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

Comparing ray/src/rt/ambcomp.c (file contents):
Revision 1.6 by greg, Thu Jun 13 10:54:00 1991 UTC vs.
Revision 2.49 by greg, Wed May 7 01:16:02 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(INTERNAL, "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 *)calloc(hp->ns*hp->ns, sizeof(float));
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	+	b = bright(ap[0].v);
240	+	if (i) {                /* from above */
241	+	d2 = b - bright(ap[-hp->ns].v);
242	+	d2 *= d2;
243	+	ep[0] += d2;
244	+	ep[-hp->ns] += d2;
245	+	}
246	+	if (j) {                /* from behind */
247	+	d2 = b - bright(ap[-1].v);
248	+	d2 *= d2;
249	+	ep[0] += d2;
250	+	ep[-1] += d2;
251	+	}
252	+	}
253	+	/* correct for number of neighbors */
254	+	earr[0] *= 2.f;
255	+	earr[hp->ns-1] *= 2.f;
256	+	earr[(hp->ns-1)*hp->ns] *= 2.f;
257	+	earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f;
258	+	for (i = 1; i < hp->ns-1; i++) {
259	+	earr[i*hp->ns] *= 4./3.;
260	+	earr[i*hp->ns + hp->ns-1] *= 4./3.;
261	+	}
262	+	for (j = 1; j < hp->ns-1; j++) {
263	+	earr[j] *= 4./3.;
264	+	earr[(hp->ns-1)*hp->ns + j] *= 4./3.;
265	+	}
266	+	return(earr);
267	+	}
268	+
269	+
270	+	/* Perform super-sampling on hemisphere (introduces bias) */
271	+	static void
272	+	ambsupersamp(double acol[3], AMBHEMI *hp, int cnt)
273	+	{
274	+	float   *earr = getambdiffs(hp);
275	+	double  e2sum = 0;
276	+	AMBSAMP *ap;
277	+	RAY     ar;
278	+	COLOR   asum;
279	+	float   *ep;
280	+	int     i, j, n;
281	+
282	+	if (earr == NULL)               /* just skip calc. if no memory */
283	+	return;
284	+	/* add up estimated variances */
285	+	for (ep = earr + hp->ns*hp->ns; ep-- > earr; )
286	+	e2sum += *ep;
287	+	ep = earr;                      /* perform super-sampling */
288	+	for (ap = hp->sa, i = 0; i < hp->ns; i++)
289	+	for (j = 0; j < hp->ns; j++, ap++) {
290	+	int     nss = *ep/e2sum*cnt + frandom();
291	+	setcolor(asum, 0., 0., 0.);
292	+	for (n = 1; n <= nss; n++) {
293	+	if (!getambsamp(&ar, hp, i, j, n)) {
294	+	nss = n-1;
295	+	break;
296	+	}
297	+	addcolor(asum, ar.rcol);
298	+	}
299	+	if (nss) {              /* update returned ambient value */
300	+	const double    ssf = 1./(nss + 1);
301	+	for (n = 3; n--; )
302	+	acol[n] += ssf*colval(asum,n) +
303	+	(ssf - 1.)*colval(ap->v,n);
304	+	}
305	+	e2sum -= *ep++;         /* update remainders */
306	+	cnt -= nss;
307	+	}
308	+	free(earr);
309	+	}
310	+
311	+
312	+	/* Compute vertex flags, indicating farthest in each direction */
313	+	static uby8 *
314	+	vertex_flags(AMBHEMI *hp)
315	+	{
316	+	uby8    *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8));
317	+	uby8    *vf;
318	+	AMBSAMP *ap;
319	+	int     i, j;
320	+
321	+	if (vflags == NULL)
322	+	error(SYSTEM, "out of memory in vertex_flags()");
323	+	vf = vflags;
324	+	ap = hp->sa;            /* compute farthest along first row */
325	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++)
326	+	if (ap[0].d <= ap[1].d)
327	+	vf[0] |= 1<<VDB_X;
328	+	else
329	+	vf[1] |= 1<<VDB_x;
330	+	++vf; ++ap;
331	+	/* flag subsequent rows */
332	+	for (i = 1; i < hp->ns; i++) {
333	+	for (j = 0; j < hp->ns-1; j++, vf++, ap++) {
334	+	if (ap[0].d <= ap[-hp->ns].d)   /* row before */
335	+	vf[0] |= 1<<VDB_y;
336	+	else
337	+	vf[-hp->ns] |= 1<<VDB_Y;
338	+	if (ap[0].d <= ap[1-hp->ns].d)  /* diagonal we care about */
339	+	vf[0] |= 1<<VDB_Xy;
340	+	else
341	+	vf[1-hp->ns] |= 1<<VDB_xY;
342	+	if (ap[0].d <= ap[1].d)         /* column after */
343	+	vf[0] |= 1<<VDB_X;
344	+	else
345	+	vf[1] |= 1<<VDB_x;
346	+	}
347	+	if (ap[0].d <= ap[-hp->ns].d)       /* final column edge */
348	+	vf[0] |= 1<<VDB_y;
349	+	else
350	+	vf[-hp->ns] |= 1<<VDB_Y;
351	+	++vf; ++ap;
352	+	}
353	+	return(vflags);
354	+	}
355	+
356	+
357	+	/* Return brightness of farthest ambient sample */
358	+	static double
359	+	back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags)
360	+	{
361	+	const int       v0 = ambndx(hp,i,j);
362	+	const int       tflags = (1<<dbit1 | 1<<dbit2);
363	+	int             v1, v2;
364	+
365	+	if ((vflags[v0] & tflags) == tflags)    /* is v0 the farthest? */
366	+	return(colval(hp->sa[v0].v,CIEY));
367	+	v1 = adjacent_verti(hp, i, j, dbit1);
368	+	if (vflags[v0] & 1<<dbit2)              /* v1 farthest if v0>v2 */
369	+	return(colval(hp->sa[v1].v,CIEY));
370	+	v2 = adjacent_verti(hp, i, j, dbit2);
371	+	if (vflags[v0] & 1<<dbit1)              /* v2 farthest if v0>v1 */
