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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.93
Committed: Tue Apr 16 23:32:20 2024 UTC (7 weeks, 5 days ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.92: +37 -11 lines
Log Message: 
perf(rpict,rtrace,rvu): Improved ambient sampling (-as) to reduce bias

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.93 static const char RCSid[] = "$Id: ambcomp.c,v 2.92 2024/04/05 01:10:26 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 2.88 RREAL spt[2];
104     double zd;
105 greg 2.61 /* generate hemispherical sample */
106 greg 2.26 /* ambient coefficient for weight */
107     if (ambacc > FTINY)
108 greg 2.90 setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
109 greg 2.26 else
110 greg 2.90 copyscolor(ar.rcoef, hp->acoef);
111 greg 2.92 if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0)
112 greg 2.41 return(0);
113 greg 2.26 if (ambacc > FTINY) {
114 greg 2.90 smultscolor(ar.rcoef, hp->acoef);
115     scalescolor(ar.rcoef, 1./AVGREFL);
116 greg 2.41 }
117     hlist[0] = hp->rp->rno;
118 greg 2.46 hlist[1] = j;
119     hlist[2] = i;
120 greg 2.41 multisamp(spt, 2, urand(ilhash(hlist,3)+n));
121 greg 2.73 resample:
122 greg 2.88 square2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
123 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
124     for (ii = 3; ii--; )
125 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
126 greg 2.26 spt[1]*hp->uy[ii] +
127 greg 2.92 zd*hp->onrm[ii];
128 greg 2.61 checknorm(ar.rdir);
129 greg 2.73 /* avoid coincident samples */
130     if (!n && ambcollision(hp, i, j, ar.rdir)) {
131     spt[0] = frandom(); spt[1] = frandom();
132 greg 2.75 goto resample; /* reject this sample */
133 greg 2.73 }
134 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
135 greg 2.61 rayvalue(&ar); /* evaluate ray */
136     ndims--;
137 greg 2.83 zd = raydistance(&ar);
138     if (zd <= FTINY)
139 greg 2.61 return(0); /* should never happen */
140 greg 2.90 smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */
141 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
142     ap->d = 1.0/zd;
143 greg 2.61 if (!n) { /* record first vertex & value */
144 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
145     zd = 10.0*thescene.cusize + 1000.;
146     VSUM(ap->p, ar.rorg, ar.rdir, zd);
147 greg 2.90 copyscolor(ap->v, ar.rcol);
148 greg 2.61 } else { /* else update recorded value */
149 greg 2.90 sopscolor(hp->acol, -=, ap->v);
150 greg 2.61 zd = 1.0/(double)(n+1);
151 greg 2.90 scalescolor(ar.rcol, zd);
152 greg 2.61 zd *= (double)n;
153 greg 2.90 scalescolor(ap->v, zd);
154     saddscolor(ap->v, ar.rcol);
155 greg 2.61 }
156 greg 2.90 saddscolor(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 2.93 const double normf = 1./(pbright(hp->acoef) + FTINY);
166 greg 2.55 float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
167 greg 2.93 float *ep, *earr2;
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 greg 2.90 b = pbright(ap[0].v);
178 greg 2.41 if (i) { /* from above */
179 greg 2.90 b1 = pbright(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 2.90 b1 = pbright(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 2.90 b1 = pbright(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 2.93 earr[0] *= 6./3.;
202     earr[hp->ns-1] *= 6./3.;
203     earr[(hp->ns-1)*hp->ns] *= 6./3.;
204     earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.;
205 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
206 greg 2.93 earr[i*hp->ns] *= 6./5.;
207     earr[i*hp->ns + hp->ns-1] *= 6./5.;
208 greg 2.41 }
209     for (j = 1; j < hp->ns-1; j++) {
210 greg 2.93 earr[j] *= 6./5.;
211     earr[(hp->ns-1)*hp->ns + j] *= 6./5.;
212     }
213     /* preen map to avoid cliffs */
214     earr2 = (float *)malloc(hp->ns*hp->ns*sizeof(float));
215     if (earr2 == NULL)
216     return(earr);
217     memcpy(earr2, earr, hp->ns*hp->ns*sizeof(float));
218     for (i = 0; i < hp->ns-1; i++) {
219     float *ep2 = earr2 + i*hp->ns;
220     ep = earr + i*hp->ns;
221     for (j = 0; j < hp->ns-1; j++, ep2++, ep++) {
222     if (ep2[1] < .5*ep2[0]) {
223     ep[0] -= .125*ep2[0];
224     ep[1] += .125*ep2[0];
225     } else if (ep2[1] > 2.*ep2[0]) {
226     ep[1] -= .125*ep2[1];
227     ep[0] += .125*ep2[1];
228     }
229     if (ep2[hp->ns] < .5*ep2[0]) {
230     ep[0] -= .125*ep2[0];
231     ep[hp->ns] += .125*ep2[0];
232     } else if (ep2[hp->ns] > 2.*ep2[0]) {
