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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.89
Committed: Tue Apr 19 00:36:34 2022 UTC (2 years ago) by greg
Content type: text/plain
Branch: MAIN
CVS Tags: rad5R4
Changes since 2.88: +4 -4 lines
Log Message: 
fix: Avoid NaN's with ambient super-sampling in perfectly black regions

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.89 static const char RCSid[] = "$Id: ambcomp.c,v 2.88 2021/12/15 01:38:50 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 2.44 COLOR v; /* hemisphere sample value */
30 greg 2.83 float d; /* reciprocal distance */
31 greg 2.44 FVECT p; /* intersection point */
32     } 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 2.26 COLOR acoef; /* division contribution coefficient */
39 greg 2.61 double acol[3]; /* accumulated color */
40     FVECT ux, uy; /* tangent axis unit vectors */
41 greg 2.44 AMBSAMP sa[1]; /* sample array (extends struct) */
42 greg 2.26 } AMBHEMI; /* ambient sample hemisphere */
43    
44 greg 2.56 #define AI(h,i,j) ((i)*(h)->ns + (j))
45     #define ambsam(h,i,j) (h)->sa[AI(h,i,j)]
46 greg 2.26
47 greg 2.27 typedef struct {
48 greg 2.35 FVECT r_i, r_i1, e_i, rcp, rI2_eJ2;
49     double I1, I2;
50 greg 2.27 } FFTRI; /* vectors and coefficients for Hessian calculation */
51    
52 greg 2.26
53 greg 2.61 static int
54 greg 2.73 ambcollision( /* proposed direciton collides? */
55     AMBHEMI *hp,
56     int i,
57     int j,
58     FVECT dv
59     )
60     {
61 greg 2.74 double cos_thresh;
62     int ii, jj;
63 greg 2.75 /* min. spacing = 1/4th division */
64     cos_thresh = (PI/4.)/(double)hp->ns;
65 greg 2.74 cos_thresh = 1. - .5*cos_thresh*cos_thresh;
66     /* check existing neighbors */
67 greg 2.73 for (ii = i-1; ii <= i+1; ii++) {
68     if (ii < 0) continue;
69     if (ii >= hp->ns) break;
70     for (jj = j-1; jj <= j+1; jj++) {
71     AMBSAMP *ap;
72     FVECT avec;
73     double dprod;
74     if (jj < 0) continue;
75     if (jj >= hp->ns) break;
76     if ((ii==i) & (jj==j)) continue;
77     ap = &ambsam(hp,ii,jj);
78 greg 2.74 if (ap->d <= .5/FHUGE)
79     continue; /* no one home */
80 greg 2.73 VSUB(avec, ap->p, hp->rp->rop);
81     dprod = DOT(avec, dv);
82     if (dprod >= cos_thresh*VLEN(avec))
83     return(1); /* collision */
84     }
85     }
86 greg 2.74 return(0); /* nothing to worry about */
87 greg 2.73 }
88    
89    
90     static int
91 greg 2.61 ambsample( /* initial ambient division sample */
92     AMBHEMI *hp,
93     int i,
94     int j,
95     int n
96 greg 2.26 )
97     {
98 greg 2.61 AMBSAMP *ap = &ambsam(hp,i,j);
99     RAY ar;
100 greg 2.41 int hlist[3], ii;
101 greg 2.88 RREAL spt[2];
102     double zd;
103 greg 2.61 /* generate hemispherical sample */
104 greg 2.26 /* ambient coefficient for weight */
105     if (ambacc > FTINY)
106 greg 2.61 setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
107 greg 2.26 else
108 greg 2.61 copycolor(ar.rcoef, hp->acoef);
109 greg 2.62 if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0)
110 greg 2.41 return(0);
111 greg 2.26 if (ambacc > FTINY) {
112 greg 2.61 multcolor(ar.rcoef, hp->acoef);
113     scalecolor(ar.rcoef, 1./AVGREFL);
114 greg 2.41 }
115     hlist[0] = hp->rp->rno;
116 greg 2.46 hlist[1] = j;
117     hlist[2] = i;
118 greg 2.41 multisamp(spt, 2, urand(ilhash(hlist,3)+n));
119 greg 2.73 resample:
120 greg 2.88 square2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
121 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
122     for (ii = 3; ii--; )
123 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
124 greg 2.26 spt[1]*hp->uy[ii] +
125     zd*hp->rp->ron[ii];
126 greg 2.61 checknorm(ar.rdir);
127 greg 2.73 /* avoid coincident samples */
128     if (!n && ambcollision(hp, i, j, ar.rdir)) {
129     spt[0] = frandom(); spt[1] = frandom();
130 greg 2.75 goto resample; /* reject this sample */
