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

Comparing ray/src/rt/ambcomp.c (file contents):
Revision 1.7 by greg, Thu Jun 13 12:00:29 1991 UTC vs.
Revision 2.48 by greg, Sun May 4 01:02:13 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	+	/* #define AHEM_MARG    1.2     /* hem margin */
27	+
28	+	extern void             SDsquare2disk(double ds[2], double seedx, double seedy);
29	+
30	+	/* vertex direction bit positions */
31	+	#define VDB_xy  0
32	+	#define VDB_y   01
33	+	#define VDB_x   02
34	+	#define VDB_Xy  03
35	+	#define VDB_xY  04
36	+	#define VDB_X   05
37	+	#define VDB_Y   06
38	+	#define VDB_XY  07
39	+	/* get opposite vertex direction bit */
40	+	#define VDB_OPP(f)      (~(f) & 07)
41	+	/* adjacent triangle vertex flags */
42	+	static const int  adjacent_trifl[8] = {
43	+	0,                      /* forbidden diagonal */
44	+	1<<VDB_x|1<<VDB_y|1<<VDB_Xy,
45	+	1<<VDB_y|1<<VDB_x|1<<VDB_xY,
46	+	1<<VDB_y|1<<VDB_Xy|1<<VDB_X,
47	+	1<<VDB_x|1<<VDB_xY|1<<VDB_Y,
48	+	1<<VDB_Xy|1<<VDB_X|1<<VDB_Y,
49	+	1<<VDB_xY|1<<VDB_Y|1<<VDB_X,
50	+	0,                      /* forbidden diagonal */
51	+	};
52	+
53		typedef struct {
54	<	short  t, p;            /* theta, phi indices */
55	<	COLOR  v;               /* value sum */
56	<	float  r;               /* 1/distance sum */
57	<	float  k;               /* variance for this division */
22	<	int  n;                 /* number of subsamples */
23	<	}  AMBSAMP;             /* ambient sample division */
54	>	COLOR   v;              /* hemisphere sample value */
55	>	float   d;              /* reciprocal distance (1/rt) */
56	>	FVECT   p;              /* intersection point */
57	>	} AMBSAMP;              /* sample value */
58
59		typedef struct {
60	<	FVECT  ux, uy, uz;      /* x, y and z axis directions */
61	<	short  nt, np;          /* number of theta and phi directions */
60	>	RAY     *rp;            /* originating ray sample */
61	>	FVECT   ux, uy;         /* tangent axis unit vectors */
62	>	int     ns;             /* number of samples per axis */
63	>	COLOR   acoef;          /* division contribution coefficient */
64	>	AMBSAMP sa[1];          /* sample array (extends struct) */
65		}  AMBHEMI;             /* ambient sample hemisphere */
66
67	<	extern double  sin(), cos(), sqrt();
67	>	#define ambndx(h,i,j)   ((i)*(h)->ns + (j))
68	>	#define ambsam(h,i,j)   (h)->sa[ambndx(h,i,j)]
69
70	+	typedef struct {
71	+	FVECT   r_i, r_i1, e_i, rcp, rI2_eJ2;
72	+	double  I1, I2;
73	+	int     valid;
74	+	} FFTRI;                /* vectors and coefficients for Hessian calculation */
75
76	+
77	+	/* Get index for adjacent vertex */
78		static int
79	<	ambcmp(d1, d2)                          /* decreasing order */
35	<	AMBSAMP  *d1, *d2;
79	>	adjacent_verti(AMBHEMI *hp, int i, int j, int dbit)
80		{
81	<	if (d1->k < d2->k)
82	<	return(1);
83	<	if (d1->k > d2->k)
84	<	return(-1);
85	<	return(0);
81	>	int     i0 = i*hp->ns + j;
82	>
83	>	switch (dbit) {
84	>	case VDB_y:     return(i0 - hp->ns);
85	>	case VDB_x:     return(i0 - 1);
86	>	case VDB_Xy:    return(i0 - hp->ns + 1);
87	>	case VDB_xY:    return(i0 + hp->ns - 1);
88	>	case VDB_X:     return(i0 + 1);
89	>	case VDB_Y:     return(i0 + hp->ns);
90	>	/* the following should never occur */
91	>	case VDB_xy:    return(i0 - hp->ns - 1);
92	>	case VDB_XY:    return(i0 + hp->ns + 1);
93	>	}
94	>	return(-1);
95		}
96
97
98	+	/* Get vertex direction bit for the opposite edge to complete triangle */
99		static int
100	<	ambnorm(d1, d2)                         /* standard order */
47	<	AMBSAMP  *d1, *d2;
100	>	vdb_edge(int db1, int db2)
101		{
102	<	register int  c;
102	>	switch (db1) {
103	>	case VDB_x:     return(db2==VDB_y ? VDB_Xy : VDB_Y);
104	>	case VDB_y:     return(db2==VDB_x ? VDB_xY : VDB_X);
105	>	case VDB_X:     return(db2==VDB_Xy ? VDB_y : VDB_xY);
106	>	case VDB_Y:     return(db2==VDB_xY ? VDB_x : VDB_Xy);
107	>	case VDB_xY:    return(db2==VDB_x ? VDB_y : VDB_X);
108	>	case VDB_Xy:    return(db2==VDB_y ? VDB_x : VDB_Y);
109	>	}
110	>	error(INTERNAL, "forbidden diagonal in vdb_edge()");
111	>	return(-1);
112	>	}
113
114	<	if (c = d1->t - d2->t)
115	<	return(c);
116	<	return(d1->p - d2->p);
114	>
115	>	static AMBHEMI *
116	>	inithemi(                       /* initialize sampling hemisphere */
117	>	COLOR   ac,
118	>	RAY     *r,
119	>	double  wt
120	>	)
121	>	{
122	>	AMBHEMI *hp;
123	>	double  d;
124	>	int     n, i;
125	>	/* set number of divisions */
126	>	if (ambacc <= FTINY &&
127	>	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
128	>	wt = d;                 /* avoid ray termination */