233     ep[hp->ns] -= .125*ep2[hp->ns];
234     ep[0] += .125*ep2[hp->ns];
235     }
236     }
237 greg 2.41 }
238 greg 2.93 free(earr2);
239 greg 2.41 return(earr);
240     }
241    
242    
243 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
244 greg 2.41 static void
245 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
246 greg 2.41 {
247     float *earr = getambdiffs(hp);
248 greg 2.54 double e2rem = 0;
249 greg 2.41 float *ep;
250 greg 2.55 int i, j, n, nss;
251 greg 2.41
252     if (earr == NULL) /* just skip calc. if no memory */
253     return;
254 greg 2.54 /* accumulate estimated variances */
255 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
256     e2rem += *--ep;
257 greg 2.41 ep = earr; /* perform super-sampling */
258 greg 2.81 for (i = 0; i < hp->ns; i++)
259     for (j = 0; j < hp->ns; j++) {
260 greg 2.55 if (e2rem <= FTINY)
261     goto done; /* nothing left to do */
262     nss = *ep/e2rem*cnt + frandom();
263 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
264 greg 2.77 if (!--cnt) goto done;
265 greg 2.61 e2rem -= *ep++; /* update remainder */
266 greg 2.41 }
267 greg 2.55 done:
268 greg 2.41 free(earr);
269     }
270    
271    
272 greg 2.61 static AMBHEMI *
273     samp_hemi( /* sample indirect hemisphere */
274 greg 2.90 SCOLOR rcol,
275 greg 2.61 RAY *r,
276     double wt
277     )
278     {
279 greg 2.92 int backside = (wt < 0);
280 greg 2.61 AMBHEMI *hp;
281     double d;
282     int n, i, j;
283 greg 2.77 /* insignificance check */
284 greg 2.90 d = sintens(rcol);
285     if (d <= FTINY)
286 greg 2.77 return(NULL);
287 greg 2.61 /* set number of divisions */
288 greg 2.92 if (backside) wt = -wt;
289 greg 2.61 if (ambacc <= FTINY &&
290 greg 2.90 wt > (d *= 0.8*r->rweight/(ambdiv*minweight)))
291 greg 2.61 wt = d; /* avoid ray termination */
292     n = sqrt(ambdiv * wt) + 0.5;
293 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
294     if (n < i) /* use minimum number of samples? */
295 greg 2.61 n = i;
296     /* allocate sampling array */
297     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
298     if (hp == NULL)
299     error(SYSTEM, "out of memory in samp_hemi");
300 greg 2.92
301     if (backside) {
302     hp->atyp = TAMBIENT;
303     hp->onrm[0] = -r->ron[0];
304     hp->onrm[1] = -r->ron[1];
305     hp->onrm[2] = -r->ron[2];
306     } else {
307     hp->atyp = RAMBIENT;
308     VCOPY(hp->onrm, r->ron);
309     }
310 greg 2.61 hp->rp = r;
311     hp->ns = n;
312 greg 2.90 scolorblack(hp->acol);
313 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
314 greg 2.61 hp->sampOK = 0;
315     /* assign coefficient */
316 greg 2.90 copyscolor(hp->acoef, rcol);
317 greg 2.61 d = 1.0/(n*n);
318 greg 2.90 scalescolor(hp->acoef, d);
319 greg 2.61 /* make tangent plane axes */
320 greg 2.92 if (!getperpendicular(hp->ux, hp->onrm, 1))
321 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
322 greg 2.92 VCROSS(hp->uy, hp->onrm, hp->ux);
323 greg 2.61 /* sample divisions */
324     for (i = hp->ns; i--; )
325     for (j = hp->ns; j--; )
326     hp->sampOK += ambsample(hp, i, j, 0);
327 greg 2.90 copyscolor(rcol, hp->acol);
328 greg 2.61 if (!hp->sampOK) { /* utter failure? */
329     free(hp);
330     return(NULL);
331     }
332     if (hp->sampOK < hp->ns*hp->ns) {
333     hp->sampOK *= -1; /* soft failure */
334     return(hp);
335     }
336 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
337     return(hp); /* don't bother super-sampling */
338 greg 2.61 n = ambssamp*wt + 0.5;
339     if (n > 8) { /* perform super-sampling? */
340     ambsupersamp(hp, n);
341 greg 2.90 copyscolor(rcol, hp->acol);
342 greg 2.61 }
343     return(hp); /* all is well */
344     }
345    
346    
347 greg 2.46 /* Return brightness of farthest ambient sample */
348     static double
349 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
350 greg 2.46 {
351 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
352     if (hp->sa[n1].d <= hp->sa[n3].d)
353 greg 2.90 return(hp->sa[n1].v[0]);
354     return(hp->sa[n3].v[0]);
355 greg 2.56 }
356     if (hp->sa[n2].d <= hp->sa[n3].d)
357 greg 2.90 return(hp->sa[n2].v[0]);
358     return(hp->sa[n3].v[0]);
359 greg 2.46 }
360    
361    
362 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
363     static void
364 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
365 greg 2.27 {
366 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
367     int ii;
368    
369     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
