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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.94
Committed: Wed Apr 17 17:34:11 2024 UTC (4 weeks, 2 days ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.93: +20 -33 lines
Log Message: 
fix(rtrace,rpict,rvu,rcontrib): Fixed divide-by-zero and sample initialization for indirect calc

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.94 static const char RCSid[] = "$Id: ambcomp.c,v 2.93 2024/04/16 23:32:20 greg Exp $";
3 greg 1.1 #endif
4     /*
5     * Routines to compute "ambient" values using Monte Carlo
6 greg 2.9 *
7 greg 2.27 * 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 greg 2.46 * 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 greg 2.9 * Declarations of external symbols in ambient.h
16     */
17    
18 greg 2.10 #include "copyright.h"
19 greg 1.1
20     #include "ray.h"
21 greg 2.25 #include "ambient.h"
22     #include "random.h"
23 greg 1.1
24 greg 2.86 #ifndef MINADIV
25     #define MINADIV 7 /* minimum # divisions in each dimension */
26     #endif
27    
28 greg 2.26 typedef struct {
29 greg 2.90 FVECT p; /* intersection point */
30 greg 2.83 float d; /* reciprocal distance */
31 greg 2.90 SCOLOR v; /* hemisphere sample value */
32 greg 2.44 } AMBSAMP; /* sample value */
33    
34     typedef struct {
35 greg 2.26 RAY *rp; /* originating ray sample */
36     int ns; /* number of samples per axis */
37 greg 2.61 int sampOK; /* acquired full sample set? */
38 greg 2.92 int atyp; /* RAMBIENT or TAMBIENT */
39 greg 2.90 SCOLOR acoef; /* division contribution coefficient */
40     SCOLOR acol; /* accumulated color */
41 greg 2.92 FVECT onrm; /* oriented unperturbed surface normal */
42 greg 2.61 FVECT ux, uy; /* tangent axis unit vectors */
43 greg 2.44 AMBSAMP sa[1]; /* sample array (extends struct) */
44 greg 2.26 } AMBHEMI; /* ambient sample hemisphere */
45    
46 greg 2.56 #define AI(h,i,j) ((i)*(h)->ns + (j))
47     #define ambsam(h,i,j) (h)->sa[AI(h,i,j)]
48 greg 2.26
49 greg 2.27 typedef struct {
50 greg 2.35 FVECT r_i, r_i1, e_i, rcp, rI2_eJ2;
51     double I1, I2;
52 greg 2.27 } FFTRI; /* vectors and coefficients for Hessian calculation */
53    
54 greg 2.26
55 greg 2.61 static int
56 greg 2.73 ambcollision( /* proposed direciton collides? */
57     AMBHEMI *hp,
58     int i,
59     int j,
60     FVECT dv
61     )
62     {
63 greg 2.74 double cos_thresh;
64     int ii, jj;
65 greg 2.75 /* min. spacing = 1/4th division */
66     cos_thresh = (PI/4.)/(double)hp->ns;
67 greg 2.74 cos_thresh = 1. - .5*cos_thresh*cos_thresh;
68     /* check existing neighbors */
69 greg 2.73 for (ii = i-1; ii <= i+1; ii++) {
70     if (ii < 0) continue;
71     if (ii >= hp->ns) break;
72     for (jj = j-1; jj <= j+1; jj++) {
73     AMBSAMP *ap;
74     FVECT avec;
75     double dprod;
76     if (jj < 0) continue;
77     if (jj >= hp->ns) break;
78     if ((ii==i) & (jj==j)) continue;
79     ap = &ambsam(hp,ii,jj);
80 greg 2.74 if (ap->d <= .5/FHUGE)
81     continue; /* no one home */
82 greg 2.73 VSUB(avec, ap->p, hp->rp->rop);
83     dprod = DOT(avec, dv);
84     if (dprod >= cos_thresh*VLEN(avec))
85     return(1); /* collision */
86     }
87     }
88 greg 2.74 return(0); /* nothing to worry about */
89 greg 2.73 }
90    
91    
92     static int
93 greg 2.61 ambsample( /* initial ambient division sample */
94     AMBHEMI *hp,
95     int i,
96     int j,
97     int n
98 greg 2.26 )
99     {
100 greg 2.61 AMBSAMP *ap = &ambsam(hp,i,j);
101     RAY ar;
102 greg 2.41 int hlist[3], ii;
103 greg 2.94 double ss[2];
104 greg 2.88 RREAL spt[2];
105     double zd;
106 greg 2.61 /* generate hemispherical sample */
107 greg 2.26 /* ambient coefficient for weight */
108     if (ambacc > FTINY)
109 greg 2.90 setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
110 greg 2.26 else
111 greg 2.90 copyscolor(ar.rcoef, hp->acoef);
112 greg 2.92 if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0)
113 greg 2.41 return(0);
114 greg 2.26 if (ambacc > FTINY) {
115 greg 2.90 smultscolor(ar.rcoef, hp->acoef);
116     scalescolor(ar.rcoef, 1./AVGREFL);
117 greg 2.41 }
118     hlist[0] = hp->rp->rno;
