSAMP  *d1, *d2;
98	>	vdb_edge(int db1, int db2)
99		{
100	<	register int  c;
100	>	switch (db1) {
101	>	case VDB_x:     return(db2==VDB_y ? VDB_Xy : VDB_Y);
102	>	case VDB_y:     return(db2==VDB_x ? VDB_xY : VDB_X);
103	>	case VDB_X:     return(db2==VDB_Xy ? VDB_y : VDB_xY);
104	>	case VDB_Y:     return(db2==VDB_xY ? VDB_x : VDB_Xy);
105	>	case VDB_xY:    return(db2==VDB_x ? VDB_y : VDB_X);
106	>	case VDB_Xy:    return(db2==VDB_y ? VDB_x : VDB_Y);
107	>	}
108	>	error(CONSISTENCY, "forbidden diagonal in vdb_edge()");
109	>	return(-1);
110	>	}
111
112	<	if (c = d1->t - d2->t)
113	<	return(c);
114	<	return(d1->p - d2->p);
112	>
113	>	static AMBHEMI *
114	>	inithemi(                       /* initialize sampling hemisphere */
115	>	COLOR   ac,
116	>	RAY     *r,
117	>	double  wt
118	>	)
119	>	{
120	>	AMBHEMI *hp;
121	>	double  d;
122	>	int     n, i;
123	>	/* set number of divisions */
124	>	if (ambacc <= FTINY &&
125	>	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
126	>	wt = d;                 /* avoid ray termination */
127	>	n = sqrt(ambdiv * wt) + 0.5;
128	>	i = 1 + 5*(ambacc > FTINY);     /* minimum number of samples */
129	>	if (n < i)
130	>	n = i;
131	>	/* allocate sampling array */
132	>	hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
133	>	if (hp == NULL)
134	>	return(NULL);
135	>	hp->rp = r;
136	>	hp->ns = n;
137	>	/* assign coefficient */
138	>	copycolor(hp->acoef, ac);
139	>	d = 1.0/(n*n);
140	>	scalecolor(hp->acoef, d);
141	>	/* make tangent plane axes */
142	>	hp->uy[0] = 0.5 - frandom();
143	>	hp->uy[1] = 0.5 - frandom();
144	>	hp->uy[2] = 0.5 - frandom();
145	>	for (i = 3; i--; )
146	>	if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6))
147	>	break;
148	>	if (i < 0)
149	>	error(CONSISTENCY, "bad ray direction in inithemi");
150	>	hp->uy[i] = 1.0;
151	>	VCROSS(hp->ux, hp->uy, r->ron);
152	>	normalize(hp->ux);
153	>	VCROSS(hp->uy, r->ron, hp->ux);
154	>	/* we're ready to sample */
155	>	return(hp);
156		}
157
158
159	<	divsample(dp, h, r)                     /* sample a division */
160	<	register AMBSAMP  *dp;
161	<	AMBHEMI  *h;
60	<	RAY  *r;
159	>	/* Sample ambient division and apply weighting coefficient */
160	>	static int
161	>	getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n)
162		{
163	+	int     hlist[3], ii;
164	+	double  spt[2], zd;
165	+	/* ambient coefficient for weight */
166	+	if (ambacc > FTINY)
167	+	setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL);
168	+	else
169	+	copycolor(arp->rcoef, hp->acoef);
170	+	if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0)
171	+	return(0);
172	+	if (ambacc > FTINY) {
173	+	multcolor(arp->rcoef, hp->acoef);
174	+	scalecolor(arp->rcoef, 1./AVGREFL);
175	+	}
176	+	hlist[0] = hp->rp->rno;
177	+	hlist[1] = j;
178	+	hlist[2] = i;
179	+	multisamp(spt, 2, urand(ilhash(hlist,3)+n));
180	+	if (!n) {                       /* avoid border samples for n==0 */
181	+	if ((spt[0] < 0.1) | (spt[0] >= 0.9))
182	+	spt[0] = 0.1 + 0.8*frandom();
183	+	if ((spt[1] < 0.1) | (spt[1] >= 0.9))
184	+	spt[1] = 0.1 + 0.8*frandom();
185	+	}
186	+	SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
187	+	zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
188	+	for (ii = 3; ii--; )
189	+	arp->rdir[ii] = spt[0]*hp->ux[ii] +
190	+	spt[1]*hp->uy[ii] +
191	+	zd*hp->rp->ron[ii];
192	+	checknorm(arp->rdir);
193	+	dimlist[ndims++] = ambndx(hp,i,j) + 90171;
194	+	rayvalue(arp);                  /* evaluate ray */
195	+	ndims--;                        /* apply coefficient */
196	+	multcolor(arp->rcol, arp->rcoef);
197	+	return(1);
198	+	}
199	+
200	+
201	+	static AMBSAMP *
202	+	ambsample(                              /* initial ambient division sample */
203	+	AMBHEMI *hp,
204	+	int     i,
205	+	int     j
206	+	)
207	+	{
208	+	AMBSAMP *ap = &ambsam(hp,i,j);
209	+	RAY     ar;
210	+	/* generate hemispherical sample */
211	+	if (!getambsamp(&ar, hp, i, j, 0) || ar.rt <= FTINY) {
212	+	memset(ap, 0, sizeof(AMBSAMP));
213	+	return(NULL);
214	+	}
215	+	ap->d = 1.0/ar.rt;              /* limit vertex distance */
216	+	if (ar.rt > 10.0*thescene.cusize)
217	+	ar.rt = 10.0*thescene.cusize;
218	+	VSUM(ap->p, ar.rorg, ar.rdir, ar.rt);
219	+	copycolor(ap->v, ar.rcol);
220	+	return(ap);
221	+	}
222	+
223	+
224	+	/* Estimate errors based on ambient division differences */
225	+	static float *
226	+	getambdiffs(AMBHEMI *hp)
227	+	{
228	+	float   *earr = (float *)malloc(sizeof(float)*hp->ns*hp->ns);
229	+	float   *ep;
230	+	AMBSAMP *ap;
231	+	double  b, d2;
232	+	int     i, j;
233	+
234	+	if (earr == NULL)               /* out of memory? */
235	+	return(NULL);
236	+	/* compute squared neighbor diffs */
237	+	for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
238	+	for (j = 0; j < hp->ns; j++, ap++, ep++) {
239	+	ep[0] = FTINY;
240	+	b = bright(ap[0].v);
241	+	if (i) {                /* from above */
242	+	d2 = b - bright(ap[-hp->ns].v);
243	+	d2 *= d2;
244	+	ep[0] += d2;
245	+	ep[-hp->ns] += d2;
246	+	}
247	+	if (j) {                /* from behind */
248	+	d2 = b - bright(ap[-1].v);