370     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
371     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
372 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
373     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
374 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
375     dot_er = DOT(ftp->e_i, ftp->r_i);
376 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
377     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
378     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
379 greg 2.35 sqrt( rdot_cp );
380 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
381 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
382 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
383 greg 2.46 for (ii = 3; ii--; )
384     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
385 greg 2.27 }
386    
387    
388 greg 2.28 /* Compose 3x3 matrix from two vectors */
389 greg 2.27 static void
390     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
391     {
392     mat[0][0] = 2.0*va[0]*vb[0];
393     mat[1][1] = 2.0*va[1]*vb[1];
394     mat[2][2] = 2.0*va[2]*vb[2];
395     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
396     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
397     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
398     }
399    
400    
401     /* Compute partial 3x3 Hessian matrix for edge */
402     static void
403     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
404     {
405 greg 2.35 FVECT ncp;
406 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
407     double d1, d2, d3, d4;
408     double I3, J3, K3;
409     int i, j;
410     /* compute intermediate coefficients */
411     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
412     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
413     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
414     d4 = DOT(ftp->e_i, ftp->r_i);
415 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
416     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
417 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
418     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
419     /* intermediate matrices */
420 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
421     compose_matrix(m1, ncp, ftp->rI2_eJ2);
422 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
423     compose_matrix(m3, ftp->e_i, ftp->e_i);
424     compose_matrix(m4, ftp->r_i, ftp->e_i);
425 greg 2.35 d1 = DOT(nrm, ftp->rcp);
426 greg 2.27 d2 = -d1*ftp->I2;
427     d1 *= 2.0;
428     for (i = 3; i--; ) /* final matrix sum */
429     for (j = 3; j--; ) {
430     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
431     2.0*J3*m4[i][j] );
432     hess[i][j] += d2*(i==j);
433 greg 2.46 hess[i][j] *= -1.0/PI;
434 greg 2.27 }
435     }
436    
437    
438     /* Reverse hessian calculation result for edge in other direction */
439     static void
440     rev_hessian(FVECT hess[3])
441     {
442     int i;
443    
444     for (i = 3; i--; ) {
445     hess[i][0] = -hess[i][0];
446     hess[i][1] = -hess[i][1];
447     hess[i][2] = -hess[i][2];
448     }
449     }
450    
451    
452     /* Add to radiometric Hessian from the given triangle */
453     static void
454     add2hessian(FVECT hess[3], FVECT ehess1[3],
455 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
456 greg 2.27 {
457     int i, j;
458    
459     for (i = 3; i--; )
460     for (j = 3; j--; )
461     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
462     }
463    
464    
465     /* Compute partial displacement form factor gradient for edge */
466     static void
467     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
468     {
469 greg 2.35 FVECT ncp;
470 greg 2.27 double f1;
471     int i;
472    
473 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
474     VCROSS(ncp, nrm, ftp->e_i);
475 greg 2.27 for (i = 3; i--; )
476 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
477 greg 2.27 }
478    
479    
480     /* Reverse gradient calculation result for edge in other direction */
481     static void
482     rev_gradient(FVECT grad)
483     {
484     grad[0] = -grad[0];
485     grad[1] = -grad[1];
486     grad[2] = -grad[2];
487     }
488    
489    
490     /* Add to displacement gradient from the given triangle */
491     static void
492 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
493 greg 2.27 {
494     int i;
495    
496     for (i = 3; i--; )