129	>	n = sqrt(ambdiv * wt) + 0.5;
130	>	i = 1 + 5*(ambacc > FTINY);     /* minimum number of samples */
131	>	if (n < i)
132	>	n = i;
133	>	/* allocate sampling array */
134	>	hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
135	>	if (hp == NULL)
136	>	return(NULL);
137	>	hp->rp = r;
138	>	hp->ns = n;
139	>	/* assign coefficient */
140	>	copycolor(hp->acoef, ac);
141	>	d = 1.0/(n*n);
142	>	scalecolor(hp->acoef, d);
143	>	/* make tangent plane axes */
144	>	hp->uy[0] = 0.5 - frandom();
145	>	hp->uy[1] = 0.5 - frandom();
146	>	hp->uy[2] = 0.5 - frandom();
147	>	for (i = 3; i--; )
148	>	if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6))
149	>	break;
150	>	if (i < 0)
151	>	error(CONSISTENCY, "bad ray direction in inithemi");
152	>	hp->uy[i] = 1.0;
153	>	VCROSS(hp->ux, hp->uy, r->ron);
154	>	normalize(hp->ux);
155	>	VCROSS(hp->uy, r->ron, hp->ux);
156	>	/* we're ready to sample */
157	>	return(hp);
158		}
159
160
161	<	divsample(dp, h, r)                     /* sample a division */
162	<	register AMBSAMP  *dp;
163	<	AMBHEMI  *h;
60	<	RAY  *r;
161	>	/* Sample ambient division and apply weighting coefficient */
162	>	static int
163	>	getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n)
164		{
165	+	int     hlist[3], ii;
166	+	double  spt[2], zd;
167	+	/* ambient coefficient for weight */
168	+	if (ambacc > FTINY)
169	+	setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL);
170	+	else
171	+	copycolor(arp->rcoef, hp->acoef);
172	+	if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0)
173	+	return(0);
174	+	if (ambacc > FTINY) {
175	+	multcolor(arp->rcoef, hp->acoef);
176	+	scalecolor(arp->rcoef, 1./AVGREFL);
177	+	}
178	+	hlist[0] = hp->rp->rno;
179	+	hlist[1] = j;
180	+	hlist[2] = i;
181	+	multisamp(spt, 2, urand(ilhash(hlist,3)+n));
182	+	if (!n) {                       /* avoid border samples for n==0 */
183	+	if ((spt[0] < 0.1) | (spt[0] >= 0.9))
184	+	spt[0] = 0.1 + 0.8*frandom();
185	+	if ((spt[1] < 0.1) | (spt[1] >= 0.9))
186	+	spt[1] = 0.1 + 0.8*frandom();
187	+	}
188	+	SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
189	+	zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
190	+	for (ii = 3; ii--; )
191	+	arp->rdir[ii] = spt[0]*hp->ux[ii] +
192	+	spt[1]*hp->uy[ii] +
193	+	zd*hp->rp->ron[ii];
194	+	checknorm(arp->rdir);
195	+	dimlist[ndims++] = ambndx(hp,i,j) + 90171;
196	+	rayvalue(arp);                  /* evaluate ray */
197	+	ndims--;                        /* apply coefficient */
198	+	multcolor(arp->rcol, arp->rcoef);
199	+	return(1);
200	+	}
201	+
202	+
203	+	static AMBSAMP *
204	+	ambsample(                              /* initial ambient division sample */
205	+	AMBHEMI *hp,
206	+	int     i,
207	+	int     j
208	+	)
209	+	{
210	+	AMBSAMP *ap = &ambsam(hp,i,j);
211	+	RAY     ar;
212	+	/* generate hemispherical sample */
213	+	if (!getambsamp(&ar, hp, i, j, 0) || ar.rt <= FTINY) {
214	+	memset(ap, 0, sizeof(AMBSAMP));
215	+	return(NULL);
216	+	}
217	+	ap->d = 1.0/ar.rt;              /* limit vertex distance */
218	+	if (ar.rt > 10.0*thescene.cusize)
219	+	ar.rt = 10.0*thescene.cusize;
220	+	VSUM(ap->p, ar.rorg, ar.rdir, ar.rt);
221	+	copycolor(ap->v, ar.rcol);
222	+	return(ap);
223	+	}
224	+
225	+
226	+	/* Estimate errors based on ambient division differences */
227	+	static float *
228	+	getambdiffs(AMBHEMI *hp)
229	+	{
230	+	float   *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
231	+	float   *ep;
232	+	AMBSAMP *ap;
233	+	double  b, d2;
234	+	int     i, j;
235	+
236	+	if (earr == NULL)               /* out of memory? */
237	+	return(NULL);
238	+	/* compute squared neighbor diffs */
239	+	for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
240	+	for (j = 0; j < hp->ns; j++, ap++, ep++) {
241	+	b = bright(ap[0].v);
242	+	if (i) {                /* from above */
243	+	d2 = b - bright(ap[-hp->ns].v);
244	+	d2 *= d2;
245	+	ep[0] += d2;
246	+	ep[-hp->ns] += d2;
247	+	}
248	+	if (j) {                /* from behind */
249	+	d2 = b - bright(ap[-1].v);
250	+	d2 *= d2;
251	+	ep[0] += d2;
252	+	ep[-1] += d2;
253	+	}
254	+	}
255	+	/* correct for number of neighbors */
256	+	earr[0] *= 2.f;
257	+	earr[hp->ns-1] *= 2.f;
258	+	earr[(hp->ns-1)*hp->ns] *= 2.f;
259	+	earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f;
260	+	for (i = 1; i < hp->ns-1; i++) {
261	+	earr[i*hp->ns] *= 4./3.;
262	+	earr[i*hp->ns + hp->ns-1] *= 4./3.;
263	+	}
264	+	for (j = 1; j < hp->ns-1; j++) {
265	+	earr[j] *= 4./3.;
266	+	earr[(hp->ns-1)*hp->ns + j] *= 4./3.;
267	+	}
268	+	return(earr);
269	+	}
270	+
271	+
272	+	/* Perform super-sampling on hemisphere (introduces bias) */
273	+	static void