249	+	d2 *= d2;
250	+	ep[0] += d2;
251	+	ep[-1] += d2;
252	+	}
253	+	}
254	+	/* correct for number of neighbors */
255	+	earr[0] *= 2.f;
256	+	earr[hp->ns-1] *= 2.f;
257	+	earr[(hp->ns-1)*hp->ns] *= 2.f;
258	+	earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f;
259	+	for (i = 1; i < hp->ns-1; i++) {
260	+	earr[i*hp->ns] *= 4./3.;
261	+	earr[i*hp->ns + hp->ns-1] *= 4./3.;
262	+	}
263	+	for (j = 1; j < hp->ns-1; j++) {
264	+	earr[j] *= 4./3.;
265	+	earr[(hp->ns-1)*hp->ns + j] *= 4./3.;
266	+	}
267	+	return(earr);
268	+	}
269	+
270	+
271	+	/* Perform super-sampling on hemisphere (introduces bias) */
272	+	static void
273	+	ambsupersamp(double acol[3], AMBHEMI *hp, int cnt)
274	+	{
275	+	float   *earr = getambdiffs(hp);
276	+	double  e2rem = 0;
277	+	AMBSAMP *ap;
278	+	RAY     ar;
279	+	double  asum[3];
280	+	float   *ep;
281	+	int     i, j, n;
282	+
283	+	if (earr == NULL)               /* just skip calc. if no memory */
284	+	return;
285	+	/* accumulate estimated variances */
286	+	for (ep = earr + hp->ns*hp->ns; ep-- > earr; )
287	+	e2rem += *ep;
288	+	ep = earr;                      /* perform super-sampling */
289	+	for (ap = hp->sa, i = 0; i < hp->ns; i++)
290	+	for (j = 0; j < hp->ns; j++, ap++) {
291	+	int     nss = *ep/e2rem*cnt + frandom();
292	+	asum[0] = asum[1] = asum[2] = 0.0;
293	+	for (n = 1; n <= nss; n++) {
294	+	if (!getambsamp(&ar, hp, i, j, n)) {
295	+	nss = n-1;
296	+	break;
297	+	}
298	+	addcolor(asum, ar.rcol);
299	+	}
300	+	if (nss) {              /* update returned ambient value */
301	+	const double    ssf = 1./(nss + 1.);
302	+	for (n = 3; n--; )
303	+	acol[n] += ssf*asum[n] +
304	+	(ssf - 1.)*colval(ap->v,n);
305	+	}
306	+	e2rem -= *ep++;         /* update remainders */
307	+	cnt -= nss;
308	+	}
309	+	free(earr);
310	+	}
311	+
312	+
313	+	/* Compute vertex flags, indicating farthest in each direction */
314	+	static uby8 *
315	+	vertex_flags(AMBHEMI *hp)
316	+	{
317	+	uby8    *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8));
318	+	uby8    *vf;
319	+	AMBSAMP *ap;
320	+	int     i, j;
321	+
322	+	if (vflags == NULL)
323	+	error(SYSTEM, "out of memory in vertex_flags()");
324	+	vf = vflags;
325	+	ap = hp->sa;            /* compute farthest along first row */
326	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++)
327	+	if (ap[0].d <= ap[1].d)
328	+	vf[0] |= 1<<VDB_X;
329	+	else
330	+	vf[1] |= 1<<VDB_x;
331	+	++vf; ++ap;
332	+	/* flag subsequent rows */
333	+	for (i = 1; i < hp->ns; i++) {
334	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++) {
335	+	if (ap[0].d <= ap[-hp->ns].d)   /* row before */
336	+	vf[0] |= 1<<VDB_y;
337	+	else
338	+	vf[-hp->ns] |= 1<<VDB_Y;
339	+	if (ap[0].d <= ap[1-hp->ns].d)  /* diagonal we care about */
340	+	vf[0] |= 1<<VDB_Xy;
341	+	else
342	+	vf[1-hp->ns] |= 1<<VDB_xY;
343	+	if (ap[0].d <= ap[1].d)         /* column after */
344	+	vf[0] |= 1<<VDB_X;
345	+	else
346	+	vf[1] |= 1<<VDB_x;
347	+	}
348	+	if (ap[0].d <= ap[-hp->ns].d)       /* final column edge */
349	+	vf[0] |= 1<<VDB_y;
350	+	else
351	+	vf[-hp->ns] |= 1<<VDB_Y;
352	+	++vf; ++ap;
353	+	}
354	+	return(vflags);
355	+	}
356	+
357	+
358	+	/* Return brightness of farthest ambient sample */
359	+	static double
360	+	back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags)
361	+	{
362	+	const int       v0 = ambndx(hp,i,j);
363	+	const int       tflags = (1<<dbit1 | 1<<dbit2);
364	+	int             v1, v2;
365	+
366	+	if ((vflags[v0] & tflags) == tflags)    /* is v0 the farthest? */
367	+	return(colval(hp->sa[v0].v,CIEY));
368	+	v1 = adjacent_verti(hp, i, j, dbit1);
369	+	if (vflags[v0] & 1<<dbit2)              /* v1 farthest if v0>v2 */
370	+	return(colval(hp->sa[v1].v,CIEY));
371	+	v2 = adjacent_verti(hp, i, j, dbit2);
372	+	if (vflags[v0] & 1<<dbit1)              /* v2 farthest if v0>v1 */
373	+	return(colval(hp->sa[v2].v,CIEY));
374	+	/* else check if v1>v2 */
375	+	if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2))
376	+	return(colval(hp->sa[v1].v,CIEY));
377	+	return(colval(hp->sa[v2].v,CIEY));
378	+	}
379	+
380	+
381	+	/* Compute vectors and coefficients for Hessian/gradient calcs */
382	+	static void
383	+	comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags)
384	+	{
385	+	const int       i0 = ambndx(hp,i,j);
386	+	double          rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
387	+	int             i1, ii;
388	+
389	+	ftp->valid = 0;                 /* check if we can skip this edge */
390	+	ii = adjacent_trifl[dbit];
391	+	if ((vflags[i0] & ii) == ii)    /* cancels if vertex used as value */
392	+	return;
393	+	i1 = adjacent_verti(hp, i, j, dbit);
394	+	ii = adjacent_trifl[VDB_OPP(dbit)];
395	+	if ((vflags[i1] & ii) == ii)    /* on either end (for both triangles) */
396	+	return;
397	+	/* else go ahead with calculation */
398	+	VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop);
399	+	VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop);
400	+	VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p);
401	+	VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