372	+	return(colval(hp->sa[v2].v,CIEY));
373	+	/* else check if v1>v2 */
374	+	if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2))
375	+	return(colval(hp->sa[v1].v,CIEY));
376	+	return(colval(hp->sa[v2].v,CIEY));
377	+	}
378	+
379	+
380	+	/* Compute vectors and coefficients for Hessian/gradient calcs */
381	+	static void
382	+	comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags)
383	+	{
384	+	const int       i0 = ambndx(hp,i,j);
385	+	double          rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
386	+	int             i1, ii;
387	+
388	+	ftp->valid = 0;                 /* check if we can skip this edge */
389	+	ii = adjacent_trifl[dbit];
390	+	if ((vflags[i0] & ii) == ii)    /* cancels if vertex used as value */
391	+	return;
392	+	i1 = adjacent_verti(hp, i, j, dbit);
393	+	ii = adjacent_trifl[VDB_OPP(dbit)];
394	+	if ((vflags[i1] & ii) == ii)    /* on either end (for both triangles) */
395	+	return;
396	+	/* else go ahead with calculation */
397	+	VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop);
398	+	VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop);
399	+	VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p);
400	+	VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
401	+	rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
402	+	dot_e = DOT(ftp->e_i,ftp->e_i);
403	+	dot_er = DOT(ftp->e_i, ftp->r_i);
404	+	rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
405	+	rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
406	+	ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
407	+	sqrt( rdot_cp );
408	+	ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
409	+	dot_e*ftp->I1 )*0.5*rdot_cp;
410	+	J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
411	+	for (ii = 3; ii--; )
412	+	ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
413	+	ftp->valid++;
414	+	}
415	+
416	+
417	+	/* Compose 3x3 matrix from two vectors */
418	+	static void
419	+	compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
420	+	{
421	+	mat[0][0] = 2.0*va[0]*vb[0];
422	+	mat[1][1] = 2.0*va[1]*vb[1];
423	+	mat[2][2] = 2.0*va[2]*vb[2];
424	+	mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
425	+	mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
426	+	mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
427	+	}
428	+
429	+
430	+	/* Compute partial 3x3 Hessian matrix for edge */
431	+	static void
432	+	comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
433	+	{
434	+	FVECT   ncp;
435	+	FVECT   m1[3], m2[3], m3[3], m4[3];
436	+	double  d1, d2, d3, d4;
437	+	double  I3, J3, K3;
438	+	int     i, j;
439	+
440	+	if (!ftp->valid) {              /* preemptive test */
441	+	memset(hess, 0, sizeof(FVECT)*3);
442	+	return;
443	+	}
444	+	/* compute intermediate coefficients */
445	+	d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
446	+	d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
447	+	d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
448	+	d4 = DOT(ftp->e_i, ftp->r_i);
449	+	I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
450	+	/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
451	+	J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
452	+	K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
453	+	/* intermediate matrices */
454	+	VCROSS(ncp, nrm, ftp->e_i);
455	+	compose_matrix(m1, ncp, ftp->rI2_eJ2);
456	+	compose_matrix(m2, ftp->r_i, ftp->r_i);
457	+	compose_matrix(m3, ftp->e_i, ftp->e_i);
458	+	compose_matrix(m4, ftp->r_i, ftp->e_i);
459	+	d1 = DOT(nrm, ftp->rcp);
460	+	d2 = -d1*ftp->I2;
461	+	d1 *= 2.0;
462	+	for (i = 3; i--; )              /* final matrix sum */
463	+	for (j = 3; j--; ) {
464	+	hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
465	+	2.0*J3*m4[i][j] );
466	+	hess[i][j] += d2*(i==j);
467	+	hess[i][j] *= -1.0/PI;
468	+	}
469	+	}
470	+
471	+
472	+	/* Reverse hessian calculation result for edge in other direction */
473	+	static void
474	+	rev_hessian(FVECT hess[3])
475	+	{
476	+	int     i;
477	+
478	+	for (i = 3; i--; ) {
479	+	hess[i][0] = -hess[i][0];
480	+	hess[i][1] = -hess[i][1];
481	+	hess[i][2] = -hess[i][2];
482	+	}
483	+	}
484	+
485	+
486	+	/* Add to radiometric Hessian from the given triangle */
487	+	static void
488	+	add2hessian(FVECT hess[3], FVECT ehess1[3],
489	+	FVECT ehess2[3], FVECT ehess3[3], double v)
490	+	{
491	+	int     i, j;
492	+
493	+	for (i = 3; i--; )
494	+	for (j = 3; j--; )