274	+	ambsupersamp(double acol[3], AMBHEMI *hp, int cnt)
275	+	{
276	+	float   *earr = getambdiffs(hp);
277	+	double  e2sum = 0;
278	+	AMBSAMP *ap;
279	+	RAY     ar;
280	+	COLOR   asum;
281	+	float   *ep;
282	+	int     i, j, n;
283	+
284	+	if (earr == NULL)               /* just skip calc. if no memory */
285	+	return;
286	+	/* add up estimated variances */
287	+	for (ep = earr + hp->ns*hp->ns; ep-- > earr; )
288	+	e2sum += *ep;
289	+	ep = earr;                      /* perform super-sampling */
290	+	for (ap = hp->sa, i = 0; i < hp->ns; i++)
291	+	for (j = 0; j < hp->ns; j++, ap++) {
292	+	int     nss = *ep/e2sum*cnt + frandom();
293	+	setcolor(asum, 0., 0., 0.);
294	+	for (n = 1; n <= nss; n++) {
295	+	if (!getambsamp(&ar, hp, i, j, n)) {
296	+	nss = n-1;
297	+	break;
298	+	}
299	+	addcolor(asum, ar.rcol);
300	+	}
301	+	if (nss) {              /* update returned ambient value */
302	+	const double    ssf = 1./(nss + 1);
303	+	for (n = 3; n--; )
304	+	acol[n] += ssf*colval(asum,n) +
305	+	(ssf - 1.)*colval(ap->v,n);
306	+	}
307	+	e2sum -= *ep++;         /* update remainders */
308	+	cnt -= nss;
309	+	}
310	+	free(earr);
311	+	}
312	+
313	+
314	+	/* Compute vertex flags, indicating farthest in each direction */
315	+	static uby8 *
316	+	vertex_flags(AMBHEMI *hp)
317	+	{
318	+	uby8    *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8));
319	+	uby8    *vf;
320	+	AMBSAMP *ap;
321	+	int     i, j;
322	+
323	+	if (vflags == NULL)
324	+	error(SYSTEM, "out of memory in vertex_flags()");
325	+	vf = vflags;
326	+	ap = hp->sa;            /* compute farthest along first row */
327	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++)
328	+	if (ap[0].d <= ap[1].d)
329	+	vf[0] |= 1<<VDB_X;
330	+	else
331	+	vf[1] |= 1<<VDB_x;
332	+	++vf; ++ap;
333	+	/* flag subsequent rows */
334	+	for (i = 1; i < hp->ns; i++) {
335	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++) {
336	+	if (ap[0].d <= ap[-hp->ns].d)   /* row before */
337	+	vf[0] |= 1<<VDB_y;
338	+	else
339	+	vf[-hp->ns] |= 1<<VDB_Y;
340	+	if (ap[0].d <= ap[1-hp->ns].d)  /* diagonal we care about */
341	+	vf[0] |= 1<<VDB_Xy;
342	+	else
343	+	vf[1-hp->ns] |= 1<<VDB_xY;
344	+	if (ap[0].d <= ap[1].d)         /* column after */
345	+	vf[0] |= 1<<VDB_X;
346	+	else
347	+	vf[1] |= 1<<VDB_x;
348	+	}
349	+	if (ap[0].d <= ap[-hp->ns].d)       /* final column edge */
350	+	vf[0] |= 1<<VDB_y;
351	+	else
352	+	vf[-hp->ns] |= 1<<VDB_Y;
353	+	++vf; ++ap;
354	+	}
355	+	return(vflags);
356	+	}
357	+
358	+
359	+	/* Return brightness of farthest ambient sample */
360	+	static double
361	+	back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags)
362	+	{
363	+	const int       v0 = ambndx(hp,i,j);
364	+	const int       tflags = (1<<dbit1 | 1<<dbit2);
365	+	int             v1, v2;
366	+
367	+	if ((vflags[v0] & tflags) == tflags)    /* is v0 the farthest? */
368	+	return(colval(hp->sa[v0].v,CIEY));
369	+	v1 = adjacent_verti(hp, i, j, dbit1);
370	+	if (vflags[v0] & 1<<dbit2)              /* v1 farthest if v0>v2 */
371	+	return(colval(hp->sa[v1].v,CIEY));
372	+	v2 = adjacent_verti(hp, i, j, dbit2);
373	+	if (vflags[v0] & 1<<dbit1)              /* v2 farthest if v0>v1 */
374	+	return(colval(hp->sa[v2].v,CIEY));
375	+	/* else check if v1>v2 */
376	+	if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2))
377	+	return(colval(hp->sa[v1].v,CIEY));
378	+	return(colval(hp->sa[v2].v,CIEY));
379	+	}
380	+
381	+
382	+	/* Compute vectors and coefficients for Hessian/gradient calcs */
383	+	static void
384	+	comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags)
385	+	{
386	+	const int       i0 = ambndx(hp,i,j);
387	+	double          rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
388	+	int             i1, ii;
389	+
390	+	ftp->valid = 0;                 /* check if we can skip this edge */
391	+	ii = adjacent_trifl[dbit];
392	+	if ((vflags[i0] & ii) == ii)    /* cancels if vertex used as value */
393	+	return;
394	+	i1 = adjacent_verti(hp, i, j, dbit);
395	+	ii = adjacent_trifl[VDB_OPP(dbit)];
396	+	if ((vflags[i1] & ii) == ii)    /* on either end (for both triangles) */
397	+	return;
398	+	/* else go ahead with calculation */
399	+	VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop);
400	+	VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop);
401	+	VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p);
402	+	VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
403	+	rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
404	+	dot_e = DOT(ftp->e_i,ftp->e_i);
405	+	dot_er = DOT(ftp->e_i, ftp->r_i);
406	+	rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