119 greg 2.94 hlist[1] = AI(hp,i,j);
120     hlist[2] = samplendx;
121     multisamp(ss, 2, urand(ilhash(hlist,3)+n));
122 greg 2.73 resample:
123 greg 2.94 square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns);
124 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
125     for (ii = 3; ii--; )
126 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
127 greg 2.26 spt[1]*hp->uy[ii] +
128 greg 2.92 zd*hp->onrm[ii];
129 greg 2.61 checknorm(ar.rdir);
130 greg 2.73 /* avoid coincident samples */
131 greg 2.94 if (!n && hp->ns >= 4 && ambcollision(hp, i, j, ar.rdir)) {
132     ss[0] = frandom(); ss[1] = frandom();
133 greg 2.75 goto resample; /* reject this sample */
134 greg 2.73 }
135 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
136 greg 2.61 rayvalue(&ar); /* evaluate ray */
137     ndims--;
138 greg 2.83 zd = raydistance(&ar);
139     if (zd <= FTINY)
140 greg 2.61 return(0); /* should never happen */
141 greg 2.90 smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */
142 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
143     ap->d = 1.0/zd;
144 greg 2.61 if (!n) { /* record first vertex & value */
145 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
146     zd = 10.0*thescene.cusize + 1000.;
147     VSUM(ap->p, ar.rorg, ar.rdir, zd);
148 greg 2.90 copyscolor(ap->v, ar.rcol);
149 greg 2.61 } else { /* else update recorded value */
150 greg 2.90 sopscolor(hp->acol, -=, ap->v);
151 greg 2.61 zd = 1.0/(double)(n+1);
152 greg 2.90 scalescolor(ar.rcol, zd);
153 greg 2.61 zd *= (double)n;
154 greg 2.90 scalescolor(ap->v, zd);
155     saddscolor(ap->v, ar.rcol);
156 greg 2.61 }
157 greg 2.90 saddscolor(hp->acol, ap->v); /* add to our sum */
158 greg 2.41 return(1);
159     }
160    
161    
162 greg 2.82 /* Estimate variance based on ambient division differences */
163 greg 2.41 static float *
164     getambdiffs(AMBHEMI *hp)
165     {
166 greg 2.93 const double normf = 1./(pbright(hp->acoef) + FTINY);
167 greg 2.94 float *earr = (float *)calloc(2*hp->ns*hp->ns, sizeof(float));
168     float *ep;
169 greg 2.42 AMBSAMP *ap;
170 greg 2.81 double b, b1, d2;
171 greg 2.41 int i, j;
172    
173     if (earr == NULL) /* out of memory? */
174     return(NULL);
175 greg 2.81 /* sum squared neighbor diffs */
176 greg 2.42 for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
177     for (j = 0; j < hp->ns; j++, ap++, ep++) {
178 greg 2.90 b = pbright(ap[0].v);
179 greg 2.41 if (i) { /* from above */
180 greg 2.90 b1 = pbright(ap[-hp->ns].v);
181 greg 2.82 d2 = b - b1;
182 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
183 greg 2.41 ep[0] += d2;
184     ep[-hp->ns] += d2;
185     }
186 greg 2.55 if (!j) continue;
187     /* from behind */
188 greg 2.90 b1 = pbright(ap[-1].v);
189 greg 2.82 d2 = b - b1;
190 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
191 greg 2.55 ep[0] += d2;
192     ep[-1] += d2;
193     if (!i) continue;
194     /* diagonal */
195 greg 2.90 b1 = pbright(ap[-hp->ns-1].v);
196 greg 2.82 d2 = b - b1;
197 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
198 greg 2.55 ep[0] += d2;
199     ep[-hp->ns-1] += d2;
200 greg 2.41 }
201     /* correct for number of neighbors */
202 greg 2.93 earr[0] *= 6./3.;
203     earr[hp->ns-1] *= 6./3.;
204     earr[(hp->ns-1)*hp->ns] *= 6./3.;
205     earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.;
206 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
207 greg 2.93 earr[i*hp->ns] *= 6./5.;
208     earr[i*hp->ns + hp->ns-1] *= 6./5.;
209 greg 2.41 }
210     for (j = 1; j < hp->ns-1; j++) {
211 greg 2.93 earr[j] *= 6./5.;
212     earr[(hp->ns-1)*hp->ns + j] *= 6./5.;
213     }
214 greg 2.94 /* blur map to reduce bias */
215     memcpy(earr+hp->ns*hp->ns, earr, hp->ns*hp->ns*sizeof(float));
216 greg 2.93 for (i = 0; i < hp->ns-1; i++) {
217 greg 2.94 float *ep2;
218 greg 2.93 ep = earr + i*hp->ns;
219 greg 2.94 ep2 = ep + hp->ns*hp->ns;
220     for (j = 0; j < hp->ns-1; j++, ep++, ep2++) {
221     ep[0] += .125*(ep2[1] + ep2[hp->ns]) - .5*ep2[0];
222     ep[1] += .125*ep2[0];
223     ep[hp->ns] += .125*ep2[0];
224 greg 2.93 }
225 greg 2.41 }
226     return(earr);
227     }