495	+	hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
496	+	}
497	+
498	+
499	+	/* Compute partial displacement form factor gradient for edge */
500	+	static void
501	+	comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
502	+	{
503	+	FVECT   ncp;
504	+	double  f1;
505	+	int     i;
506	+
507	+	if (!ftp->valid) {              /* preemptive test */
508	+	memset(grad, 0, sizeof(FVECT));
509	+	return;
510	+	}
511	+	f1 = 2.0*DOT(nrm, ftp->rcp);
512	+	VCROSS(ncp, nrm, ftp->e_i);
513	+	for (i = 3; i--; )
514	+	grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
515	+	}
516	+
517	+
518	+	/* Reverse gradient calculation result for edge in other direction */
519	+	static void
520	+	rev_gradient(FVECT grad)
521	+	{
522	+	grad[0] = -grad[0];
523	+	grad[1] = -grad[1];
524	+	grad[2] = -grad[2];
525	+	}
526	+
527	+
528	+	/* Add to displacement gradient from the given triangle */
529	+	static void
530	+	add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
531	+	{
532	+	int     i;
533	+
534	+	for (i = 3; i--; )
535	+	grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
536	+	}
537	+
538	+
539	+	/* Compute anisotropic radii and eigenvector directions */
540	+	static int
541	+	eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
542	+	{
543	+	double  hess2[2][2];
544	+	FVECT   a, b;
545	+	double  evalue[2], slope1, xmag1;
546	+	int     i;
547	+	/* project Hessian to sample plane */
548	+	for (i = 3; i--; ) {
549	+	a[i] = DOT(hessian[i], uv[0]);
550	+	b[i] = DOT(hessian[i], uv[1]);
551	+	}
552	+	hess2[0][0] = DOT(uv[0], a);
553	+	hess2[0][1] = DOT(uv[0], b);
554	+	hess2[1][0] = DOT(uv[1], a);
555	+	hess2[1][1] = DOT(uv[1], b);
556	+	/* compute eigenvalue(s) */
557	+	i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
558	+	hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
559	+	if (i == 1)                     /* double-root (circle) */
560	+	evalue[1] = evalue[0];
561	+	if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
562	+	((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) )
563	+	error(INTERNAL, "bad eigenvalue calculation");
564	+
565	+	if (evalue[0] > evalue[1]) {
566	+	ra[0] = sqrt(sqrt(4.0/evalue[0]));
567	+	ra[1] = sqrt(sqrt(4.0/evalue[1]));
568	+	slope1 = evalue[1];
569	+	} else {
570	+	ra[0] = sqrt(sqrt(4.0/evalue[1]));
571	+	ra[1] = sqrt(sqrt(4.0/evalue[0]));
572	+	slope1 = evalue[0];
573	+	}
574	+	/* compute unit eigenvectors */
575	+	if (fabs(hess2[0][1]) <= FTINY)
576	+	return;                 /* uv OK as is */
577	+	slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
578	+	xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
579	+	for (i = 3; i--; ) {
580	+	b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
581	+	a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
582	+	}
583	+	VCOPY(uv[0], a);
584	+	VCOPY(uv[1], b);
585	+	}
586	+
587	+
588	+	static void
589	+	ambHessian(                             /* anisotropic radii & pos. gradient */
590	+	AMBHEMI *hp,
591	+	FVECT   uv[2],                  /* returned */
592	+	float   ra[2],                  /* returned (optional) */
593	+	float   pg[2]                   /* returned (optional) */
594	+	)
595	+	{
596	+	static char     memerrmsg[] = "out of memory in ambHessian()";
597	+	FVECT           (*hessrow)[3] = NULL;
598	+	FVECT           *gradrow = NULL;
599	+	uby8            *vflags;
600	+	FVECT           hessian[3];
601	+	FVECT           gradient;
602	+	FFTRI           fftr;
603	+	int             i, j;
604	+	/* be sure to assign unit vectors */
605	+	VCOPY(uv[0], hp->ux);
606	+	VCOPY(uv[1], hp->uy);
607	+	/* clock-wise vertex traversal from sample POV */
608	+	if (ra != NULL) {               /* initialize Hessian row buffer */
609	+	hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
610	+	if (hessrow == NULL)
611	+	error(SYSTEM, memerrmsg);
612	+	memset(hessian, 0, sizeof(hessian));
613	+	} else if (pg == NULL)          /* bogus call? */
614	+	return;
615	+	if (pg != NULL) {               /* initialize form factor row buffer */
616	+	gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
617	+	if (gradrow == NULL)
618	+	error(SYSTEM, memerrmsg);
619	+	memset(gradient, 0, sizeof(gradient));
620	+	}
621	+	/* get vertex position flags */
622	+	vflags = vertex_flags(hp);
623	+	/* compute first row of edges */
624	+	for (j = 0; j < hp->ns-1; j++) {
625	+	comp_fftri(&fftr, hp, 0, j, VDB_X, vflags);
626	+	if (hessrow != NULL)