407	+	rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
408	+	ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
409	+	sqrt( rdot_cp );
410	+	ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
411	+	dot_e*ftp->I1 )*0.5*rdot_cp;
412	+	J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
413	+	for (ii = 3; ii--; )
414	+	ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
415	+	ftp->valid++;
416	+	}
417	+
418	+
419	+	/* Compose 3x3 matrix from two vectors */
420	+	static void
421	+	compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
422	+	{
423	+	mat[0][0] = 2.0*va[0]*vb[0];
424	+	mat[1][1] = 2.0*va[1]*vb[1];
425	+	mat[2][2] = 2.0*va[2]*vb[2];
426	+	mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
427	+	mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
428	+	mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
429	+	}
430	+
431	+
432	+	/* Compute partial 3x3 Hessian matrix for edge */
433	+	static void
434	+	comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
435	+	{
436	+	FVECT   ncp;
437	+	FVECT   m1[3], m2[3], m3[3], m4[3];
438	+	double  d1, d2, d3, d4;
439	+	double  I3, J3, K3;
440	+	int     i, j;
441	+
442	+	if (!ftp->valid) {              /* preemptive test */
443	+	memset(hess, 0, sizeof(FVECT)*3);
444	+	return;
445	+	}
446	+	/* compute intermediate coefficients */
447	+	d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
448	+	d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
449	+	d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
450	+	d4 = DOT(ftp->e_i, ftp->r_i);
451	+	I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
452	+	/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
453	+	J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
454	+	K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
455	+	/* intermediate matrices */
456	+	VCROSS(ncp, nrm, ftp->e_i);
457	+	compose_matrix(m1, ncp, ftp->rI2_eJ2);
458	+	compose_matrix(m2, ftp->r_i, ftp->r_i);
459	+	compose_matrix(m3, ftp->e_i, ftp->e_i);
460	+	compose_matrix(m4, ftp->r_i, ftp->e_i);
461	+	d1 = DOT(nrm, ftp->rcp);
462	+	d2 = -d1*ftp->I2;
463	+	d1 *= 2.0;
464	+	for (i = 3; i--; )              /* final matrix sum */
465	+	for (j = 3; j--; ) {
466	+	hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
467	+	2.0*J3*m4[i][j] );
468	+	hess[i][j] += d2*(i==j);
469	+	hess[i][j] *= -1.0/PI;
470	+	}
471	+	}
472	+
473	+
474	+	/* Reverse hessian calculation result for edge in other direction */
475	+	static void
476	+	rev_hessian(FVECT hess[3])
477	+	{
478	+	int     i;
479	+
480	+	for (i = 3; i--; ) {
481	+	hess[i][0] = -hess[i][0];
482	+	hess[i][1] = -hess[i][1];
483	+	hess[i][2] = -hess[i][2];
484	+	}
485	+	}
486	+
487	+
488	+	/* Add to radiometric Hessian from the given triangle */
489	+	static void
490	+	add2hessian(FVECT hess[3], FVECT ehess1[3],
491	+	FVECT ehess2[3], FVECT ehess3[3], double v)
492	+	{
493	+	int     i, j;
494	+
495	+	for (i = 3; i--; )
496	+	for (j = 3; j--; )
497	+	hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
498	+	}
499	+
500	+
501	+	/* Compute partial displacement form factor gradient for edge */
502	+	static void
503	+	comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
504	+	{
505	+	FVECT   ncp;
506	+	double  f1;
507	+	int     i;
508	+
509	+	if (!ftp->valid) {              /* preemptive test */
510	+	memset(grad, 0, sizeof(FVECT));
511	+	return;
512	+	}
513	+	f1 = 2.0*DOT(nrm, ftp->rcp);
514	+	VCROSS(ncp, nrm, ftp->e_i);
515	+	for (i = 3; i--; )
516	+	grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
517	+	}
518	+
519	+
520	+	/* Reverse gradient calculation result for edge in other direction */
521	+	static void
522	+	rev_gradient(FVECT grad)
523	+	{
524	+	grad[0] = -grad[0];
525	+	grad[1] = -grad[1];
526	+	grad[2] = -grad[2];
527	+	}
528	+
529	+
530	+	/* Add to displacement gradient from the given triangle */
531	+	static void
532	+	add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
533	+	{
534	+	int     i;
535	+
536	+	for (i = 3; i--; )
537	+	grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
538	+	}
539	+
540	+
541	+	/* Compute anisotropic radii and eigenvector directions */
542	+	static int
543	+	eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
544	+	{
545	+	double  hess2[2][2];
546	+	FVECT   a, b;
547	+	double  evalue[2], slope1, xmag1;
548	+	int     i;
549	+	/* project Hessian to sample plane */
550	+	for (i = 3; i--; ) {
551	+	a[i] = DOT(hessian[i], uv[0]);
552	+	b[i] = DOT(hessian[i], uv[1]);
553	+	}
554	+	hess2[0][0] = DOT(uv[0], a);
555	+	hess2[0][1] = DOT(uv[0], b);
556	+	hess2[1][0] = DOT(uv[1], a);