131 greg 2.73 }
132 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
133 greg 2.61 rayvalue(&ar); /* evaluate ray */
134     ndims--;
135 greg 2.83 zd = raydistance(&ar);
136     if (zd <= FTINY)
137 greg 2.61 return(0); /* should never happen */
138     multcolor(ar.rcol, ar.rcoef); /* apply coefficient */
139 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
140     ap->d = 1.0/zd;
141 greg 2.61 if (!n) { /* record first vertex & value */
142 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
143     zd = 10.0*thescene.cusize + 1000.;
144     VSUM(ap->p, ar.rorg, ar.rdir, zd);
145 greg 2.61 copycolor(ap->v, ar.rcol);
146     } else { /* else update recorded value */
147     hp->acol[RED] -= colval(ap->v,RED);
148     hp->acol[GRN] -= colval(ap->v,GRN);
149     hp->acol[BLU] -= colval(ap->v,BLU);
150     zd = 1.0/(double)(n+1);
151     scalecolor(ar.rcol, zd);
152     zd *= (double)n;
153     scalecolor(ap->v, zd);
154     addcolor(ap->v, ar.rcol);
155     }
156     addcolor(hp->acol, ap->v); /* add to our sum */
157 greg 2.41 return(1);
158     }
159    
160    
161 greg 2.82 /* Estimate variance based on ambient division differences */
162 greg 2.41 static float *
163     getambdiffs(AMBHEMI *hp)
164     {
165 greg 2.77 const double normf = 1./bright(hp->acoef);
166 greg 2.55 float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
167 greg 2.41 float *ep;
168 greg 2.42 AMBSAMP *ap;
169 greg 2.81 double b, b1, d2;
170 greg 2.41 int i, j;
171    
172     if (earr == NULL) /* out of memory? */
173     return(NULL);
174 greg 2.81 /* sum squared neighbor diffs */
175 greg 2.42 for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
176     for (j = 0; j < hp->ns; j++, ap++, ep++) {
177     b = bright(ap[0].v);
178 greg 2.41 if (i) { /* from above */
179 greg 2.81 b1 = bright(ap[-hp->ns].v);
180 greg 2.82 d2 = b - b1;
181 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
182 greg 2.41 ep[0] += d2;
183     ep[-hp->ns] += d2;
184     }
185 greg 2.55 if (!j) continue;
186     /* from behind */
187 greg 2.81 b1 = bright(ap[-1].v);
188 greg 2.82 d2 = b - b1;
189 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
190 greg 2.55 ep[0] += d2;
191     ep[-1] += d2;
192     if (!i) continue;
193     /* diagonal */
194 greg 2.81 b1 = bright(ap[-hp->ns-1].v);
195 greg 2.82 d2 = b - b1;
196 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
197 greg 2.55 ep[0] += d2;
198     ep[-hp->ns-1] += d2;
199 greg 2.41 }
200     /* correct for number of neighbors */
201 greg 2.55 earr[0] *= 8./3.;
202     earr[hp->ns-1] *= 8./3.;
203     earr[(hp->ns-1)*hp->ns] *= 8./3.;
204     earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.;
205 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
206 greg 2.55 earr[i*hp->ns] *= 8./5.;
207     earr[i*hp->ns + hp->ns-1] *= 8./5.;
208 greg 2.41 }
209     for (j = 1; j < hp->ns-1; j++) {
210 greg 2.55 earr[j] *= 8./5.;
211     earr[(hp->ns-1)*hp->ns + j] *= 8./5.;
212 greg 2.41 }
213     return(earr);
214     }
215    
216    
217 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
218 greg 2.41 static void
219 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
220 greg 2.41 {
221     float *earr = getambdiffs(hp);
222 greg 2.54 double e2rem = 0;
223 greg 2.41 float *ep;
224 greg 2.55 int i, j, n, nss;
225 greg 2.41
226     if (earr == NULL) /* just skip calc. if no memory */
227     return;
228 greg 2.54 /* accumulate estimated variances */
229 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
230     e2rem += *--ep;
231 greg 2.41 ep = earr; /* perform super-sampling */
232 greg 2.81 for (i = 0; i < hp->ns; i++)
233     for (j = 0; j < hp->ns; j++) {
234 greg 2.55 if (e2rem <= FTINY)
235     goto done; /* nothing left to do */
236     nss = *ep/e2rem*cnt + frandom();
237 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