627	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
628	+	if (gradrow != NULL)
629	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
630	+	}
631	+	/* sum each row of triangles */
632	+	for (i = 0; i < hp->ns-1; i++) {
633	+	FVECT       hesscol[3];     /* compute first vertical edge */
634	+	FVECT       gradcol;
635	+	comp_fftri(&fftr, hp, i, 0, VDB_Y, vflags);
636	+	if (hessrow != NULL)
637	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
638	+	if (gradrow != NULL)
639	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
640	+	for (j = 0; j < hp->ns-1; j++) {
641	+	FVECT   hessdia[3];     /* compute triangle contributions */
642	+	FVECT   graddia;
643	+	double  backg;
644	+	backg = back_ambval(hp, i, j, VDB_X, VDB_Y, vflags);
645	+	/* diagonal (inner) edge */
646	+	comp_fftri(&fftr, hp, i, j+1, VDB_xY, vflags);
647	+	if (hessrow != NULL) {
648	+	comp_hessian(hessdia, &fftr, hp->rp->ron);
649	+	rev_hessian(hesscol);
650	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
651	+	}
652	+	if (gradrow != NULL) {
653	+	comp_gradient(graddia, &fftr, hp->rp->ron);
654	+	rev_gradient(gradcol);
655	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
656	+	}
657	+	/* initialize edge in next row */
658	+	comp_fftri(&fftr, hp, i+1, j+1, VDB_x, vflags);
659	+	if (hessrow != NULL)
660	+	comp_hessian(hessrow[j], &fftr, hp->rp->ron);
661	+	if (gradrow != NULL)
662	+	comp_gradient(gradrow[j], &fftr, hp->rp->ron);
663	+	/* new column edge & paired triangle */
664	+	backg = back_ambval(hp, i+1, j+1, VDB_x, VDB_y, vflags);
665	+	comp_fftri(&fftr, hp, i, j+1, VDB_Y, vflags);
666	+	if (hessrow != NULL) {
667	+	comp_hessian(hesscol, &fftr, hp->rp->ron);
668	+	rev_hessian(hessdia);
669	+	add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
670	+	if (i < hp->ns-2)
671	+	rev_hessian(hessrow[j]);
672	+	}
673	+	if (gradrow != NULL) {
674	+	comp_gradient(gradcol, &fftr, hp->rp->ron);
675	+	rev_gradient(graddia);
676	+	add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
677	+	if (i < hp->ns-2)
678	+	rev_gradient(gradrow[j]);
679	+	}
680	+	}
681	+	}
682	+	/* release row buffers */
683	+	if (hessrow != NULL) free(hessrow);
684	+	if (gradrow != NULL) free(gradrow);
685	+	free(vflags);
686	+
687	+	if (ra != NULL)                 /* extract eigenvectors & radii */
688	+	eigenvectors(uv, ra, hessian);
689	+	if (pg != NULL) {               /* tangential position gradient */
690	+	pg[0] = DOT(gradient, uv[0]);
691	+	pg[1] = DOT(gradient, uv[1]);
692	+	}
693	+	}
694	+
695	+
696	+	/* Compute direction gradient from a hemispherical sampling */
697	+	static void
698	+	ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
699	+	{
700	+	AMBSAMP *ap;
701	+	double  dgsum[2];
702	+	int     n;
703	+	FVECT   vd;
704	+	double  gfact;
705	+
706	+	dgsum[0] = dgsum[1] = 0.0;      /* sum values times -tan(theta) */
707	+	for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
708	+	/* use vector for azimuth + 90deg */
709	+	VSUB(vd, ap->p, hp->rp->rop);
710	+	/* brightness over cosine factor */
711	+	gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
712	+	/* sine = proj_radius/vd_length */
713	+	dgsum[0] -= DOT(uv[1], vd) * gfact;
714	+	dgsum[1] += DOT(uv[0], vd) * gfact;
715	+	}
716	+	dg[0] = dgsum[0] / (hp->ns*hp->ns);
717	+	dg[1] = dgsum[1] / (hp->ns*hp->ns);
718	+	}
719	+
720	+
721	+	/* Compute potential light leak direction flags for cache value */
722	+	static uint32
723	+	ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
724	+	{
725	+	uint32  flgs = 0;
726	+	int     i, j;
727	+	/* circle around perimeter */
728	+	for (i = 0; i < hp->ns; i++)
729	+	for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
730	+	AMBSAMP *ap = &ambsam(hp,i,j);
731	+	FVECT   vec;
732	+	double  u, v;
733	+	double  ang;
734	+	int     abp;
735	+	if (ap->d <= FTINY)
736	+	continue;
737	+	VSUB(vec, ap->p, hp->rp->rop);
738	+	u = DOT(vec, uv[0]) * ap->d;
739	+	v = DOT(vec, uv[1]) * ap->d;
740	+	if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= 1.0)
741	+	continue;       /* occluder outside ellipse */
742	+	ang = atan2a(v, u);     /* else set direction flags */
743	+	ang += 2.0*PI*(ang < 0);
744	+	ang *= 16./PI;
745	+	if ((ang < .5) | (ang >= 31.5))
746	+	flgs |= 0x80000001;
747	+	else
748	+	flgs |= 3L<<(int)(ang-.5);
749	+	}
750	+	return(flgs);
751	+	}
752	+
753	+
754	+	int
755	+	doambient(                              /* compute ambient component */