402	+	rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
403	+	dot_e = DOT(ftp->e_i,ftp->e_i);
404	+	dot_er = DOT(ftp->e_i, ftp->r_i);
405	+	rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
406	+	rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
407	+	ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
408	+	sqrt( rdot_cp );
409	+	ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
410	+	dot_e*ftp->I1 )*0.5*rdot_cp;
411	+	J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
412	+	for (ii = 3; ii--; )
413	+	ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
414	+	ftp->valid++;
415	+	}
416	+
417	+
418	+	/* Compose 3x3 matrix from two vectors */
419	+	static void
420	+	compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
421	+	{
422	+	mat[0][0] = 2.0*va[0]*vb[0];
423	+	mat[1][1] = 2.0*va[1]*vb[1];
424	+	mat[2][2] = 2.0*va[2]*vb[2];
425	+	mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
426	+	mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
427	+	mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
428	+	}
429	+
430	+
431	+	/* Compute partial 3x3 Hessian matrix for edge */
432	+	static void
433	+	comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
434	+	{
435	+	FVECT   ncp;
436	+	FVECT   m1[3], m2[3], m3[3], m4[3];
437	+	double  d1, d2, d3, d4;
438	+	double  I3, J3, K3;
439	+	int     i, j;
440	+
441	+	if (!ftp->valid) {              /* preemptive test */
442	+	memset(hess, 0, sizeof(FVECT)*3);
443	+	return;
444	+	}
445	+	/* compute intermediate coefficients */
446	+	d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
447	+	d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
448	+	d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
449	+	d4 = DOT(ftp->e_i, ftp->r_i);
450	+	I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
451	+	/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
452	+	J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
453	+	K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
454	+	/* intermediate matrices */
455	+	VCROSS(ncp, nrm, ftp->e_i);
456	+	compose_matrix(m1, ncp, ftp->rI2_eJ2);
457	+	compose_matrix(m2, ftp->r_i, ftp->r_i);
458	+	compose_matrix(m3, ftp->e_i, ftp->e_i);
459	+	compose_matrix(m4, ftp->r_i, ftp->e_i);
460	+	d1 = DOT(nrm, ftp->rcp);
461	+	d2 = -d1*ftp->I2;
462	+	d1 *= 2.0;
463	+	for (i = 3; i--; )              /* final matrix sum */
464	+	for (j = 3; j--; ) {
465	+	hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
466	+	2.0*J3*m4[i][j] );
467	+	hess[i][j] += d2*(i==j);
468	+	hess[i][j] *= -1.0/PI;
469	+	}
470	+	}
471	+
472	+
473	+	/* Reverse hessian calculation result for edge in other direction */
474	+	static void
475	+	rev_hessian(FVECT hess[3])
476	+	{
477	+	int     i;
478	+
479	+	for (i = 3; i--; ) {
480	+	hess[i][0] = -hess[i][0];
481	+	hess[i][1] = -hess[i][1];
482	+	hess[i][2] = -hess[i][2];
483	+	}
484	+	}
485	+
486	+
487	+	/* Add to radiometric Hessian from the given triangle */
488	+	static void
489	+	add2hessian(FVECT hess[3], FVECT ehess1[3],
490	+	FVECT ehess2[3], FVECT ehess3[3], double v)
491	+	{
492	+	int     i, j;
493	+
494	+	for (i = 3; i--; )
495	+	for (j = 3; j--; )
496	+	hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
497	+	}
498	+
499	+
500	+	/* Compute partial displacement form factor gradient for edge */
501	+	static void
502	+	comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
503	+	{
504	+	FVECT   ncp;
505	+	double  f1;
506	+	int     i;
507	+
508	+	if (!ftp->valid) {              /* preemptive test */
509	+	memset(grad, 0, sizeof(FVECT));
510	+	return;
511	+	}
512	+	f1 = 2.0*DOT(nrm, ftp->rcp);
513	+	VCROSS(ncp, nrm, ftp->e_i);
514	+	for (i = 3; i--; )
515	+	grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
516	+	}
517	+
518	+
519	+	/* Reverse gradient calculation result for edge in other direction */
520	+	static void
521	+	rev_gradient(FVECT grad)
522	+	{
523	+	grad[0] = -grad[0];
524	+	grad[1] = -grad[1];
525	+	grad[2] = -grad[2];
526	+	}
527	+
528	+
529	+	/* Add to displacement gradient from the given triangle */
530	+	static void
531	+	add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
532	+	{
533	+	int     i;
534	+
535	+	for (i = 3; i--; )
536	+	grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
537	+	}
538	+
539	+
540	+	/* Compute anisotropic radii and eigenvector directions */
541	+	static void
542	+	eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
543	+	{
544	+	double  hess2[2][2];
545	+	FVECT   a, b;
546	+	double  evalue[2], slope1, xmag1;
547	+	int     i;
548	+	/* project Hessian to sample plane */
549	+	for (i = 3; i--; ) {
550	+	a[i] = DOT(hessian[i], uv[0]);
551	+	b[i] = DOT(hessian[i], uv[1]);
552	+	}
553	+	hess2[0][0] = DOT(uv[0], a);
554	+	hess2[0][1] = DOT(uv[0], b);
555	+	hess2[1][0] = DOT(uv[1], a);
556	+	hess2[1][1] = DOT(uv[1], b);
557	+	/* compute eigenvalue(s) */
558	+	i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
559	+	hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
560	+	if (i == 1)                     /* double-root (circle) */
561	+	evalue[1] = evalue[0];