557	+	hess2[1][1] = DOT(uv[1], b);
558	+	/* compute eigenvalue(s) */
559	+	i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
560	+	hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
561	+	if (i == 1)                     /* double-root (circle) */
562	+	evalue[1] = evalue[0];
563	+	if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
564	+	((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) )
565	+	error(INTERNAL, "bad eigenvalue calculation");
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	+	/* Make sure radii don't extend beyond what we see in our periphery */
724	+	static int
725	+	hem_radii(AMBHEMI *hp, FVECT uv[2], float ra[2])
726	+	{
727	+	#ifdef AHEM_MARG
728	+	#define MAXDACCUM       47
729	+	const double    hemarg = AHEM_MARG*ambacc;      /* hem margin */
730	+	float           radivisor2[MAXDACCUM+1];
731	+	int             i, j, k = hp->ns/10 + 1;        /* around 5%ile */
732	+	const int       n2accum = (k < MAXDACCUM) ? k : MAXDACCUM ;
733	+	int             na = 0;
734	+	double          d;
735	+	/* circle around perimeter */
736	+	for (i = 0; i < hp->ns; i++)
737	+	for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
738	+	AMBSAMP *ap = &ambsam(hp,i,j);
739	+	double  radiv2 = 0;
740	+	FVECT   vec;
741	+	if (ap->d <= FTINY)
742	+	continue;
743	+	VSUB(vec, ap->p, hp->rp->rop);
744	+	for (k = 2; k--; ) {
745	+	d = ap->d * DOT(vec, uv[k]) * ra[k];
746	+	radiv2 += d*d;
747	+	}
748	+	radiv2 *= hemarg*hemarg * ap->d * ap->d;
749	+	if (radiv2 <= 1.0)
750	+	continue;
751	+	/* insert in percentile list */
752	+	for (k = na; k && radiv2 > radivisor2[k-1]; k--)
753	+	radivisor2[k] = radivisor2[k-1];
754	+	radivisor2[k] = radiv2;
755	+	na += (na < n2accum);
756	+	}
757	+	if (na < n2accum)               /* current radii are OK? */
758	+	return(0);
759	+	/* else apply divisor */
760	+	d = 1.0/sqrt(radivisor2[na-1]);
761	+	ra[0] *= d;
762	+	ra[1] *= d;
763	+	return(1);
764	+	#undef MAXDACCUM
765	+	#else
766	+	return(0);
767	+	#endif
768	+	}
769	+
770	+
771	+	int
772	+	doambient(                              /* compute ambient component */
773	+	COLOR   rcol,                   /* input/output color */
774	+	RAY     *r,
775	+	double  wt,
776	+	FVECT   uv[2],                  /* returned (optional) */
777	+	float   ra[2],                  /* returned (optional) */
778	+	float   pg[2],                  /* returned (optional) */
779	+	float   dg[2]                   /* returned (optional) */
780	+	)
781	+	{
782	+	AMBHEMI *hp = inithemi(rcol, r, wt);
783	+	int     cnt;
784	+	FVECT   my_uv[2];
785	+	double  d, K, acol[3];
786	+	AMBSAMP *ap;
787	+	int     i, j;
788	+	/* check/initialize */
789	+	if (hp == NULL)
790	+	return(0);
791	+	if (uv != NULL)
792	+	memset(uv, 0, sizeof(FVECT)*2);
793	+	if (ra != NULL)
794	+	ra[0] = ra[1] = 0.0;
795	+	if (pg != NULL)
796	+	pg[0] = pg[1] = 0.0;
797	+	if (dg != NULL)
798	+	dg[0] = dg[1] = 0.0;
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 > 0)
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	+	}
834	+	ap = hp->sa;                    /* relative Y channel from here on... */
835	+	for (i = hp->ns*hp->ns; i--; ap++)
836	+	colval(ap->v,CIEY) = bright(ap->v)*d + K;
837	+
838	+	if (uv == NULL)                 /* make sure we have axis pointers */
839	+	uv = my_uv;
840	+	/* compute radii & pos. gradient */
841	+	ambHessian(hp, uv, ra, pg);
842	+
843	+	if (dg != NULL)                 /* compute direction gradient */
844	+	ambdirgrad(hp, uv, dg);
845	+
846	+	if (ra != NULL) {               /* scale/clamp radii */
847	+	if (pg != NULL) {
848	+	if (ra[0]*(d = fabs(pg[0])) > 1.0)
849	+	ra[0] = 1.0/d;
850	+	if (ra[1]*(d = fabs(pg[1])) > 1.0)
851	+	ra[1] = 1.0/d;
852	+	if (ra[0] > ra[1])
853	+	ra[0] = ra[1];
854	+	}
855	+	hem_radii(hp, uv, ra);
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	+	if (pg != NULL) {       /* cap gradient if necessary */
870	+	d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
871	+	if (d > 1.0) {
872	+	d = 1.0/sqrt(d);
873	+	pg[0] *= d;
874	+	pg[1] *= d;
875	+	}
876	+	}
877	+	}
878	+	free(hp);                       /* clean up and return */
879	+	return(1);
880	+	}
881	+
882	+
883	+	#else /* ! NEWAMB */
884	+
885	+
886	+	void
887	+	inithemi(                       /* initialize sampling hemisphere */
888	+	AMBHEMI  *hp,
889	+	COLOR ac,
890	+	RAY  *r,
891	+	double  wt
892	+	)
893	+	{
894	+	double  d;
895	+	int  i;
896	+	/* set number of divisions */
897	+	if (ambacc <= FTINY &&
898	+	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
899	+	wt = d;                 /* avoid ray termination */