756	+	COLOR   rcol,                   /* input/output color */
757	+	RAY     *r,
758	+	double  wt,
759	+	FVECT   uv[2],                  /* returned (optional) */
760	+	float   ra[2],                  /* returned (optional) */
761	+	float   pg[2],                  /* returned (optional) */
762	+	float   dg[2],                  /* returned (optional) */
763	+	uint32  *crlp                   /* returned (optional) */
764	+	)
765	+	{
766	+	AMBHEMI *hp = inithemi(rcol, r, wt);
767	+	int     cnt;
768	+	FVECT   my_uv[2];
769	+	double  d, K, acol[3];
770	+	AMBSAMP *ap;
771	+	int     i, j;
772	+	/* check/initialize */
773	+	if (hp == NULL)
774	+	return(0);
775	+	if (uv != NULL)
776	+	memset(uv, 0, sizeof(FVECT)*2);
777	+	if (ra != NULL)
778	+	ra[0] = ra[1] = 0.0;
779	+	if (pg != NULL)
780	+	pg[0] = pg[1] = 0.0;
781	+	if (dg != NULL)
782	+	dg[0] = dg[1] = 0.0;
783	+	if (crlp != NULL)
784	+	*crlp = 0;
785	+	/* sample the hemisphere */
786	+	acol[0] = acol[1] = acol[2] = 0.0;
787	+	cnt = 0;
788	+	for (i = hp->ns; i--; )
789	+	for (j = hp->ns; j--; )
790	+	if ((ap = ambsample(hp, i, j)) != NULL) {
791	+	addcolor(acol, ap->v);
792	+	++cnt;
793	+	}
794	+	if (!cnt) {
795	+	setcolor(rcol, 0.0, 0.0, 0.0);
796	+	free(hp);
797	+	return(0);              /* no valid samples */
798	+	}
799	+	if (cnt < hp->ns*hp->ns) {      /* incomplete sampling? */
800	+	copycolor(rcol, acol);
801	+	free(hp);
802	+	return(-1);             /* return value w/o Hessian */
803	+	}
804	+	cnt = ambssamp*wt + 0.5;        /* perform super-sampling? */
805	+	if (cnt > 0)
806	+	ambsupersamp(acol, hp, cnt);
807	+	copycolor(rcol, acol);          /* final indirect irradiance/PI */
808	+	if ((ra == NULL) & (pg == NULL) & (dg == NULL)) {
809	+	free(hp);
810	+	return(-1);             /* no radius or gradient calc. */
811	+	}
812	+	if ((d = bright(acol)) > FTINY) {       /* normalize Y values */
813	+	d = 0.99*(hp->ns*hp->ns)/d;
814	+	K = 0.01;
815	+	} else {                        /* or fall back on geometric Hessian */
816	+	K = 1.0;
817	+	pg = NULL;
818	+	dg = NULL;
819	+	}
820	+	ap = hp->sa;                    /* relative Y channel from here on... */
821	+	for (i = hp->ns*hp->ns; i--; ap++)
822	+	colval(ap->v,CIEY) = bright(ap->v)*d + K;
823	+
824	+	if (uv == NULL)                 /* make sure we have axis pointers */
825	+	uv = my_uv;
826	+	/* compute radii & pos. gradient */
827	+	ambHessian(hp, uv, ra, pg);
828	+
829	+	if (dg != NULL)                 /* compute direction gradient */
830	+	ambdirgrad(hp, uv, dg);
831	+
832	+	if (ra != NULL) {               /* scale/clamp radii */
833	+	if (pg != NULL) {
834	+	if (ra[0]*(d = fabs(pg[0])) > 1.0)
835	+	ra[0] = 1.0/d;
836	+	if (ra[1]*(d = fabs(pg[1])) > 1.0)
837	+	ra[1] = 1.0/d;
838	+	if (ra[0] > ra[1])
839	+	ra[0] = ra[1];
840	+	}
841	+	if (ra[0] < minarad) {
842	+	ra[0] = minarad;
843	+	if (ra[1] < minarad)
844	+	ra[1] = minarad;
845	+	}
846	+	ra[0] *= d = 1.0/sqrt(sqrt(wt));
847	+	if ((ra[1] *= d) > 2.0*ra[0])
848	+	ra[1] = 2.0*ra[0];
849	+	if (ra[1] > maxarad) {
850	+	ra[1] = maxarad;
851	+	if (ra[0] > maxarad)
852	+	ra[0] = maxarad;
853	+	}
854	+	if (crlp != NULL)       /* flag encroached directions */
855	+	*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
856	+	if (pg != NULL) {       /* cap gradient if necessary */
857	+	d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
858	+	if (d > 1.0) {
859	+	d = 1.0/sqrt(d);
860	+	pg[0] *= d;
861	+	pg[1] *= d;
862	+	}
863	+	}
864	+	}
865	+	free(hp);                       /* clean up and return */
866	+	return(1);
867	+	}
868	+
869	+
870	+	#else /* ! NEWAMB */
871	+
872	+
873	+	void
874	+	inithemi(                       /* initialize sampling hemisphere */
875	+	AMBHEMI  *hp,
876	+	COLOR ac,
877	+	RAY  *r,
878	+	double  wt
879	+	)
880	+	{
881	+	double  d;
882	+	int  i;
883	+	/* set number of divisions */
884	+	if (ambacc <= FTINY &&
885	+	wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
886	+	wt = d;                 /* avoid ray termination */
887	+	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
888	+	i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
889	+	if (hp->nt < i)
890	+	hp->nt = i;
891	+	hp->np = PI * hp->nt + 0.5;
892	+	/* set number of super-samples */
893	+	hp->ns = ambssamp * wt + 0.5;
894	+	/* assign coefficient */
895	+	copycolor(hp->acoef, ac);
896	+	d = 1.0/(hp->nt*hp->np);
897	+	scalecolor(hp->acoef, d);
898	+	/* make axes */
899	+	VCOPY(hp->uz, r->ron);