228    
229    
230 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
231 greg 2.41 static void
232 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
233 greg 2.41 {
234     float *earr = getambdiffs(hp);
235 greg 2.54 double e2rem = 0;
236 greg 2.41 float *ep;
237 greg 2.55 int i, j, n, nss;
238 greg 2.41
239     if (earr == NULL) /* just skip calc. if no memory */
240     return;
241 greg 2.54 /* accumulate estimated variances */
242 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
243     e2rem += *--ep;
244 greg 2.41 ep = earr; /* perform super-sampling */
245 greg 2.81 for (i = 0; i < hp->ns; i++)
246     for (j = 0; j < hp->ns; j++) {
247 greg 2.55 if (e2rem <= FTINY)
248     goto done; /* nothing left to do */
249     nss = *ep/e2rem*cnt + frandom();
250 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
251 greg 2.77 if (!--cnt) goto done;
252 greg 2.61 e2rem -= *ep++; /* update remainder */
253 greg 2.41 }
254 greg 2.55 done:
255 greg 2.41 free(earr);
256     }
257    
258    
259 greg 2.61 static AMBHEMI *
260     samp_hemi( /* sample indirect hemisphere */
261 greg 2.90 SCOLOR rcol,
262 greg 2.61 RAY *r,
263     double wt
264     )
265     {
266 greg 2.92 int backside = (wt < 0);
267 greg 2.61 AMBHEMI *hp;
268     double d;
269     int n, i, j;
270 greg 2.77 /* insignificance check */
271 greg 2.90 d = sintens(rcol);
272     if (d <= FTINY)
273 greg 2.77 return(NULL);
274 greg 2.61 /* set number of divisions */
275 greg 2.92 if (backside) wt = -wt;
276 greg 2.61 if (ambacc <= FTINY &&
277 greg 2.94 wt > (d *= 0.8*r->rweight/(ambdiv*minweight + 1e-20)))
278 greg 2.61 wt = d; /* avoid ray termination */
279     n = sqrt(ambdiv * wt) + 0.5;
280 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
281     if (n < i) /* use minimum number of samples? */
282 greg 2.61 n = i;
283     /* allocate sampling array */
284     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
285     if (hp == NULL)
286     error(SYSTEM, "out of memory in samp_hemi");
287 greg 2.92
288     if (backside) {
289     hp->atyp = TAMBIENT;
290     hp->onrm[0] = -r->ron[0];
291     hp->onrm[1] = -r->ron[1];
292     hp->onrm[2] = -r->ron[2];
293     } else {
294     hp->atyp = RAMBIENT;
295     VCOPY(hp->onrm, r->ron);
296     }
297 greg 2.61 hp->rp = r;
298     hp->ns = n;
299 greg 2.90 scolorblack(hp->acol);
300 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
301 greg 2.61 hp->sampOK = 0;
302     /* assign coefficient */
303 greg 2.90 copyscolor(hp->acoef, rcol);
304 greg 2.61 d = 1.0/(n*n);
305 greg 2.90 scalescolor(hp->acoef, d);
306 greg 2.61 /* make tangent plane axes */
307 greg 2.92 if (!getperpendicular(hp->ux, hp->onrm, 1))
308 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
309 greg 2.92 VCROSS(hp->uy, hp->onrm, hp->ux);
310 greg 2.61 /* sample divisions */
311     for (i = hp->ns; i--; )
312     for (j = hp->ns; j--; )
313     hp->sampOK += ambsample(hp, i, j, 0);
314 greg 2.90 copyscolor(rcol, hp->acol);
315 greg 2.61 if (!hp->sampOK) { /* utter failure? */
316     free(hp);
317     return(NULL);
318     }
319     if (hp->sampOK < hp->ns*hp->ns) {
320     hp->sampOK *= -1; /* soft failure */
321     return(hp);
322     }
323 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
324     return(hp); /* don't bother super-sampling */
325 greg 2.61 n = ambssamp*wt + 0.5;
326 greg 2.94 if (n >= 4*hp->ns) { /* perform super-sampling? */
327 greg 2.61 ambsupersamp(hp, n);
328 greg 2.90 copyscolor(rcol, hp->acol);
329 greg 2.61 }
330     return(hp); /* all is well */
331     }
332    
333    
334 greg 2.46 /* Return brightness of farthest ambient sample */
335     static double
336 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
337 greg 2.46 {
338 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
339     if (hp->sa[n1].d <= hp->sa[n3].d)
340 greg 2.90 return(hp->sa[n1].v[0]);
341     return(hp->sa[n3].v[0]);
342 greg 2.56 }
343     if (hp->sa[n2].d <= hp->sa[n3].d)
344 greg 2.90 return(hp->sa[n2].v[0]);
345     return(hp->sa[n3].v[0]);
346 greg 2.46 }
347    
348    
349 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
350     static void