900	+	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
901	+	i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
902	+	if (hp->nt < i)
903	+	hp->nt = i;
904	+	hp->np = PI * hp->nt + 0.5;
905	+	/* set number of super-samples */
906	+	hp->ns = ambssamp * wt + 0.5;
907	+	/* assign coefficient */
908	+	copycolor(hp->acoef, ac);
909	+	d = 1.0/(hp->nt*hp->np);
910	+	scalecolor(hp->acoef, d);
911	+	/* make axes */
912	+	VCOPY(hp->uz, r->ron);
913	+	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
914	+	for (i = 0; i < 3; i++)
915	+	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
916	+	break;
917	+	if (i >= 3)
918	+	error(CONSISTENCY, "bad ray direction in inithemi");
919	+	hp->uy[i] = 1.0;
920	+	fcross(hp->ux, hp->uy, hp->uz);
921	+	normalize(hp->ux);
922	+	fcross(hp->uy, hp->uz, hp->ux);
923	+	}
924	+
925	+
926	+	int
927	+	divsample(                              /* sample a division */
928	+	AMBSAMP  *dp,
929	+	AMBHEMI  *h,
930	+	RAY  *r
931	+	)
932	+	{
933		RAY  ar;
934	<	int  hlist[4];
934	>	int  hlist[3];
935	>	double  spt[2];
936		double  xd, yd, zd;
937		double  b2;
938		double  phi;
939	<	register int  i;
940	<
941	<	if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
939	>	int  i;
940	>	/* ambient coefficient for weight */
941	>	if (ambacc > FTINY)
942	>	setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
943	>	else
944	>	copycolor(ar.rcoef, h->acoef);
945	>	if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
946		return(-1);
947	+	if (ambacc > FTINY) {
948	+	multcolor(ar.rcoef, h->acoef);
949	+	scalecolor(ar.rcoef, 1./AVGREFL);
950	+	}
951		hlist[0] = r->rno;
952		hlist[1] = dp->t;
953		hlist[2] = dp->p;
954	<	hlist[3] = 0;
955	<	zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
956	<	hlist[3] = 1;
957	<	phi = 2.0*PI * (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
958	<	xd = cos(phi) * zd;
79	<	yd = sin(phi) * zd;
954	>	multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
955	>	zd = sqrt((dp->t + spt[0])/h->nt);
956	>	phi = 2.0*PI * (dp->p + spt[1])/h->np;
957	>	xd = tcos(phi) * zd;
958	>	yd = tsin(phi) * zd;
959		zd = sqrt(1.0 - zd*zd);
960		for (i = 0; i < 3; i++)
961		ar.rdir[i] =    xd*h->ux[i] +
962		yd*h->uy[i] +
963		zd*h->uz[i];
964	+	checknorm(ar.rdir);
965		dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
966		rayvalue(&ar);
967		ndims--;
968	+	multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
969		addcolor(dp->v, ar.rcol);
970	<	if (ar.rt < FHUGE)
970	>	/* use rt to improve gradient calc */
971	>	if (ar.rt > FTINY && ar.rt < FHUGE)
972		dp->r += 1.0/ar.rt;
973		/* (re)initialize error */
974		if (dp->n++) {
#	Line 99 | Line 981 | RAY  *r;
981		}
982
983
984	+	static int
985	+	ambcmp(                                 /* decreasing order */
986	+	const void *p1,
987	+	const void *p2
988	+	)
989	+	{
990	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
991	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
992	+
993	+	if (d1->k < d2->k)
994	+	return(1);
995	+	if (d1->k > d2->k)
996	+	return(-1);
997	+	return(0);
998	+	}
999	+
1000	+
1001	+	static int
1002	+	ambnorm(                                /* standard order */
1003	+	const void *p1,
1004	+	const void *p2
1005	+	)
1006	+	{
1007	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
1008	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
1009	+	int     c;
1010	+
1011	+	if ( (c = d1->t - d2->t) )
1012	+	return(c);
1013	+	return(d1->p - d2->p);
1014	+	}
1015	+
1016	+
1017		double
1018	<	doambient(acol, r, pg, dg)              /* compute ambient component */
1019	<	COLOR  acol;
1020	<	RAY  *r;
1021	<	FVECT  pg, dg;
1018	>	doambient(                              /* compute ambient component */
1019	>	COLOR  rcol,
1020	>	RAY  *r,
1021	>	double  wt,
1022	>	FVECT  pg,
1023	>	FVECT  dg
1024	>	)
1025		{
1026	<	double  b, d;
1026	>	double  b, d=0;
1027		AMBHEMI  hemi;
1028		AMBSAMP  *div;
1029		AMBSAMP  dnew;
1030	<	register AMBSAMP  *dp;
1030	>	double  acol[3];
1031	>	AMBSAMP  *dp;
1032		double  arad;
1033	<	int  ndivs, ns;
1034	<	register int  i, j;
116	<	/* initialize color */
117	<	setcolor(acol, 0.0, 0.0, 0.0);
1033	>	int  divcnt;
1034	>	int  i, j;
1035		/* initialize hemisphere */
1036	<	inithemi(&hemi, r);
1037	<	ndivs = hemi.nt * hemi.np;
1038	<	if (ndivs == 0)
1036	>	inithemi(&hemi, rcol, r, wt);
1037	>	divcnt = hemi.nt * hemi.np;
1038	>	/* initialize */
1039	>	if (pg != NULL)
1040	>	pg[0] = pg[1] = pg[2] = 0.0;
1041	>	if (dg != NULL)
1042	>	dg[0] = dg[1] = dg[2] = 0.0;
1043	>	setcolor(rcol, 0.0, 0.0, 0.0);
1044	>	if (divcnt == 0)
1045		return(0.0);
1046	<	/* set number of super-samples */