900	+	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
901	+	for (i = 0; i < 3; i++)
902	+	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
903	+	break;
904	+	if (i >= 3)
905	+	error(CONSISTENCY, "bad ray direction in inithemi");
906	+	hp->uy[i] = 1.0;
907	+	fcross(hp->ux, hp->uy, hp->uz);
908	+	normalize(hp->ux);
909	+	fcross(hp->uy, hp->uz, hp->ux);
910	+	}
911	+
912	+
913	+	int
914	+	divsample(                              /* sample a division */
915	+	AMBSAMP  *dp,
916	+	AMBHEMI  *h,
917	+	RAY  *r
918	+	)
919	+	{
920		RAY  ar;
921	<	int  hlist[4];
921	>	int  hlist[3];
922	>	double  spt[2];
923		double  xd, yd, zd;
924		double  b2;
925		double  phi;
926	<	register int  i;
927	<
928	<	if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
926	>	int  i;
927	>	/* ambient coefficient for weight */
928	>	if (ambacc > FTINY)
929	>	setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
930	>	else
931	>	copycolor(ar.rcoef, h->acoef);
932	>	if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
933		return(-1);
934	+	if (ambacc > FTINY) {
935	+	multcolor(ar.rcoef, h->acoef);
936	+	scalecolor(ar.rcoef, 1./AVGREFL);
937	+	}
938		hlist[0] = r->rno;
939		hlist[1] = dp->t;
940		hlist[2] = dp->p;
941	<	hlist[3] = 0;
942	<	zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
943	<	hlist[3] = 1;
944	<	phi = 2.0*PI * (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
945	<	xd = cos(phi) * zd;
79	<	yd = sin(phi) * zd;
941	>	multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
942	>	zd = sqrt((dp->t + spt[0])/h->nt);
943	>	phi = 2.0*PI * (dp->p + spt[1])/h->np;
944	>	xd = tcos(phi) * zd;
945	>	yd = tsin(phi) * zd;
946		zd = sqrt(1.0 - zd*zd);
947		for (i = 0; i < 3; i++)
948		ar.rdir[i] =    xd*h->ux[i] +
949		yd*h->uy[i] +
950		zd*h->uz[i];
951	+	checknorm(ar.rdir);
952		dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
953		rayvalue(&ar);
954		ndims--;
955	+	multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
956		addcolor(dp->v, ar.rcol);
957	<	if (ar.rt < FHUGE)
957	>	/* use rt to improve gradient calc */
958	>	if (ar.rt > FTINY && ar.rt < FHUGE)
959		dp->r += 1.0/ar.rt;
960		/* (re)initialize error */
961		if (dp->n++) {
#	Line 99 | Line 968 | RAY  *r;
968		}
969
970
971	+	static int
972	+	ambcmp(                                 /* decreasing order */
973	+	const void *p1,
974	+	const void *p2
975	+	)
976	+	{
977	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
978	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
979	+
980	+	if (d1->k < d2->k)
981	+	return(1);
982	+	if (d1->k > d2->k)
983	+	return(-1);
984	+	return(0);
985	+	}
986	+
987	+
988	+	static int
989	+	ambnorm(                                /* standard order */
990	+	const void *p1,
991	+	const void *p2
992	+	)
993	+	{
994	+	const AMBSAMP   *d1 = (const AMBSAMP *)p1;
995	+	const AMBSAMP   *d2 = (const AMBSAMP *)p2;
996	+	int     c;
997	+
998	+	if ( (c = d1->t - d2->t) )
999	+	return(c);
1000	+	return(d1->p - d2->p);
1001	+	}
1002	+
1003	+
1004		double
1005	<	doambient(acol, r, pg, dg)              /* compute ambient component */
1006	<	COLOR  acol;
1007	<	RAY  *r;
1008	<	FVECT  pg, dg;
1005	>	doambient(                              /* compute ambient component */
1006	>	COLOR  rcol,
1007	>	RAY  *r,
1008	>	double  wt,
1009	>	FVECT  pg,
1010	>	FVECT  dg
1011	>	)
1012		{
1013	<	double  b, d;
1013	>	double  b, d=0;
1014		AMBHEMI  hemi;
1015		AMBSAMP  *div;
1016		AMBSAMP  dnew;
1017	<	register AMBSAMP  *dp;
1017	>	double  acol[3];
1018	>	AMBSAMP  *dp;
1019		double  arad;
1020	<	int  ndivs, ns;
1021	<	register int  i, j;
116	<	/* initialize color */
117	<	setcolor(acol, 0.0, 0.0, 0.0);
1020	>	int  divcnt;
1021	>	int  i, j;
1022		/* initialize hemisphere */
1023	<	inithemi(&hemi, r);
1024	<	ndivs = hemi.nt * hemi.np;
1025	<	if (ndivs == 0)
1023	>	inithemi(&hemi, rcol, r, wt);
1024	>	divcnt = hemi.nt * hemi.np;
1025	>	/* initialize */
1026	>	if (pg != NULL)
1027	>	pg[0] = pg[1] = pg[2] = 0.0;
1028	>	if (dg != NULL)
1029	>	dg[0] = dg[1] = dg[2] = 0.0;
1030	>	setcolor(rcol, 0.0, 0.0, 0.0);
1031	>	if (divcnt == 0)
1032		return(0.0);
1033	<	/* set number of super-samples */
1034	<	ns = ambssamp * r->rweight + 0.5;
1035	<	if (ns > 0 || pg != NULL || dg != NULL) {
126	<	div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
1033	>	/* allocate super-samples */
1034	>	if (hemi.ns > 0 || pg != NULL || dg != NULL) {
1035	>	div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP));