238 greg 2.77 if (!--cnt) goto done;
239 greg 2.61 e2rem -= *ep++; /* update remainder */
240 greg 2.41 }
241 greg 2.55 done:
242 greg 2.41 free(earr);
243     }
244    
245    
246 greg 2.61 static AMBHEMI *
247     samp_hemi( /* sample indirect hemisphere */
248     COLOR rcol,
249     RAY *r,
250     double wt
251     )
252     {
253     AMBHEMI *hp;
254     double d;
255     int n, i, j;
256 greg 2.77 /* insignificance check */
257     if (bright(rcol) <= FTINY)
258     return(NULL);
259 greg 2.61 /* set number of divisions */
260     if (ambacc <= FTINY &&
261     wt > (d = 0.8*intens(rcol)*r->rweight/(ambdiv*minweight)))
262     wt = d; /* avoid ray termination */
263     n = sqrt(ambdiv * wt) + 0.5;
264 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
265     if (n < i) /* use minimum number of samples? */
266 greg 2.61 n = i;
267     /* allocate sampling array */
268     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
269     if (hp == NULL)
270     error(SYSTEM, "out of memory in samp_hemi");
271     hp->rp = r;
272     hp->ns = n;
273     hp->acol[RED] = hp->acol[GRN] = hp->acol[BLU] = 0.0;
274 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
275 greg 2.61 hp->sampOK = 0;
276     /* assign coefficient */
277     copycolor(hp->acoef, rcol);
278     d = 1.0/(n*n);
279     scalecolor(hp->acoef, d);
280     /* make tangent plane axes */
281 greg 2.70 if (!getperpendicular(hp->ux, r->ron, 1))
282 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
283     VCROSS(hp->uy, r->ron, hp->ux);
284     /* sample divisions */
285     for (i = hp->ns; i--; )
286     for (j = hp->ns; j--; )
287     hp->sampOK += ambsample(hp, i, j, 0);
288     copycolor(rcol, hp->acol);
289     if (!hp->sampOK) { /* utter failure? */
290     free(hp);
291     return(NULL);
292     }
293     if (hp->sampOK < hp->ns*hp->ns) {
294     hp->sampOK *= -1; /* soft failure */
295     return(hp);
296     }
297 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
298     return(hp); /* don't bother super-sampling */
299 greg 2.61 n = ambssamp*wt + 0.5;
300     if (n > 8) { /* perform super-sampling? */
301     ambsupersamp(hp, n);
302     copycolor(rcol, hp->acol);
303     }
304     return(hp); /* all is well */
305     }
306    
307    
308 greg 2.46 /* Return brightness of farthest ambient sample */
309     static double
310 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
311 greg 2.46 {
312 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
313     if (hp->sa[n1].d <= hp->sa[n3].d)
314     return(colval(hp->sa[n1].v,CIEY));
315     return(colval(hp->sa[n3].v,CIEY));
316     }
317     if (hp->sa[n2].d <= hp->sa[n3].d)
318     return(colval(hp->sa[n2].v,CIEY));
319     return(colval(hp->sa[n3].v,CIEY));
320 greg 2.46 }
321    
322    
323 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
324     static void
325 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
326 greg 2.27 {
327 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
328     int ii;
329    
330     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
331     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
332     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
333 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
334     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
335 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
336     dot_er = DOT(ftp->e_i, ftp->r_i);
337 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
338     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
339     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
340 greg 2.35 sqrt( rdot_cp );
341 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
342 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
343 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
344 greg 2.46 for (ii = 3; ii--; )
345     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