1047	<	ns = ambssamp * r->rweight + 0.5;
1048	<	if (ns > 0 || pg != NULL || dg != NULL) {
126	<	div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
1046	>	/* allocate super-samples */
1047	>	if (hemi.ns > 0 || pg != NULL || dg != NULL) {
1048	>	div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP));
1049		if (div == NULL)
1050		error(SYSTEM, "out of memory in doambient");
1051		} else
1052		div = NULL;
1053		/* sample the divisions */
1054		arad = 0.0;
1055	+	acol[0] = acol[1] = acol[2] = 0.0;
1056		if ((dp = div) == NULL)
1057		dp = &dnew;
1058	+	divcnt = 0;
1059		for (i = 0; i < hemi.nt; i++)
1060		for (j = 0; j < hemi.np; j++) {
1061		dp->t = i; dp->p = j;
1062		setcolor(dp->v, 0.0, 0.0, 0.0);
1063		dp->r = 0.0;
1064		dp->n = 0;
1065	<	if (divsample(dp, &hemi, r) < 0)
1066	<	goto oopsy;
1065	>	if (divsample(dp, &hemi, r) < 0) {
1066	>	if (div != NULL)
1067	>	dp++;
1068	>	continue;
1069	>	}
1070	>	arad += dp->r;
1071	>	divcnt++;
1072		if (div != NULL)
1073		dp++;
1074	<	else {
1074	>	else
1075		addcolor(acol, dp->v);
147	–	arad += dp->r;
148	–	}
1076		}
1077	<	if (ns > 0) {                   /* perform super-sampling */
1077	>	if (!divcnt) {
1078	>	if (div != NULL)
1079	>	free((void *)div);
1080	>	return(0.0);            /* no samples taken */
1081	>	}
1082	>	if (divcnt < hemi.nt*hemi.np) {
1083	>	pg = dg = NULL;         /* incomplete sampling */
1084	>	hemi.ns = 0;
1085	>	} else if (arad > FTINY && divcnt/arad < minarad) {
1086	>	hemi.ns = 0;            /* close enough */
1087	>	} else if (hemi.ns > 0) {       /* else perform super-sampling? */
1088		comperrs(div, &hemi);                   /* compute errors */
1089	<	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
1089	>	qsort(div, divcnt, sizeof(AMBSAMP), ambcmp);    /* sort divs */
1090		/* super-sample */
1091	<	for (i = ns; i > 0; i--) {
1092	<	copystruct(&dnew, div);
1093	<	if (divsample(&dnew, &hemi, r) < 0)
1094	<	goto oopsy;
1095	<	/* reinsert */
1096	<	dp = div;
1097	<	j = ndivs < i ? ndivs : i;
1091	>	for (i = hemi.ns; i > 0; i--) {
1092	>	dnew = *div;
1093	>	if (divsample(&dnew, &hemi, r) < 0) {
1094	>	dp++;
1095	>	continue;
1096	>	}
1097	>	dp = div;               /* reinsert */
1098	>	j = divcnt < i ? divcnt : i;
1099		while (--j > 0 && dnew.k < dp[1].k) {
1100	<	copystruct(dp, dp+1);
1100	>	*dp = *(dp+1);
1101		dp++;
1102		}
1103	<	copystruct(dp, &dnew);
1103	>	*dp = dnew;
1104		}
1105		if (pg != NULL || dg != NULL)   /* restore order */
1106	<	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
1106	>	qsort(div, divcnt, sizeof(AMBSAMP), ambnorm);
1107		}
1108		/* compute returned values */
1109		if (div != NULL) {
1110	<	for (i = ndivs, dp = div; i-- > 0; dp++) {
1110	>	arad = 0.0;             /* note: divcnt may be < nt*np */
1111	>	for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) {
1112		arad += dp->r;
1113		if (dp->n > 1) {
1114		b = 1.0/dp->n;
#	Line 181 | Line 1120 | FVECT  pg, dg;
1120		}
1121		b = bright(acol);
1122		if (b > FTINY) {
1123	<	b = ndivs/b;
1123	>	b = 1.0/b;      /* compute & normalize gradient(s) */
1124		if (pg != NULL) {
1125		posgradient(pg, div, &hemi);
1126		for (i = 0; i < 3; i++)
#	Line 192 | Line 1131 | FVECT  pg, dg;
1131		for (i = 0; i < 3; i++)
1132		dg[i] *= b;
1133		}
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;
1134		}
1135	<	free((char *)div);
1135	>	free((void *)div);
1136		}
1137	<	b = 1.0/ndivs;
206	<	scalecolor(acol, b);
1137	>	copycolor(rcol, acol);
1138		if (arad <= FTINY)
208	–	arad = FHUGE;
209	–	else
210	–	arad = (ndivs+ns)/arad;
211	–	if (arad > maxarad)
1139		arad = maxarad;
1140	<	else if (arad < minarad)
1140	>	else
1141	>	arad = (divcnt+hemi.ns)/arad;
1142	>	if (pg != NULL) {               /* reduce radius if gradient large */
1143	>	d = DOT(pg,pg);
1144	>	if (d*arad*arad > 1.0)
1145	>	arad = 1.0/sqrt(d);
1146	>	}
1147	>	if (arad < minarad) {
1148		arad = minarad;
1149	<	arad /= sqrt(r->rweight);
1150	<	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);
1149	>	if (pg != NULL && d*arad*arad > 1.0) {  /* cap gradient */
1150	>	d = 1.0/arad/sqrt(d);
1151		for (i = 0; i < 3; i++)
1152		pg[i] *= d;
1153		}
1154		}
1155	+	if ((arad /= sqrt(wt)) > maxarad)
1156	+	arad = maxarad;
1157		return(arad);
225	–	oopsy:
226	–	if (div != NULL)
227	–	free((char *)div);
228	–	return(0.0);
1158		}
1159
1160
1161	<	inithemi(hp, r)                 /* initialize sampling hemisphere */
1162	<	register AMBHEMI  *hp;
1163	<	RAY  *r;
1161	>	void
1162	>	comperrs(                       /* compute initial error estimates */
1163	>	AMBSAMP  *da,   /* assumes standard ordering */