351 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
352 greg 2.27 {
353 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
354     int ii;
355    
356     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
357     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
358     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
359 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
360     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
361 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
362     dot_er = DOT(ftp->e_i, ftp->r_i);
363 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
364     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
365     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
366 greg 2.35 sqrt( rdot_cp );
367 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
368 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
369 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
370 greg 2.46 for (ii = 3; ii--; )
371     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
372 greg 2.27 }
373    
374    
375 greg 2.28 /* Compose 3x3 matrix from two vectors */
376 greg 2.27 static void
377     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
378     {
379     mat[0][0] = 2.0*va[0]*vb[0];
380     mat[1][1] = 2.0*va[1]*vb[1];
381     mat[2][2] = 2.0*va[2]*vb[2];
382     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
383     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
384     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
385     }
386    
387    
388     /* Compute partial 3x3 Hessian matrix for edge */
389     static void
390     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
391     {
392 greg 2.35 FVECT ncp;
393 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
394     double d1, d2, d3, d4;
395     double I3, J3, K3;
396     int i, j;
397     /* compute intermediate coefficients */
398     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
399     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
400     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
401     d4 = DOT(ftp->e_i, ftp->r_i);
402 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
403     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
404 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
405     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
406     /* intermediate matrices */
407 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
408     compose_matrix(m1, ncp, ftp->rI2_eJ2);
409 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
410     compose_matrix(m3, ftp->e_i, ftp->e_i);
411     compose_matrix(m4, ftp->r_i, ftp->e_i);
412 greg 2.35 d1 = DOT(nrm, ftp->rcp);
413 greg 2.27 d2 = -d1*ftp->I2;
414     d1 *= 2.0;
415     for (i = 3; i--; ) /* final matrix sum */
416     for (j = 3; j--; ) {
417     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
418     2.0*J3*m4[i][j] );
419     hess[i][j] += d2*(i==j);
420 greg 2.46 hess[i][j] *= -1.0/PI;
421 greg 2.27 }
422     }
423    
424    
425     /* Reverse hessian calculation result for edge in other direction */
426     static void
427     rev_hessian(FVECT hess[3])
428     {
429     int i;
430    
431     for (i = 3; i--; ) {
432     hess[i][0] = -hess[i][0];
433     hess[i][1] = -hess[i][1];
434     hess[i][2] = -hess[i][2];
435     }
436     }
437    
438    
439     /* Add to radiometric Hessian from the given triangle */
440     static void
441     add2hessian(FVECT hess[3], FVECT ehess1[3],
442 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
443 greg 2.27 {
444     int i, j;
445    
446     for (i = 3; i--; )
447     for (j = 3; j--; )
448     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
449     }
450    
451    
452     /* Compute partial displacement form factor gradient for edge */
453     static void
454     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
455     {
456 greg 2.35 FVECT ncp;
457 greg 2.27 double f1;
458     int i;
459    
460 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
461     VCROSS(ncp, nrm, ftp->e_i);
462 greg 2.27 for (i = 3; i--; )
463 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