346 greg 2.27 }
347    
348    
349 greg 2.28 /* Compose 3x3 matrix from two vectors */
350 greg 2.27 static void
351     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
352     {
353     mat[0][0] = 2.0*va[0]*vb[0];
354     mat[1][1] = 2.0*va[1]*vb[1];
355     mat[2][2] = 2.0*va[2]*vb[2];
356     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
357     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
358     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
359     }
360    
361    
362     /* Compute partial 3x3 Hessian matrix for edge */
363     static void
364     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
365     {
366 greg 2.35 FVECT ncp;
367 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
368     double d1, d2, d3, d4;
369     double I3, J3, K3;
370     int i, j;
371     /* compute intermediate coefficients */
372     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
373     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
374     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
375     d4 = DOT(ftp->e_i, ftp->r_i);
376 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
377     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
378 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
379     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
380     /* intermediate matrices */
381 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
382     compose_matrix(m1, ncp, ftp->rI2_eJ2);
383 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
384     compose_matrix(m3, ftp->e_i, ftp->e_i);
385     compose_matrix(m4, ftp->r_i, ftp->e_i);
386 greg 2.35 d1 = DOT(nrm, ftp->rcp);
387 greg 2.27 d2 = -d1*ftp->I2;
388     d1 *= 2.0;
389     for (i = 3; i--; ) /* final matrix sum */
390     for (j = 3; j--; ) {
391     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
392     2.0*J3*m4[i][j] );
393     hess[i][j] += d2*(i==j);
394 greg 2.46 hess[i][j] *= -1.0/PI;
395 greg 2.27 }
396     }
397    
398    
399     /* Reverse hessian calculation result for edge in other direction */
400     static void
401     rev_hessian(FVECT hess[3])
402     {
403     int i;
404    
405     for (i = 3; i--; ) {
406     hess[i][0] = -hess[i][0];
407     hess[i][1] = -hess[i][1];
408     hess[i][2] = -hess[i][2];
409     }
410     }
411    
412    
413     /* Add to radiometric Hessian from the given triangle */
414     static void
415     add2hessian(FVECT hess[3], FVECT ehess1[3],
416 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
417 greg 2.27 {
418     int i, j;
419    
420     for (i = 3; i--; )
421     for (j = 3; j--; )
422     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
423     }
424    
425    
426     /* Compute partial displacement form factor gradient for edge */
427     static void
428     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
429     {
430 greg 2.35 FVECT ncp;
431 greg 2.27 double f1;
432     int i;
433    
434 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
435     VCROSS(ncp, nrm, ftp->e_i);
436 greg 2.27 for (i = 3; i--; )
437 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
438 greg 2.27 }
439    
440    
441     /* Reverse gradient calculation result for edge in other direction */
442     static void
443     rev_gradient(FVECT grad)
444     {
445     grad[0] = -grad[0];
446     grad[1] = -grad[1];
447     grad[2] = -grad[2];
448     }
449    
450    
451     /* Add to displacement gradient from the given triangle */
452     static void
453 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
454 greg 2.27 {
455     int i;
456    
457     for (i = 3; i--; )
458     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
459     }
460    
461    
462     /* Compute anisotropic radii and eigenvector directions */
463 greg 2.53 static void
464 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