562	+	if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
563	+	((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
564	+	ra[0] = ra[1] = maxarad;
565	+	return;
566	+	}
567	+	if (evalue[0] > evalue[1]) {
568	+	ra[0] = sqrt(sqrt(4.0/evalue[0]));
569	+	ra[1] = sqrt(sqrt(4.0/evalue[1]));
570	+	slope1 = evalue[1];
571	+	} else {
572	+	ra[0] = sqrt(sqrt(4.0/evalue[1]));
573	+	ra[1] = sqrt(sqrt(4.0/evalue[0]));
574	+	slope1 = evalue[0];
575	+	}
576	+	/* compute unit eigenvectors */
577	+	if (fabs(hess2[0][1]) <= FTINY)
578	+	return;                 /* uv OK as is */
579	+	slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
580	+	xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
581	+	for (i = 3; i--; ) {
582	+	b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
583	+	a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
584	+	}
585	+	VCOPY(uv[0], a);
586	+	VCOPY(uv[1], b);
587	+	}
588	+
589	+
590	+	static void
591	+	ambHessian(                             /* anisotropic radii & pos. gradient */
592	+	AMBHEMI *hp,
593	+	FVECT   uv[2],                  /* returned */
594	+	float   ra[2],                  /* returned (optional) */
595	+	float   pg[2]                   /* returned (optional) */
596	+	)
597	+	{
598	+	static char     memerrmsg[] = "out of memory in ambHessian()";
599	+	FVECT           (*hessrow)[3] = NULL;
600	+	FVECT           *gradrow = NULL;
601	+	uby8            *vflags;
602	+	FVECT           hessian[3];
603	+	FVECT           gradient;
604	+	FFTRI           fftr;
605	+	int             i, j;
606	+	/* be sure to assign unit vectors */
607	+	VCOPY(uv[0], hp->ux);
608	+	VCOPY(uv[1], hp->uy);
609	+	/* clock-wise vertex traversal from sample POV */
610	+	if (ra != NULL) {               /* initialize Hessian row buffer */
611	+	hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
612	+	if (hessrow == NULL)
613	+	error(SYSTEM, memerrmsg);
614	+	memset(hessian, 0, sizeof(hessian));
615	+	} else if (pg == NULL)          /* bogus call? */
616	+	return;
617	+	if (pg != NULL) {               /* initialize form factor row buffer */
618	+	gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
619	+	if (gradrow == NULL)
620	+	error(SYSTEM, memerrmsg);
621	+	memset(gradient, 0, sizeof(gradient));
622	+	}
623	+	/* get vertex position flags */
624	+	vflags = vertex_flags(hp);
625	+	/* compute first row of edges */
626	+	for (j = 0; j < hp->ns-1; j++) {
627	+	comp_fftri(&fftr, hp, 0, j, VDB_X, vflags);
628	+	if (hessrow != NULL)
629	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
630	+	if (gradrow != NULL)
631	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
632	+	}
633	+	/* sum each row of triangles */
634	+	for (i = 0; i < hp->ns-1; i++) {
635	+	FVECT       hesscol[3];     /* compute first vertical edge */
636	+	FVECT       gradcol;
637	+	comp_fftri(&fftr, hp, i, 0, VDB_Y, vflags);
638	+	if (hessrow != NULL)
639	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
640	+	if (gradrow != NULL)
641	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
642	+	for (j = 0; j < hp->ns-1; j++) {
643	+	FVECT   hessdia[3];     /* compute triangle contributions */
644	+	FVECT   graddia;
645	+	double  backg;
646	+	backg = back_ambval(hp, i, j, VDB_X, VDB_Y, vflags);
647	+	/* diagonal (inner) edge */
648	+	comp_fftri(&fftr, hp, i, j+1, VDB_xY, vflags);
649	+	if (hessrow != NULL) {
650	+	comp_hessian(hessdia, &fftr, hp->rp->ron);
651	+	rev_hessian(hesscol);
652	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
653	+	}
654	+	if (gradrow != NULL) {
655	+	comp_gradient(graddia, &fftr, hp->rp->ron);
656	+	rev_gradient(gradcol);
657	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
658	+	}
659	+	/* initialize edge in next row */
660	+	comp_fftri(&fftr, hp, i+1, j+1, VDB_x, vflags);
661	+	if (hessrow != NULL)
662	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
663	+	if (gradrow != NULL)
664	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
665	+	/* new column edge & paired triangle */
666	+	backg = back_ambval(hp, i+1, j+1, VDB_x, VDB_y, vflags);
667	+	comp_fftri(&fftr, hp, i, j+1, VDB_Y, vflags);
668	+	if (hessrow != NULL) {
669	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
670	+	rev_hessian(hessdia);
671	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
672	+	if (i < hp->ns-2)
673	+	rev_hessian(hessrow[j]);
674	+	}
675	+	if (gradrow != NULL) {
676	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
677	+	rev_gradient(graddia);
678	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
679	+	if (i < hp->ns-2)
680	+	rev_gradient(gradrow[j]);
681	+	}
682	+	}
683	+	}
684	+	/* release row buffers */
685	+	if (hessrow != NULL) free(hessrow);
686	+	if (gradrow != NULL) free(gradrow);
687	+	free(vflags);
688	+
689	+	if (ra != NULL)                 /* extract eigenvectors & radii */
690	+	eigenvectors(uv, ra, hessian);
691	+	if (pg != NULL) {               /* tangential position gradient */
692	+	pg[0] = DOT(gradient, uv[0]);
693	+	pg[1] = DOT(gradient, uv[1]);
694	+	}
695	+	}
696	+
697	+