464 greg 2.27 }
465    
466    
467     /* Reverse gradient calculation result for edge in other direction */
468     static void
469     rev_gradient(FVECT grad)
470     {
471     grad[0] = -grad[0];
472     grad[1] = -grad[1];
473     grad[2] = -grad[2];
474     }
475    
476    
477     /* Add to displacement gradient from the given triangle */
478     static void
479 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
480 greg 2.27 {
481     int i;
482    
483     for (i = 3; i--; )
484     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
485     }
486    
487    
488     /* Compute anisotropic radii and eigenvector directions */
489 greg 2.53 static void
490 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
491     {
492     double hess2[2][2];
493     FVECT a, b;
494     double evalue[2], slope1, xmag1;
495     int i;
496     /* project Hessian to sample plane */
497     for (i = 3; i--; ) {
498     a[i] = DOT(hessian[i], uv[0]);
499     b[i] = DOT(hessian[i], uv[1]);
500     }
501     hess2[0][0] = DOT(uv[0], a);
502     hess2[0][1] = DOT(uv[0], b);
503     hess2[1][0] = DOT(uv[1], a);
504     hess2[1][1] = DOT(uv[1], b);
505 greg 2.38 /* compute eigenvalue(s) */
506     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
507     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
508     if (i == 1) /* double-root (circle) */
509     evalue[1] = evalue[0];
510     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
511 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
512     ra[0] = ra[1] = maxarad;
513     return;
514     }
515 greg 2.27 if (evalue[0] > evalue[1]) {
516 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
517     ra[1] = sqrt(sqrt(4.0/evalue[1]));
518 greg 2.27 slope1 = evalue[1];
519     } else {
520 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
521     ra[1] = sqrt(sqrt(4.0/evalue[0]));
522 greg 2.27 slope1 = evalue[0];
523     }
524     /* compute unit eigenvectors */
525     if (fabs(hess2[0][1]) <= FTINY)
526     return; /* uv OK as is */
527     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
528     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
529     for (i = 3; i--; ) {
530     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
531     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
532     }
533     VCOPY(uv[0], a);
534     VCOPY(uv[1], b);
535     }
536    
537    
538 greg 2.26 static void
539     ambHessian( /* anisotropic radii & pos. gradient */
540     AMBHEMI *hp,
541     FVECT uv[2], /* returned */
542 greg 2.28 float ra[2], /* returned (optional) */
543     float pg[2] /* returned (optional) */
544 greg 2.26 )
545     {
546 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
547     FVECT (*hessrow)[3] = NULL;
548     FVECT *gradrow = NULL;
549     FVECT hessian[3];
550     FVECT gradient;
551     FFTRI fftr;
552     int i, j;
553     /* be sure to assign unit vectors */
554     VCOPY(uv[0], hp->ux);
555     VCOPY(uv[1], hp->uy);
556     /* clock-wise vertex traversal from sample POV */
557     if (ra != NULL) { /* initialize Hessian row buffer */
558 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
559 greg 2.27 if (hessrow == NULL)
560     error(SYSTEM, memerrmsg);
561     memset(hessian, 0, sizeof(hessian));
562     } else if (pg == NULL) /* bogus call? */
563     return;
564     if (pg != NULL) { /* initialize form factor row buffer */
565 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
566 greg 2.27 if (gradrow == NULL)
567     error(SYSTEM, memerrmsg);
568     memset(gradient, 0, sizeof(gradient));
569     }
570     /* compute first row of edges */
571     for (j = 0; j < hp->ns-1; j++) {
572 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
573 greg 2.27 if (hessrow != NULL)
574 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
575 greg 2.27 if (gradrow != NULL)
576 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
577 greg 2.27 }
578     /* sum each row of triangles */
579     for (i = 0; i < hp->ns-1; i++) {
580     FVECT hesscol[3]; /* compute first vertical edge */
581     FVECT gradcol;
582 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