465     {
466     double hess2[2][2];
467     FVECT a, b;
468     double evalue[2], slope1, xmag1;
469     int i;
470     /* project Hessian to sample plane */
471     for (i = 3; i--; ) {
472     a[i] = DOT(hessian[i], uv[0]);
473     b[i] = DOT(hessian[i], uv[1]);
474     }
475     hess2[0][0] = DOT(uv[0], a);
476     hess2[0][1] = DOT(uv[0], b);
477     hess2[1][0] = DOT(uv[1], a);
478     hess2[1][1] = DOT(uv[1], b);
479 greg 2.38 /* compute eigenvalue(s) */
480     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
481     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
482     if (i == 1) /* double-root (circle) */
483     evalue[1] = evalue[0];
484     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
485 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
486     ra[0] = ra[1] = maxarad;
487     return;
488     }
489 greg 2.27 if (evalue[0] > evalue[1]) {
490 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
491     ra[1] = sqrt(sqrt(4.0/evalue[1]));
492 greg 2.27 slope1 = evalue[1];
493     } else {
494 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
495     ra[1] = sqrt(sqrt(4.0/evalue[0]));
496 greg 2.27 slope1 = evalue[0];
497     }
498     /* compute unit eigenvectors */
499     if (fabs(hess2[0][1]) <= FTINY)
500     return; /* uv OK as is */
501     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
502     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
503     for (i = 3; i--; ) {
504     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
505     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
506     }
507     VCOPY(uv[0], a);
508     VCOPY(uv[1], b);
509     }
510    
511    
512 greg 2.26 static void
513     ambHessian( /* anisotropic radii & pos. gradient */
514     AMBHEMI *hp,
515     FVECT uv[2], /* returned */
516 greg 2.28 float ra[2], /* returned (optional) */
517     float pg[2] /* returned (optional) */
518 greg 2.26 )
519     {
520 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
521     FVECT (*hessrow)[3] = NULL;
522     FVECT *gradrow = NULL;
523     FVECT hessian[3];
524     FVECT gradient;
525     FFTRI fftr;
526     int i, j;
527     /* be sure to assign unit vectors */
528     VCOPY(uv[0], hp->ux);
529     VCOPY(uv[1], hp->uy);
530     /* clock-wise vertex traversal from sample POV */
531     if (ra != NULL) { /* initialize Hessian row buffer */
532 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
533 greg 2.27 if (hessrow == NULL)
534     error(SYSTEM, memerrmsg);
535     memset(hessian, 0, sizeof(hessian));
536     } else if (pg == NULL) /* bogus call? */
537     return;
538     if (pg != NULL) { /* initialize form factor row buffer */
539 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
540 greg 2.27 if (gradrow == NULL)
541     error(SYSTEM, memerrmsg);
542     memset(gradient, 0, sizeof(gradient));
543     }
544     /* compute first row of edges */
545     for (j = 0; j < hp->ns-1; j++) {
546 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
547 greg 2.27 if (hessrow != NULL)
548     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
549     if (gradrow != NULL)
550     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
551     }
552     /* sum each row of triangles */
553     for (i = 0; i < hp->ns-1; i++) {
554     FVECT hesscol[3]; /* compute first vertical edge */
555     FVECT gradcol;
556 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
557 greg 2.27 if (hessrow != NULL)
558     comp_hessian(hesscol, &fftr, hp->rp->ron);
559     if (gradrow != NULL)
560     comp_gradient(gradcol, &fftr, hp->rp->ron);
561     for (j = 0; j < hp->ns-1; j++) {
562     FVECT hessdia[3]; /* compute triangle contributions */
563     FVECT graddia;
564 greg 2.46 double backg;
565 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
566     AI(hp,i,j+1), AI(hp,i+1,j));