698	+	/* Compute direction gradient from a hemispherical sampling */
699	+	static void
700	+	ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
701	+	{
702	+	AMBSAMP *ap;
703	+	double  dgsum[2];
704	+	int     n;
705	+	FVECT   vd;
706	+	double  gfact;
707	+
708	+	dgsum[0] = dgsum[1] = 0.0;      /* sum values times -tan(theta) */
709	+	for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
710	+	/* use vector for azimuth + 90deg */
711	+	VSUB(vd, ap->p, hp->rp->rop);
712	+	/* brightness over cosine factor */
713	+	gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
714	+	/* sine = proj_radius/vd_length */
715	+	dgsum[0] -= DOT(uv[1], vd) * gfact;
716	+	dgsum[1] += DOT(uv[0], vd) * gfact;
717	+	}
718	+	dg[0] = dgsum[0] / (hp->ns*hp->ns);
719	+	dg[1] = dgsum[1] / (hp->ns*hp->ns);
720	+	}
721	+
722	+
723	+	/* Compute potential light leak direction flags for cache value */
724	+	static uint32
725	+	ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
726	+	{
727	+	const double    max_d = 1.0/(minarad*ambacc + 0.001);
728	+	const double    ang_res = 0.5*PI/(hp->ns-1);
729	+	const double    ang_step = ang_res/((int)(16/PI*ang_res) + (1+FTINY));
730	+	double          avg_d = 0;
731	+	uint32          flgs = 0;
732	+	int             i, j;
733	+	/* don't bother for a few samples */
734	+	if (hp->ns < 12)
735	+	return(0);
736	+	/* check distances overhead */
737	+	for (i = hp->ns*3/4; i-- > hp->ns>>2; )
738	+	for (j = hp->ns*3/4; j-- > hp->ns>>2; )
739	+	avg_d += ambsam(hp,i,j).d;
740	+	avg_d *= 4.0/(hp->ns*hp->ns);
741	+	if (avg_d*r0 >= 1.0)            /* ceiling too low for corral? */
742	+	return(0);
743	+	if (avg_d >= max_d)             /* insurance */
744	+	return(0);
745	+	/* else circle around perimeter */
746	+	for (i = 0; i < hp->ns; i++)
747	+	for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
748	+	AMBSAMP *ap = &ambsam(hp,i,j);
749	+	FVECT   vec;
750	+	double  u, v;
751	+	double  ang, a1;
752	+	int     abp;
753	+	if ((ap->d <= FTINY) | (ap->d >= max_d))
754	+	continue;       /* too far or too near */
755	+	VSUB(vec, ap->p, hp->rp->rop);
756	+	u = DOT(vec, uv[0]) * ap->d;
757	+	v = DOT(vec, uv[1]) * ap->d;
758	+	if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= 1.0)
759	+	continue;       /* occluder outside ellipse */
760	+	ang = atan2a(v, u);     /* else set direction flags */
761	+	for (a1 = ang-.5*ang_res; a1 <= ang+.5*ang_res; a1 += ang_step)
762	+	flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
763	+	}
764	+	return(flgs);
765	+	}
766	+
767	+
768	+	int
769	+	doambient(                              /* compute ambient component */
770	+	COLOR   rcol,                   /* input/output color */
771	+	RAY     *r,
772	+	double  wt,
773	+	FVECT   uv[2],                  /* returned (optional) */
774	+	float   ra[2],                  /* returned (optional) */
775	+	float   pg[2],                  /* returned (optional) */
776	+	float   dg[2],                  /* returned (optional) */
777	+	uint32  *crlp                   /* returned (optional) */
778	+	)
779	+	{
780	+	AMBHEMI *hp = inithemi(rcol, r, wt);
781	+	int     cnt;
782	+	FVECT   my_uv[2];
783	+	double  d, K, acol[3];
784	+	AMBSAMP *ap;
785	+	int     i, j;
786	+	/* check/initialize */
787	+	if (hp == NULL)
788	+	return(0);
789	+	if (uv != NULL)
790	+	memset(uv, 0, sizeof(FVECT)*2);
791	+	if (ra != NULL)
792	+	ra[0] = ra[1] = 0.0;
793	+	if (pg != NULL)
794	+	pg[0] = pg[1] = 0.0;
795	+	if (dg != NULL)
796	+	dg[0] = dg[1] = 0.0;
797	+	if (crlp != NULL)
798	+	*crlp = 0;
799	+	/* sample the hemisphere */
800	+	acol[0] = acol[1] = acol[2] = 0.0;
801	+	cnt = 0;
802	+	for (i = hp->ns; i--; )
803	+	for (j = hp->ns; j--; )
804	+	if ((ap = ambsample(hp, i, j)) != NULL) {
805	+	addcolor(acol, ap->v);
806	+	++cnt;
807	+	}
808	+	if (!cnt) {
809	+	setcolor(rcol, 0.0, 0.0, 0.0);
810	+	free(hp);
811	+	return(0);              /* no valid samples */
812	+	}
813	+	if (cnt < hp->ns*hp->ns) {      /* incomplete sampling? */
814	+	copycolor(rcol, acol);
815	+	free(hp);
816	+	return(-1);             /* return value w/o Hessian */
817	+	}
818	+	cnt = ambssamp*wt + 0.5;        /* perform super-sampling? */
819	+	if (cnt > 8)
820	+	ambsupersamp(acol, hp, cnt);
821	+	copycolor(rcol, acol);          /* final indirect irradiance/PI */
822	+	if ((ra == NULL) & (pg == NULL) & (dg == NULL)) {
823	+	free(hp);
824	+	return(-1);             /* no radius or gradient calc. */
825	+	}
826	+	if ((d = bright(acol)) > FTINY) {       /* normalize Y values */
827	+	d = 0.99*(hp->ns*hp->ns)/d;
828	+	K = 0.01;
829	+	} else {                        /* or fall back on geometric Hessian */
830	+	K = 1.0;
831	+	pg = NULL;
832	+	dg = NULL;
833	+	crlp = NULL;
834	+	}
835	+	ap = hp->sa;                    /* relative Y channel from here on... */
836	+	for (i = hp->ns*hp->ns; i--; ap++)
837	+	colval(ap->v,CIEY) = bright(ap->v)*d + K;
838	+
839	+	if (uv == NULL)                 /* make sure we have axis pointers */
840	+	uv = my_uv;
841	+	/* compute radii & pos. gradient */
842	+	ambHessian(hp, uv, ra, pg);
843	+