583 greg 2.27 if (hessrow != NULL)
584 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
585 greg 2.27 if (gradrow != NULL)
586 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
587 greg 2.27 for (j = 0; j < hp->ns-1; j++) {
588     FVECT hessdia[3]; /* compute triangle contributions */
589     FVECT graddia;
590 greg 2.46 double backg;
591 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
592     AI(hp,i,j+1), AI(hp,i+1,j));
593 greg 2.27 /* diagonal (inner) edge */
594 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
595 greg 2.27 if (hessrow != NULL) {
596 greg 2.92 comp_hessian(hessdia, &fftr, hp->onrm);
597 greg 2.27 rev_hessian(hesscol);
598     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
599     }
600 greg 2.39 if (gradrow != NULL) {
601 greg 2.92 comp_gradient(graddia, &fftr, hp->onrm);
602 greg 2.27 rev_gradient(gradcol);
603     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
604     }
605     /* initialize edge in next row */
606 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
607 greg 2.27 if (hessrow != NULL)
608 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
609 greg 2.27 if (gradrow != NULL)
610 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
611 greg 2.27 /* new column edge & paired triangle */
612 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
613     AI(hp,i+1,j), AI(hp,i,j+1));
614     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
615 greg 2.27 if (hessrow != NULL) {
616 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
617 greg 2.27 rev_hessian(hessdia);
618     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
619     if (i < hp->ns-2)
620     rev_hessian(hessrow[j]);
621     }
622     if (gradrow != NULL) {
623 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
624 greg 2.27 rev_gradient(graddia);
625     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
626     if (i < hp->ns-2)
627     rev_gradient(gradrow[j]);
628     }
629     }
630     }
631     /* release row buffers */
632     if (hessrow != NULL) free(hessrow);
633     if (gradrow != NULL) free(gradrow);
634    
635     if (ra != NULL) /* extract eigenvectors & radii */
636     eigenvectors(uv, ra, hessian);
637 greg 2.32 if (pg != NULL) { /* tangential position gradient */
638     pg[0] = DOT(gradient, uv[0]);
639     pg[1] = DOT(gradient, uv[1]);
640 greg 2.27 }
641     }
642    
643    
644     /* Compute direction gradient from a hemispherical sampling */
645     static void
646     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
647     {
648 greg 2.41 AMBSAMP *ap;
649     double dgsum[2];
650     int n;
651     FVECT vd;
652     double gfact;
653 greg 2.27
654 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
655 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
656     /* use vector for azimuth + 90deg */
657     VSUB(vd, ap->p, hp->rp->rop);
658 greg 2.29 /* brightness over cosine factor */
659 greg 2.92 gfact = ap->v[0] / DOT(hp->onrm, vd);
660 greg 2.40 /* sine = proj_radius/vd_length */
661     dgsum[0] -= DOT(uv[1], vd) * gfact;
662     dgsum[1] += DOT(uv[0], vd) * gfact;
663 greg 2.26 }
664 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
665     dg[1] = dgsum[1] / (hp->ns*hp->ns);
666 greg 2.26 }
667    
668 greg 2.27
669 greg 2.49 /* Compute potential light leak direction flags for cache value */
670     static uint32
671     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
672 greg 2.47 {
673 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
674 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
675     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
676 greg 2.51 double avg_d = 0;
677 greg 2.50 uint32 flgs = 0;
678 greg 2.58 FVECT vec;
679 greg 2.62 double u, v;
680 greg 2.58 double ang, a1;
681 greg 2.50 int i, j;
682 greg 2.52 /* don't bother for a few samples */
683 greg 2.72 if (hp->ns < 8)
684 greg 2.52 return(0);
685     /* check distances overhead */
686 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
687     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
688     avg_d += ambsam(hp,i,j).d;
689     avg_d *= 4.0/(hp->ns*hp->ns);