567 greg 2.27 /* diagonal (inner) edge */
568 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
569 greg 2.27 if (hessrow != NULL) {
570     comp_hessian(hessdia, &fftr, hp->rp->ron);
571     rev_hessian(hesscol);
572     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
573     }
574 greg 2.39 if (gradrow != NULL) {
575 greg 2.27 comp_gradient(graddia, &fftr, hp->rp->ron);
576     rev_gradient(gradcol);
577     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
578     }
579     /* initialize edge in next row */
580 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
581 greg 2.27 if (hessrow != NULL)
582     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
583     if (gradrow != NULL)
584     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
585     /* new column edge & paired triangle */
586 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
587     AI(hp,i+1,j), AI(hp,i,j+1));
588     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
589 greg 2.27 if (hessrow != NULL) {
590     comp_hessian(hesscol, &fftr, hp->rp->ron);
591     rev_hessian(hessdia);
592     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
593     if (i < hp->ns-2)
594     rev_hessian(hessrow[j]);
595     }
596     if (gradrow != NULL) {
597     comp_gradient(gradcol, &fftr, hp->rp->ron);
598     rev_gradient(graddia);
599     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
600     if (i < hp->ns-2)
601     rev_gradient(gradrow[j]);
602     }
603     }
604     }
605     /* release row buffers */
606     if (hessrow != NULL) free(hessrow);
607     if (gradrow != NULL) free(gradrow);
608    
609     if (ra != NULL) /* extract eigenvectors & radii */
610     eigenvectors(uv, ra, hessian);
611 greg 2.32 if (pg != NULL) { /* tangential position gradient */
612     pg[0] = DOT(gradient, uv[0]);
613     pg[1] = DOT(gradient, uv[1]);
614 greg 2.27 }
615     }
616    
617    
618     /* Compute direction gradient from a hemispherical sampling */
619     static void
620     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
621     {
622 greg 2.41 AMBSAMP *ap;
623     double dgsum[2];
624     int n;
625     FVECT vd;
626     double gfact;
627 greg 2.27
628 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
629 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
630     /* use vector for azimuth + 90deg */
631     VSUB(vd, ap->p, hp->rp->rop);
632 greg 2.29 /* brightness over cosine factor */
633     gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
634 greg 2.40 /* sine = proj_radius/vd_length */
635     dgsum[0] -= DOT(uv[1], vd) * gfact;
636     dgsum[1] += DOT(uv[0], vd) * gfact;
637 greg 2.26 }
638 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
639     dg[1] = dgsum[1] / (hp->ns*hp->ns);
640 greg 2.26 }
641    
642 greg 2.27
643 greg 2.49 /* Compute potential light leak direction flags for cache value */
644     static uint32
645     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
646 greg 2.47 {
647 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
648 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
649     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
650 greg 2.51 double avg_d = 0;
651 greg 2.50 uint32 flgs = 0;
652 greg 2.58 FVECT vec;
653 greg 2.62 double u, v;
654 greg 2.58 double ang, a1;
655 greg 2.50 int i, j;
656 greg 2.52 /* don't bother for a few samples */
657 greg 2.72 if (hp->ns < 8)
658 greg 2.52 return(0);
659     /* check distances overhead */
660 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
661     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
662     avg_d += ambsam(hp,i,j).d;
663     avg_d *= 4.0/(hp->ns*hp->ns);
664 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
665     return(0);
666     if (avg_d >= max_d) /* insurance */
667 greg 2.51 return(0);
668     /* else circle around perimeter */
669 greg 2.47 for (i = 0; i < hp->ns; i++)