1164	>	AMBHEMI  *hp
1165	>	)
1166		{
236	–	register int  i;
237	–	/* set number of divisions */
238	–	hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
239	–	hp->np = 2 * hp->nt;
240	–	/* make axes */
241	–	VCOPY(hp->uz, r->ron);
242	–	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
243	–	for (i = 0; i < 3; i++)
244	–	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
245	–	break;
246	–	if (i >= 3)
247	–	error(CONSISTENCY, "bad ray direction in inithemi");
248	–	hp->uy[i] = 1.0;
249	–	fcross(hp->ux, hp->uy, hp->uz);
250	–	normalize(hp->ux);
251	–	fcross(hp->uy, hp->uz, hp->ux);
252	–	}
253	–
254	–
255	–	comperrs(da, hp)                /* compute initial error estimates */
256	–	AMBSAMP  *da;           /* assumes standard ordering */
257	–	register AMBHEMI  *hp;
258	–	{
1167		double  b, b2;
1168		int  i, j;
1169	<	register AMBSAMP  *dp;
1169	>	AMBSAMP  *dp;
1170		/* sum differences from neighbors */
1171		dp = da;
1172		for (i = 0; i < hp->nt; i++)
#	Line 302 | Line 1210 | register AMBHEMI  *hp;
1210		}
1211
1212
1213	<	posgradient(gv, da, hp)                         /* compute position gradient */
1214	<	FVECT  gv;
1215	<	AMBSAMP  *da;                   /* assumes standard ordering */
1216	<	AMBHEMI  *hp;
1213	>	void
1214	>	posgradient(                                    /* compute position gradient */
1215	>	FVECT  gv,
1216	>	AMBSAMP  *da,                   /* assumes standard ordering */
1217	>	AMBHEMI  *hp
1218	>	)
1219		{
1220	<	register int  i, j;
1221	<	double  b, d;
1220	>	int  i, j;
1221	>	double  nextsine, lastsine, b, d;
1222		double  mag0, mag1;
1223		double  phi, cosp, sinp, xd, yd;
1224	<	register AMBSAMP  *dp;
1224	>	AMBSAMP  *dp;
1225
1226		xd = yd = 0.0;
1227		for (j = 0; j < hp->np; j++) {
1228		dp = da + j;
1229		mag0 = mag1 = 0.0;
1230	+	lastsine = 0.0;
1231		for (i = 0; i < hp->nt; i++) {
1232		#ifdef  DEBUG
1233		if (dp->t != i || dp->p != j)
#	Line 327 | Line 1238 | AMBHEMI  *hp;
1238		if (i > 0) {
1239		d = dp[-hp->np].r;
1240		if (dp[0].r > d) d = dp[0].r;
1241	<	d *= 1.0 - sqrt((double)i/hp->nt);
1241	>	/* sin(t)*cos(t)^2 */
1242	>	d *= lastsine * (1.0 - (double)i/hp->nt);
1243		mag0 += d*(b - bright(dp[-hp->np].v));
1244		}
1245	+	nextsine = sqrt((double)(i+1)/hp->nt);
1246		if (j > 0) {
1247		d = dp[-1].r;
1248		if (dp[0].r > d) d = dp[0].r;
1249	<	mag1 += d*(b - bright(dp[-1].v));
1249	>	mag1 += d * (nextsine - lastsine) *
1250	>	(b - bright(dp[-1].v));
1251		} else {
1252		d = dp[hp->np-1].r;
1253		if (dp[0].r > d) d = dp[0].r;
1254	<	mag1 += d*(b - bright(dp[hp->np-1].v));
1254	>	mag1 += d * (nextsine - lastsine) *
1255	>	(b - bright(dp[hp->np-1].v));
1256		}
1257		dp += hp->np;
1258	+	lastsine = nextsine;
1259		}
1260	<	if (hp->nt > 1) {
345	<	mag0 /= (double)hp->np;
346	<	mag1 /= (double)hp->nt;
347	<	}
1260	>	mag0 *= 2.0*PI / hp->np;
1261		phi = 2.0*PI * (double)j/hp->np;
1262	<	cosp = cos(phi); sinp = sin(phi);
1262	>	cosp = tcos(phi); sinp = tsin(phi);
1263		xd += mag0*cosp - mag1*sinp;
1264		yd += mag0*sinp + mag1*cosp;
1265		}
1266		for (i = 0; i < 3; i++)
1267	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/PI;
1267	>	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI;
1268		}
1269
1270
1271	<	dirgradient(gv, da, hp)                         /* compute direction gradient */
1272	<	FVECT  gv;
1273	<	AMBSAMP  *da;                   /* assumes standard ordering */
1274	<	AMBHEMI  *hp;
1271	>	void
1272	>	dirgradient(                                    /* compute direction gradient */
1273	>	FVECT  gv,
1274	>	AMBSAMP  *da,                   /* assumes standard ordering */
1275	>	AMBHEMI  *hp
1276	>	)
1277		{
1278	<	register int  i, j;
1278	>	int  i, j;
1279		double  mag;
1280		double  phi, xd, yd;
1281	<	register AMBSAMP  *dp;
1281	>	AMBSAMP  *dp;
1282
1283		xd = yd = 0.0;
1284		for (j = 0; j < hp->np; j++) {
#	Line 375 | Line 1290 | AMBHEMI  *hp;
1290		error(CONSISTENCY,
1291		"division order in dirgradient");
1292		#endif
1293	<	mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
1293	>	/* tan(t) */
1294	>	mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
1295		dp += hp->np;
1296		}
1297		phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
1298	<	xd += mag * cos(phi);
1299	<	yd += mag * sin(phi);
1298	>	xd += mag * tcos(phi);
1299	>	yd += mag * tsin(phi);
1300		}
1301		for (i = 0; i < 3; i++)
1302	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*PI/(hp->nt*hp->np);
1302	>	gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
1303		}
1304	+
1305	+	#endif  /* ! NEWAMB */

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