690 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
691     return(0);
692     if (avg_d >= max_d) /* insurance */
693 greg 2.51 return(0);
694     /* else circle around perimeter */
695 greg 2.47 for (i = 0; i < hp->ns; i++)
696     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
697     AMBSAMP *ap = &ambsam(hp,i,j);
698 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
699     continue; /* too far or too near */
700 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
701 greg 2.62 u = DOT(vec, uv[0]);
702     v = DOT(vec, uv[1]);
703     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
704 greg 2.49 continue; /* occluder outside ellipse */
705     ang = atan2a(v, u); /* else set direction flags */
706 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
707 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
708 greg 2.47 }
709 greg 2.49 return(flgs);
710 greg 2.47 }
711    
712    
713 greg 2.26 int
714     doambient( /* compute ambient component */
715 greg 2.90 SCOLOR rcol, /* input/output color */
716 greg 2.26 RAY *r,
717 greg 2.92 double wt, /* negative for back side */
718 greg 2.27 FVECT uv[2], /* returned (optional) */
719     float ra[2], /* returned (optional) */
720     float pg[2], /* returned (optional) */
721 greg 2.49 float dg[2], /* returned (optional) */
722     uint32 *crlp /* returned (optional) */
723 greg 2.26 )
724     {
725 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
726 greg 2.41 FVECT my_uv[2];
727 greg 2.61 double d, K;
728 greg 2.41 AMBSAMP *ap;
729 greg 2.61 int i;
730     /* clear return values */
731 greg 2.26 if (uv != NULL)
732     memset(uv, 0, sizeof(FVECT)*2);
733     if (ra != NULL)
734     ra[0] = ra[1] = 0.0;
735     if (pg != NULL)
736     pg[0] = pg[1] = 0.0;
737     if (dg != NULL)
738     dg[0] = dg[1] = 0.0;
739 greg 2.49 if (crlp != NULL)
740     *crlp = 0;
741 greg 2.61 if (hp == NULL) /* sampling falure? */
742     return(0);
743    
744     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
745 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
746 greg 2.61 free(hp); /* Hessian not requested/possible */
747     return(-1); /* value-only return value */
748 greg 2.26 }
749 greg 2.91 if ((d = scolor_mean(rcol)) > FTINY) {
750     d = 0.99*(hp->ns*hp->ns)/d; /* normalize avg. values */
751 greg 2.38 K = 0.01;
752 greg 2.45 } else { /* or fall back on geometric Hessian */
753 greg 2.38 K = 1.0;
754     pg = NULL;
755     dg = NULL;
756 greg 2.53 crlp = NULL;
757 greg 2.38 }
758 greg 2.90 ap = hp->sa; /* single channel from here on... */
759 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
760 greg 2.90 ap->v[0] = scolor_mean(ap->v)*d + K;
761 greg 2.26
762     if (uv == NULL) /* make sure we have axis pointers */
763     uv = my_uv;
764     /* compute radii & pos. gradient */
765     ambHessian(hp, uv, ra, pg);
766 greg 2.29
767 greg 2.26 if (dg != NULL) /* compute direction gradient */
768     ambdirgrad(hp, uv, dg);
769 greg 2.29
770 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
771 greg 2.35 if (pg != NULL) {
772     if (ra[0]*(d = fabs(pg[0])) > 1.0)
773     ra[0] = 1.0/d;
774     if (ra[1]*(d = fabs(pg[1])) > 1.0)
775     ra[1] = 1.0/d;
776 greg 2.48 if (ra[0] > ra[1])
777     ra[0] = ra[1];
778 greg 2.35 }
779 greg 2.29 if (ra[0] < minarad) {
780     ra[0] = minarad;
781     if (ra[1] < minarad)
782     ra[1] = minarad;
783     }
784 greg 2.92 ra[0] *= d = 1.0/sqrt(fabs(wt));
785 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
786     ra[1] = 2.0*ra[0];
787 greg 2.28 if (ra[1] > maxarad) {
788     ra[1] = maxarad;
789     if (ra[0] > maxarad)
790     ra[0] = maxarad;
791     }
792 greg 2.53 /* flag encroached directions */
793 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
794 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
795 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
796     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
797     if (d > 1.0) {
798     d = 1.0/sqrt(d);
799     pg[0] *= d;
800     pg[1] *= d;
801     }
802     }
803 greg 2.26 }
804     free(hp); /* clean up and return */
805     return(1);
806     }