844	+	if (dg != NULL)                 /* compute direction gradient */
845	+	ambdirgrad(hp, uv, dg);
846	+
847	+	if (ra != NULL) {               /* scale/clamp radii */
848	+	if (pg != NULL) {
849	+	if (ra[0]*(d = fabs(pg[0])) > 1.0)
850	+	ra[0] = 1.0/d;
851	+	if (ra[1]*(d = fabs(pg[1])) > 1.0)
852	+	ra[1] = 1.0/d;
853	+	if (ra[0] > ra[1])
854	+	ra[0] = ra[1];
855	+	}
856	+	if (ra[0] < minarad) {
857	+	ra[0] = minarad;
858	+	if (ra[1] < minarad)
859	+	ra[1] = minarad;
860	+	}
861	+	ra[0] *= d = 1.0/sqrt(sqrt(wt));
862	+	if ((ra[1] *= d) > 2.0*ra[0])
863	+	ra[1] = 2.0*ra[0];
864	+	if (ra[1] > maxarad) {
865	+	ra[1] = maxarad;
866	+	if (ra[0] > maxarad)
867	+	ra[0] = maxarad;
868	+	}
869	+	/* flag encroached directions */
870	+	if ((wt >= 0.5-FTINY) & (crlp != NULL))
871	+	*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
872	+	if (pg != NULL) {       /* cap gradient if necessary */
873	+	d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
874	+	if (d > 1.0) {
875	+	d = 1.0/sqrt(d);
876	+	pg[0] *= d;
877	+	pg[1] *= d;
878	+	}
879	+	}
880	+	}
881	+	free(hp);                       /* clean up and return */
882	+	return(1);
883	+	}
884	+
885	+
886	+	#else /* ! NEWAMB */
887	+
888	+
889	+	void
890	+	inithemi(                       /* initialize sampling hemisphere */
891	+	AMBHEMI  *hp,
892	+	COLOR ac,
893	+	RAY  *r,
894	+	double  wt
895	+	)
896	+	{
897	+	double  d;
898	+	int  i;
899	+	/* set number of divisions */
900	+	if (ambacc <= FTINY &&
901	+	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
902	+	wt = d;                 /* avoid ray termination */
903	+	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
904	+	i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
905	+	if (hp->nt < i)
906	+	hp->nt = i;
907	+	hp->np = PI * hp->nt + 0.5;
908	+	/* set number of super-samples */
909	+	hp->ns = ambssamp * wt + 0.5;
910	+	/* assign coefficient */
911	+	copycolor(hp->acoef, ac);
912	+	d = 1.0/(hp->nt*hp->np);
913	+	scalecolor(hp->acoef, d);
914	+	/* make axes */
915	+	VCOPY(hp->uz, r->ron);
916	+	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
917	+	for (i = 0; i < 3; i++)
918	+	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
919	+	break;
920	+	if (i >= 3)
921	+	error(CONSISTENCY, "bad ray direction in inithemi");
922	+	hp->uy[i] = 1.0;
923	+	fcross(hp->ux, hp->uy, hp->uz);
924	+	normalize(hp->ux);
925	+	fcross(hp->uy, hp->uz, hp->ux);
926	+	}
927	+
928	+
929	+	int
930	+	divsample(                              /* sample a division */
931	+	AMBSAMP  *dp,
932	+	AMBHEMI  *h,
933	+	RAY  *r
934	+	)
935	+	{
936		RAY  ar;
937		int  hlist[3];
938		double  spt[2];
939		double  xd, yd, zd;
940		double  b2;
941		double  phi;
942	<	register int  i;
943	<
944	<	if (rayorigin(&ar, r, AMBIENT, AVGREFL) < 0)
942	>	int  i;
943	>	/* ambient coefficient for weight */
944	>	if (ambacc > FTINY)
945	>	setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
946	>	else
947	>	copycolor(ar.rcoef, h->acoef);
948	>	if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
949		return(-1);
950	+	if (ambacc > FTINY) {
951	+	multcolor(ar.rcoef, h->acoef);
952	+	scalecolor(ar.rcoef, 1./AVGREFL);
953	+	}
954		hlist[0] = r->rno;
955		hlist[1] = dp->t;
956		hlist[2] = dp->p;
957		multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
958		zd = sqrt((dp->t + spt[0])/h->nt);
959		phi = 2.0*PI * (dp->p + spt[1])/h->np;
960	<	xd = cos(phi) * zd;
961	<	yd = sin(phi) * zd;
960	>	xd = tcos(phi) * zd;
961	>	yd = tsin(phi) * zd;
962		zd = sqrt(1.0 - zd*zd);
963		for (i = 0; i < 3; i++)
964		ar.rdir[i] =    xd*h->ux[i] +
965		yd*h->uy[i] +
966		zd*h->uz[i];
967	+	checknorm(ar.rdir);
968		dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
969		rayvalue(&ar);
970		ndims--;
971	+	multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
972		addcolor(dp->v, ar.rcol);
973	+	/* use rt to improve gradient calc */
974		if (ar.rt > FTINY && ar.rt < FHUGE)
975		dp->r += 1.0/ar.rt;
976		/* (re)initialize error */
#	Line 99 | Line 984 | RAY  *r;
984		}
985
986
987	+	static int
988	+	ambcmp(                                 /* decreasing order */
989	+	const void *p1,
990	+	const void *p2
991	+	)
992	+	{
993	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
994	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
995	+
996	+	if (d1->k < d2->k)
997	+	return(1);
998	+	if (d1->k > d2->k)
999	+	return(-1);
1000	+	return(0);
1001	+	}
1002	+
1003	+
1004	+	static int
1005	+	ambnorm(                                /* standard order */
1006	+	const void *p1,
1007	+	const void *p2
1008	+	)
1009	+	{
1010	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
1011	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
1012	+	int     c;
1013	+
1014	+	if ( (c = d1->t - d2->t) )
1015	+	return(c);
1016	+	return(d1->p - d2->p);
1017	+	}
1018	+
1019	+
1020		double
1021	<	doambient(acol, r, wt, pg, dg)          /* compute ambient component */
1022	<	COLOR  acol;
1023	<	RAY  *r;
1024	<	double  wt;
1025	<	FVECT  pg, dg;
1021	>	doambient(                              /* compute ambient component */
1022	>	COLOR  rcol,