670     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
671     AMBSAMP *ap = &ambsam(hp,i,j);
672 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
673     continue; /* too far or too near */
674 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
675 greg 2.62 u = DOT(vec, uv[0]);
676     v = DOT(vec, uv[1]);
677     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
678 greg 2.49 continue; /* occluder outside ellipse */
679     ang = atan2a(v, u); /* else set direction flags */
680 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
681 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
682 greg 2.47 }
683 greg 2.49 return(flgs);
684 greg 2.47 }
685    
686    
687 greg 2.26 int
688     doambient( /* compute ambient component */
689     COLOR rcol, /* input/output color */
690     RAY *r,
691     double wt,
692 greg 2.27 FVECT uv[2], /* returned (optional) */
693     float ra[2], /* returned (optional) */
694     float pg[2], /* returned (optional) */
695 greg 2.49 float dg[2], /* returned (optional) */
696     uint32 *crlp /* returned (optional) */
697 greg 2.26 )
698     {
699 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
700 greg 2.41 FVECT my_uv[2];
701 greg 2.61 double d, K;
702 greg 2.41 AMBSAMP *ap;
703 greg 2.61 int i;
704     /* clear return values */
705 greg 2.26 if (uv != NULL)
706     memset(uv, 0, sizeof(FVECT)*2);
707     if (ra != NULL)
708     ra[0] = ra[1] = 0.0;
709     if (pg != NULL)
710     pg[0] = pg[1] = 0.0;
711     if (dg != NULL)
712     dg[0] = dg[1] = 0.0;
713 greg 2.49 if (crlp != NULL)
714     *crlp = 0;
715 greg 2.61 if (hp == NULL) /* sampling falure? */
716     return(0);
717    
718     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
719 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
720 greg 2.61 free(hp); /* Hessian not requested/possible */
721     return(-1); /* value-only return value */
722 greg 2.26 }
723 greg 2.61 if ((d = bright(rcol)) > FTINY) { /* normalize Y values */
724 greg 2.45 d = 0.99*(hp->ns*hp->ns)/d;
725 greg 2.38 K = 0.01;
726 greg 2.45 } else { /* or fall back on geometric Hessian */
727 greg 2.38 K = 1.0;
728     pg = NULL;
729     dg = NULL;
730 greg 2.53 crlp = NULL;
731 greg 2.38 }
732 greg 2.29 ap = hp->sa; /* relative Y channel from here on... */
733 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
734 greg 2.38 colval(ap->v,CIEY) = bright(ap->v)*d + K;
735 greg 2.26
736     if (uv == NULL) /* make sure we have axis pointers */
737     uv = my_uv;
738     /* compute radii & pos. gradient */
739     ambHessian(hp, uv, ra, pg);
740 greg 2.29
741 greg 2.26 if (dg != NULL) /* compute direction gradient */
742     ambdirgrad(hp, uv, dg);
743 greg 2.29
744 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
745 greg 2.35 if (pg != NULL) {
746     if (ra[0]*(d = fabs(pg[0])) > 1.0)
747     ra[0] = 1.0/d;
748     if (ra[1]*(d = fabs(pg[1])) > 1.0)
749     ra[1] = 1.0/d;
750 greg 2.48 if (ra[0] > ra[1])
751     ra[0] = ra[1];
752 greg 2.35 }
753 greg 2.29 if (ra[0] < minarad) {
754     ra[0] = minarad;
755     if (ra[1] < minarad)
756     ra[1] = minarad;
757     }
758 greg 2.60 ra[0] *= d = 1.0/sqrt(wt);
759 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
760     ra[1] = 2.0*ra[0];
761 greg 2.28 if (ra[1] > maxarad) {
762     ra[1] = maxarad;
763     if (ra[0] > maxarad)
764     ra[0] = maxarad;
765     }
766 greg 2.53 /* flag encroached directions */
767 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
768 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
769 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
770     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
771     if (d > 1.0) {
772     d = 1.0/sqrt(d);
773     pg[0] *= d;
774     pg[1] *= d;
775     }
776     }
777 greg 2.26 }
778     free(hp); /* clean up and return */
779     return(1);
780     }