1036		if (div == NULL)
1037		error(SYSTEM, "out of memory in doambient");
1038		} else
1039		div = NULL;
1040		/* sample the divisions */
1041		arad = 0.0;
1042	+	acol[0] = acol[1] = acol[2] = 0.0;
1043		if ((dp = div) == NULL)
1044		dp = &dnew;
1045	+	divcnt = 0;
1046		for (i = 0; i < hemi.nt; i++)
1047		for (j = 0; j < hemi.np; j++) {
1048		dp->t = i; dp->p = j;
1049		setcolor(dp->v, 0.0, 0.0, 0.0);
1050		dp->r = 0.0;
1051		dp->n = 0;
1052	<	if (divsample(dp, &hemi, r) < 0)
1053	<	goto oopsy;
1052	>	if (divsample(dp, &hemi, r) < 0) {
1053	>	if (div != NULL)
1054	>	dp++;
1055	>	continue;
1056	>	}
1057	>	arad += dp->r;
1058	>	divcnt++;
1059		if (div != NULL)
1060		dp++;
1061	<	else {
1061	>	else
1062		addcolor(acol, dp->v);
147	–	arad += dp->r;
148	–	}
1063		}
1064	<	if (ns > 0) {                   /* perform super-sampling */
1064	>	if (!divcnt) {
1065	>	if (div != NULL)
1066	>	free((void *)div);
1067	>	return(0.0);            /* no samples taken */
1068	>	}
1069	>	if (divcnt < hemi.nt*hemi.np) {
1070	>	pg = dg = NULL;         /* incomplete sampling */
1071	>	hemi.ns = 0;
1072	>	} else if (arad > FTINY && divcnt/arad < minarad) {
1073	>	hemi.ns = 0;            /* close enough */
1074	>	} else if (hemi.ns > 0) {       /* else perform super-sampling? */
1075		comperrs(div, &hemi);                   /* compute errors */
1076	<	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
1076	>	qsort(div, divcnt, sizeof(AMBSAMP), ambcmp);    /* sort divs */
1077		/* super-sample */
1078	<	for (i = ns; i > 0; i--) {
1079	<	copystruct(&dnew, div);
1080	<	if (divsample(&dnew, &hemi, r) < 0)
1081	<	goto oopsy;
1082	<	/* reinsert */
1083	<	dp = div;
1084	<	j = ndivs < i ? ndivs : i;
1078	>	for (i = hemi.ns; i > 0; i--) {
1079	>	dnew = *div;
1080	>	if (divsample(&dnew, &hemi, r) < 0) {
1081	>	dp++;
1082	>	continue;
1083	>	}
1084	>	dp = div;               /* reinsert */
1085	>	j = divcnt < i ? divcnt : i;
1086		while (--j > 0 && dnew.k < dp[1].k) {
1087	<	copystruct(dp, dp+1);
1087	>	*dp = *(dp+1);
1088		dp++;
1089		}
1090	<	copystruct(dp, &dnew);
1090	>	*dp = dnew;
1091		}
1092		if (pg != NULL || dg != NULL)   /* restore order */
1093	<	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
1093	>	qsort(div, divcnt, sizeof(AMBSAMP), ambnorm);
1094		}
1095		/* compute returned values */
1096		if (div != NULL) {
1097	<	for (i = ndivs, dp = div; i-- > 0; dp++) {
1097	>	arad = 0.0;             /* note: divcnt may be < nt*np */
1098	>	for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) {
1099		arad += dp->r;
1100		if (dp->n > 1) {
1101		b = 1.0/dp->n;
#	Line 181 | Line 1107 | FVECT  pg, dg;
1107		}
1108		b = bright(acol);
1109		if (b > FTINY) {
1110	<	b = ndivs/b;
1110	>	b = 1.0/b;      /* compute & normalize gradient(s) */
1111		if (pg != NULL) {
1112		posgradient(pg, div, &hemi);
1113		for (i = 0; i < 3; i++)
#	Line 192 | Line 1118 | FVECT  pg, dg;
1118		for (i = 0; i < 3; i++)
1119		dg[i] *= b;
1120		}
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;
1121		}
1122	<	free((char *)div);
1122	>	free((void *)div);
1123		}
1124	<	b = 1.0/ndivs;
206	<	scalecolor(acol, b);
1124	>	copycolor(rcol, acol);
1125		if (arad <= FTINY)
208	–	arad = FHUGE;
209	–	else
210	–	arad = (ndivs+ns)/arad;
211	–	if (arad > maxarad)
1126		arad = maxarad;
1127	<	else if (arad < minarad)
1127	>	else
1128	>	arad = (divcnt+hemi.ns)/arad;
1129	>	if (pg != NULL) {               /* reduce radius if gradient large */
1130	>	d = DOT(pg,pg);
1131	>	if (d*arad*arad > 1.0)
1132	>	arad = 1.0/sqrt(d);
1133	>	}
1134	>	if (arad < minarad) {
1135		arad = minarad;
1136	<	arad /= sqrt(r->rweight);
1136	>	if (pg != NULL && d*arad*arad > 1.0) {  /* cap gradient */
1137	>	d = 1.0/arad/sqrt(d);
1138	>	for (i = 0; i < 3; i++)
1139	>	pg[i] *= d;
1140	>	}
1141	>	}
1142	>	if ((arad /= sqrt(wt)) > maxarad)
1143	>	arad = maxarad;
1144		return(arad);
217	–	oopsy:
218	–	if (div != NULL)
219	–	free((char *)div);
220	–	return(0.0);
1145		}
1146
1147
1148	<	inithemi(hp, r)                 /* initialize sampling hemisphere */
1149	<	register AMBHEMI  *hp;
1150	<	RAY  *r;
1148	>	void
1149	>	comperrs(                       /* compute initial error estimates */
1150	>	AMBSAMP  *da,   /* assumes standard ordering */
1151	>	AMBHEMI  *hp
1152	>	)
1153		{
228	–	register int  i;
229	–	/* set number of divisions */
230	–	hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
231	–	hp->np = 2 * hp->nt;