1023	>	RAY  *r,
1024	>	double  wt,
1025	>	FVECT  pg,
1026	>	FVECT  dg
1027	>	)
1028		{
1029	<	double  b, d;
1029	>	double  b, d=0;
1030		AMBHEMI  hemi;
1031		AMBSAMP  *div;
1032		AMBSAMP  dnew;
1033	<	register AMBSAMP  *dp;
1033	>	double  acol[3];
1034	>	AMBSAMP  *dp;
1035		double  arad;
1036	<	int  ndivs, ns;
1037	<	register int  i, j;
117	<	/* initialize color */
118	<	setcolor(acol, 0.0, 0.0, 0.0);
1036	>	int  divcnt;
1037	>	int  i, j;
1038		/* initialize hemisphere */
1039	<	inithemi(&hemi, r, wt);
1040	<	ndivs = hemi.nt * hemi.np;
1041	<	if (ndivs == 0)
1039	>	inithemi(&hemi, rcol, r, wt);
1040	>	divcnt = hemi.nt * hemi.np;
1041	>	/* initialize */
1042	>	if (pg != NULL)
1043	>	pg[0] = pg[1] = pg[2] = 0.0;
1044	>	if (dg != NULL)
1045	>	dg[0] = dg[1] = dg[2] = 0.0;
1046	>	setcolor(rcol, 0.0, 0.0, 0.0);
1047	>	if (divcnt == 0)
1048		return(0.0);
1049	<	/* set number of super-samples */
1050	<	ns = ambssamp * wt + 0.5;
1051	<	if (ns > 0 || pg != NULL || dg != NULL) {
127	<	div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
1049	>	/* allocate super-samples */
1050	>	if (hemi.ns > 0 || pg != NULL || dg != NULL) {
1051	>	div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP));
1052		if (div == NULL)
1053		error(SYSTEM, "out of memory in doambient");
1054		} else
1055		div = NULL;
1056		/* sample the divisions */
1057		arad = 0.0;
1058	+	acol[0] = acol[1] = acol[2] = 0.0;
1059		if ((dp = div) == NULL)
1060		dp = &dnew;
1061	+	divcnt = 0;
1062		for (i = 0; i < hemi.nt; i++)
1063		for (j = 0; j < hemi.np; j++) {
1064		dp->t = i; dp->p = j;
1065		setcolor(dp->v, 0.0, 0.0, 0.0);
1066		dp->r = 0.0;
1067		dp->n = 0;
1068	<	if (divsample(dp, &hemi, r) < 0)
1069	<	goto oopsy;
1068	>	if (divsample(dp, &hemi, r) < 0) {
1069	>	if (div != NULL)
1070	>	dp++;
1071	>	continue;
1072	>	}
1073	>	arad += dp->r;
1074	>	divcnt++;
1075		if (div != NULL)
1076		dp++;
1077	<	else {
1077	>	else
1078		addcolor(acol, dp->v);
148	–	arad += dp->r;
149	–	}
1079		}
1080	<	if (ns > 0) {                   /* perform super-sampling */
1080	>	if (!divcnt) {
1081	>	if (div != NULL)
1082	>	free((void *)div);
1083	>	return(0.0);            /* no samples taken */
1084	>	}
1085	>	if (divcnt < hemi.nt*hemi.np) {
1086	>	pg = dg = NULL;         /* incomplete sampling */
1087	>	hemi.ns = 0;
1088	>	} else if (arad > FTINY && divcnt/arad < minarad) {
1089	>	hemi.ns = 0;            /* close enough */
1090	>	} else if (hemi.ns > 0) {       /* else perform super-sampling? */
1091		comperrs(div, &hemi);                   /* compute errors */
1092	<	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
1092	>	qsort(div, divcnt, sizeof(AMBSAMP), ambcmp);    /* sort divs */
1093		/* super-sample */
1094	<	for (i = ns; i > 0; i--) {
1095	<	copystruct(&dnew, div);
1096	<	if (divsample(&dnew, &hemi, r) < 0)
1097	<	goto oopsy;
1098	<	/* reinsert */
1099	<	dp = div;
1100	<	j = ndivs < i ? ndivs : i;
1094	>	for (i = hemi.ns; i > 0; i--) {
1095	>	dnew = *div;
1096	>	if (divsample(&dnew, &hemi, r) < 0) {
1097	>	dp++;
1098	>	continue;
1099	>	}
1100	>	dp = div;               /* reinsert */
1101	>	j = divcnt < i ? divcnt : i;
1102		while (--j > 0 && dnew.k < dp[1].k) {
1103	<	copystruct(dp, dp+1);
1103	>	*dp = *(dp+1);
1104		dp++;
1105		}
1106	<	copystruct(dp, &dnew);
1106	>	*dp = dnew;
1107		}
1108		if (pg != NULL || dg != NULL)   /* restore order */
1109	<	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
1109	>	qsort(div, divcnt, sizeof(AMBSAMP), ambnorm);
1110		}
1111		/* compute returned values */
1112		if (div != NULL) {
1113	<	for (i = ndivs, dp = div; i-- > 0; dp++) {
1113	>	arad = 0.0;             /* note: divcnt may be < nt*np */
1114	>	for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) {
1115		arad += dp->r;
1116		if (dp->n > 1) {
1117		b = 1.0/dp->n;
#	Line 182 | Line 1123 | FVECT  pg, dg;
1123		}
1124		b = bright(acol);
1125		if (b > FTINY) {
1126	<	b = ndivs/b;
1126	>	b = 1.0/b;      /* compute & normalize gradient(s) */
1127		if (pg != NULL) {
1128		posgradient(pg, div, &hemi);
1129		for (i = 0; i < 3; i++)
#	Line 193 | Line 1134 | FVECT  pg, dg;
1134		for (i = 0; i < 3; i++)
1135		dg[i] *= b;
1136		}
196	–	} else {
197	–	if (pg != NULL)
198	–	for (i = 0; i < 3; i++)
199	–	pg[i] = 0.0;
200	–	if (dg != NULL)
201	–	for (i = 0; i < 3; i++)
202	–	dg[i] = 0.0;
1137		}
1138	<	free((char *)div);
1138	>	free((void *)div);
1139		}
1140	<	b = 1.0/ndivs;
207	<	scalecolor(acol, b);
1140	>	copycolor(rcol, acol);
1141		if (arad <= FTINY)
1142		arad = maxarad;
1143	<	else {
1144	<	arad = (ndivs+ns)/arad;
212	<	if (arad > maxarad)
213	<	arad = maxarad;
214	<	}
1143	>	else
1144	>	arad = (divcnt+hemi.ns)/arad;
1145		if (pg != NULL) {               /* reduce radius if gradient large */
1146		d = DOT(pg,pg);
1147		if (d*arad*arad > 1.0)
#	Line 225 | Line 1155 | FVECT  pg, dg;
1155		pg[i] *= d;
1156		}
1157		}
1158	<	return(arad/sqrt(wt));
1159	<	oopsy:
1160	<	if (div != NULL)
231	<	free((char *)div);
232	<	return(0.0);
1158	>	if ((arad /= sqrt(wt)) > maxarad)
1159	>	arad = maxarad;