232	–	/* make axes */
233	–	VCOPY(hp->uz, r->ron);
234	–	hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
235	–	for (i = 0; i < 3; i++)
236	–	if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
237	–	break;
238	–	if (i >= 3)
239	–	error(CONSISTENCY, "bad ray direction in inithemi");
240	–	hp->uy[i] = 1.0;
241	–	fcross(hp->ux, hp->uy, hp->uz);
242	–	normalize(hp->ux);
243	–	fcross(hp->uy, hp->uz, hp->ux);
244	–	}
245	–
246	–
247	–	comperrs(da, hp)                /* compute initial error estimates */
248	–	AMBSAMP  *da;           /* assumes standard ordering */
249	–	register AMBHEMI  *hp;
250	–	{
1154		double  b, b2;
1155		int  i, j;
1156	<	register AMBSAMP  *dp;
1156	>	AMBSAMP  *dp;
1157		/* sum differences from neighbors */
1158		dp = da;
1159		for (i = 0; i < hp->nt; i++)
#	Line 294 | Line 1197 | register AMBHEMI  *hp;
1197		}
1198
1199
1200	<	posgradient(gv, da, hp)                         /* compute position gradient */
1201	<	FVECT  gv;
1202	<	AMBSAMP  *da;                   /* assumes standard ordering */
1203	<	AMBHEMI  *hp;
1200	>	void
1201	>	posgradient(                                    /* compute position gradient */
1202	>	FVECT  gv,
1203	>	AMBSAMP  *da,                   /* assumes standard ordering */
1204	>	AMBHEMI  *hp
1205	>	)
1206		{
1207	<	register int  i, j;
1208	<	double  b, d;
1207	>	int  i, j;
1208	>	double  nextsine, lastsine, b, d;
1209		double  mag0, mag1;
1210		double  phi, cosp, sinp, xd, yd;
1211	<	register AMBSAMP  *dp;
1211	>	AMBSAMP  *dp;
1212
1213		xd = yd = 0.0;
1214		for (j = 0; j < hp->np; j++) {
1215		dp = da + j;
1216		mag0 = mag1 = 0.0;
1217	+	lastsine = 0.0;
1218		for (i = 0; i < hp->nt; i++) {
1219		#ifdef  DEBUG
1220		if (dp->t != i || dp->p != j)
#	Line 319 | Line 1225 | AMBHEMI  *hp;
1225		if (i > 0) {
1226		d = dp[-hp->np].r;
1227		if (dp[0].r > d) d = dp[0].r;
1228	<	d *= 1.0 - sqrt((double)i/hp->nt);
1228	>	/* sin(t)*cos(t)^2 */
1229	>	d *= lastsine * (1.0 - (double)i/hp->nt);
1230		mag0 += d*(b - bright(dp[-hp->np].v));
1231		}
1232	+	nextsine = sqrt((double)(i+1)/hp->nt);
1233		if (j > 0) {
1234		d = dp[-1].r;
1235		if (dp[0].r > d) d = dp[0].r;
1236	<	mag1 += d*(b - bright(dp[-1].v));
1236	>	mag1 += d * (nextsine - lastsine) *
1237	>	(b - bright(dp[-1].v));
1238		} else {
1239		d = dp[hp->np-1].r;
1240		if (dp[0].r > d) d = dp[0].r;
1241	<	mag1 += d*(b - bright(dp[hp->np-1].v));
1241	>	mag1 += d * (nextsine - lastsine) *
1242	>	(b - bright(dp[hp->np-1].v));
1243		}
1244		dp += hp->np;
1245	+	lastsine = nextsine;
1246		}
1247	<	if (hp->nt > 1) {
337	<	mag0 /= (double)hp->np;
338	<	mag1 /= (double)hp->nt;
339	<	}
1247	>	mag0 *= 2.0*PI / hp->np;
1248		phi = 2.0*PI * (double)j/hp->np;
1249	<	cosp = cos(phi); sinp = sin(phi);
1249	>	cosp = tcos(phi); sinp = tsin(phi);
1250		xd += mag0*cosp - mag1*sinp;
1251		yd += mag0*sinp + mag1*cosp;
1252		}
1253		for (i = 0; i < 3; i++)
1254	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/PI;
1254	>	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI;
1255		}
1256
1257
1258	<	dirgradient(gv, da, hp)                         /* compute direction gradient */
1259	<	FVECT  gv;
1260	<	AMBSAMP  *da;                   /* assumes standard ordering */
1261	<	AMBHEMI  *hp;
1258	>	void
1259	>	dirgradient(                                    /* compute direction gradient */
1260	>	FVECT  gv,
1261	>	AMBSAMP  *da,                   /* assumes standard ordering */
1262	>	AMBHEMI  *hp
1263	>	)
1264		{
1265	<	register int  i, j;
1265	>	int  i, j;
1266		double  mag;
1267		double  phi, xd, yd;
1268	<	register AMBSAMP  *dp;
1268	>	AMBSAMP  *dp;
1269
1270		xd = yd = 0.0;
1271		for (j = 0; j < hp->np; j++) {
#	Line 367 | Line 1277 | AMBHEMI  *hp;
1277		error(CONSISTENCY,
1278		"division order in dirgradient");
1279		#endif
1280	<	mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
1280	>	/* tan(t) */
1281	>	mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
1282		dp += hp->np;
1283		}
1284		phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
1285	<	xd += mag * cos(phi);
1286	<	yd += mag * sin(phi);
1285	>	xd += mag * tcos(phi);
1286	>	yd += mag * tsin(phi);
1287		}
1288		for (i = 0; i < 3; i++)
1289	<	gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*PI/(hp->nt*hp->np);
1289	>	gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
1290		}
1291	+
1292	+	#endif  /* ! NEWAMB */

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