1160	>	return(arad);
1161		}
1162
1163
1164	<	inithemi(hp, r, wt)             /* initialize sampling hemisphere */
1165	<	register AMBHEMI  *hp;
1166	<	RAY  *r;
1167	<	double  wt;
1164	>	void
1165	>	comperrs(                       /* compute initial error estimates */
1166	>	AMBSAMP  *da,   /* assumes standard ordering */
1167	>	AMBHEMI  *hp
1168	>	)
1169		{
241	–	register int  i;
242	–	/* set number of divisions */
243	–	if (wt < (.25*PI)/ambdiv+FTINY) {
244	–	hp->nt = hp->np = 0;
245	–	return;                 /* zero samples */
246	–	}
247	–	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
248	–	hp->np = PI * hp->nt + 0.5;
249	–	/* make axes */
250	–	VCOPY(hp->uz, r->ron);
251	–	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
252	–	for (i = 0; i < 3; i++)
253	–	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
254	–	break;
255	–	if (i >= 3)
256	–	error(CONSISTENCY, "bad ray direction in inithemi");
257	–	hp->uy[i] = 1.0;
258	–	fcross(hp->ux, hp->uy, hp->uz);
259	–	normalize(hp->ux);
260	–	fcross(hp->uy, hp->uz, hp->ux);
261	–	}
262	–
263	–
264	–	comperrs(da, hp)                /* compute initial error estimates */
265	–	AMBSAMP  *da;           /* assumes standard ordering */
266	–	register AMBHEMI  *hp;
267	–	{
1170		double  b, b2;
1171		int  i, j;
1172	<	register AMBSAMP  *dp;
1172	>	AMBSAMP  *dp;
1173		/* sum differences from neighbors */
1174		dp = da;
1175		for (i = 0; i < hp->nt; i++)
#	Line 311 | Line 1213 | register AMBHEMI  *hp;
1213		}
1214
1215
1216	<	posgradient(gv, da, hp)                         /* compute position gradient */
1217	<	FVECT  gv;
1218	<	AMBSAMP  *da;                   /* assumes standard ordering */
1219	<	AMBHEMI  *hp;
1216	>	void
1217	>	posgradient(                                    /* compute position gradient */
1218	>	FVECT  gv,
1219	>	AMBSAMP  *da,                   /* assumes standard ordering */
1220	>	AMBHEMI  *hp
1221	>	)
1222		{
1223	<	register int  i, j;
1224	<	double  b, d;
1223	>	int  i, j;
1224	>	double  nextsine, lastsine, b, d;
1225		double  mag0, mag1;
1226		double  phi, cosp, sinp, xd, yd;
1227	<	register AMBSAMP  *dp;
1227	>	AMBSAMP  *dp;
1228
1229		xd = yd = 0.0;
1230		for (j = 0; j < hp->np; j++) {
1231		dp = da + j;
1232		mag0 = mag1 = 0.0;
1233	+	lastsine = 0.0;
1234		for (i = 0; i < hp->nt; i++) {
1235		#ifdef  DEBUG
1236		if (dp->t != i || dp->p != j)
#	Line 336 | Line 1241 | AMBHEMI  *hp;
1241		if (i > 0) {
1242		d = dp[-hp->np].r;
1243		if (dp[0].r > d) d = dp[0].r;
1244	<	d *= 1.0 - (double)i/hp->nt;    /* cos(t)^2 */
1244	>	/* sin(t)*cos(t)^2 */
1245	>	d *= lastsine * (1.0 - (double)i/hp->nt);
1246		mag0 += d*(b - bright(dp[-hp->np].v));
1247		}
1248	+	nextsine = sqrt((double)(i+1)/hp->nt);
1249		if (j > 0) {
1250		d = dp[-1].r;
1251		if (dp[0].r > d) d = dp[0].r;
1252	<	mag1 += d*(b - bright(dp[-1].v));
1252	>	mag1 += d * (nextsine - lastsine) *
1253	>	(b - bright(dp[-1].v));
1254		} else {
1255		d = dp[hp->np-1].r;
1256		if (dp[0].r > d) d = dp[0].r;
1257	<	mag1 += d*(b - bright(dp[hp->np-1].v));
1257	>	mag1 += d * (nextsine - lastsine) *
1258	>	(b - bright(dp[hp->np-1].v));
1259		}
1260		dp += hp->np;
1261	+	lastsine = nextsine;
1262		}
1263	<	if (hp->nt > 1) {
354	<	mag0 /= (double)hp->np;
355	<	mag1 /= (double)hp->nt;
356	<	}
1263	>	mag0 *= 2.0*PI / hp->np;
1264		phi = 2.0*PI * (double)j/hp->np;
1265	<	cosp = cos(phi); sinp = sin(phi);
1265	>	cosp = tcos(phi); sinp = tsin(phi);
1266		xd += mag0*cosp - mag1*sinp;
1267		yd += mag0*sinp + mag1*cosp;
1268		}
1269		for (i = 0; i < 3; i++)
1270	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/PI;
1270	>	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI;
1271		}
1272
1273
1274	<	dirgradient(gv, da, hp)                         /* compute direction gradient */
1275	<	FVECT  gv;
1276	<	AMBSAMP  *da;                   /* assumes standard ordering */
1277	<	AMBHEMI  *hp;
1274	>	void
1275	>	dirgradient(                                    /* compute direction gradient */
1276	>	FVECT  gv,
1277	>	AMBSAMP  *da,                   /* assumes standard ordering */
1278	>	AMBHEMI  *hp
1279	>	)
1280		{
1281	<	register int  i, j;
1281	>	int  i, j;
1282		double  mag;
1283		double  phi, xd, yd;
1284	<	register AMBSAMP  *dp;
1284	>	AMBSAMP  *dp;
1285
1286		xd = yd = 0.0;
1287		for (j = 0; j < hp->np; j++) {
#	Line 384 | Line 1293 | AMBHEMI  *hp;
1293		error(CONSISTENCY,
1294		"division order in dirgradient");
1295		#endif
1296	<	mag += sqrt((i+.5)/hp->nt)*bright(dp->v);  /* sin(t) */
1296	>	/* tan(t) */
1297	>	mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
1298		dp += hp->np;
1299		}
1300		phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
1301	<	xd += mag * cos(phi);
1302	<	yd += mag * sin(phi);
1301	>	xd += mag * tcos(phi);
1302	>	yd += mag * tsin(phi);
1303		}
1304		for (i = 0; i < 3; i++)
1305	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*PI/(hp->nt*hp->np);
1305	>	gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
1306		}
1307	+
1308	+	#endif  /* ! NEWAMB */

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