497     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
498     }
499    
500    
501     /* Compute anisotropic radii and eigenvector directions */
502 greg 2.53 static void
503 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
504     {
505     double hess2[2][2];
506     FVECT a, b;
507     double evalue[2], slope1, xmag1;
508     int i;
509     /* project Hessian to sample plane */
510     for (i = 3; i--; ) {
511     a[i] = DOT(hessian[i], uv[0]);
512     b[i] = DOT(hessian[i], uv[1]);
513     }
514     hess2[0][0] = DOT(uv[0], a);
515     hess2[0][1] = DOT(uv[0], b);
516     hess2[1][0] = DOT(uv[1], a);
517     hess2[1][1] = DOT(uv[1], b);
518 greg 2.38 /* compute eigenvalue(s) */
519     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
520     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
521     if (i == 1) /* double-root (circle) */
522     evalue[1] = evalue[0];
523     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
524 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
525     ra[0] = ra[1] = maxarad;
526     return;
527     }
528 greg 2.27 if (evalue[0] > evalue[1]) {
529 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
530     ra[1] = sqrt(sqrt(4.0/evalue[1]));
531 greg 2.27 slope1 = evalue[1];
532     } else {
533 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
534     ra[1] = sqrt(sqrt(4.0/evalue[0]));
535 greg 2.27 slope1 = evalue[0];
536     }
537     /* compute unit eigenvectors */
538     if (fabs(hess2[0][1]) <= FTINY)
539     return; /* uv OK as is */
540     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
541     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
542     for (i = 3; i--; ) {
543     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
544     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
545     }
546     VCOPY(uv[0], a);
547     VCOPY(uv[1], b);
548     }
549    
550    
551 greg 2.26 static void
552     ambHessian( /* anisotropic radii & pos. gradient */
553     AMBHEMI *hp,
554     FVECT uv[2], /* returned */
555 greg 2.28 float ra[2], /* returned (optional) */
556     float pg[2] /* returned (optional) */
557 greg 2.26 )
558     {
559 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
560     FVECT (*hessrow)[3] = NULL;
561     FVECT *gradrow = NULL;
562     FVECT hessian[3];
563     FVECT gradient;
564     FFTRI fftr;
565     int i, j;
566     /* be sure to assign unit vectors */
567     VCOPY(uv[0], hp->ux);
568     VCOPY(uv[1], hp->uy);
569     /* clock-wise vertex traversal from sample POV */
570     if (ra != NULL) { /* initialize Hessian row buffer */
571 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
572 greg 2.27 if (hessrow == NULL)
573     error(SYSTEM, memerrmsg);
574     memset(hessian, 0, sizeof(hessian));
575     } else if (pg == NULL) /* bogus call? */
576     return;
577     if (pg != NULL) { /* initialize form factor row buffer */
578 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
579 greg 2.27 if (gradrow == NULL)
580     error(SYSTEM, memerrmsg);
581     memset(gradient, 0, sizeof(gradient));
582     }
583     /* compute first row of edges */
584     for (j = 0; j < hp->ns-1; j++) {
585 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
586 greg 2.27 if (hessrow != NULL)
587 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
588 greg 2.27 if (gradrow != NULL)
589 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
590 greg 2.27 }
591     /* sum each row of triangles */
592     for (i = 0; i < hp->ns-1; i++) {
593     FVECT hesscol[3]; /* compute first vertical edge */
594     FVECT gradcol;
595 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
596 greg 2.27 if (hessrow != NULL)
597 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
598 greg 2.27 if (gradrow != NULL)
599 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
600 greg 2.27 for (j = 0; j < hp->ns-1; j++) {
601     FVECT hessdia[3]; /* compute triangle contributions */
602     FVECT graddia;
603 greg 2.46 double backg;
604 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
605     AI(hp,i,j+1), AI(hp,i+1,j));
606 greg 2.27 /* diagonal (inner) edge */
607 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
608 greg 2.27 if (hessrow != NULL) {
609 greg 2.92 comp_hessian(hessdia, &fftr, hp->onrm);
610 greg 2.27 rev_hessian(hesscol);
611     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
612     }
613 greg 2.39 if (gradrow != NULL) {
614 greg 2.92 comp_gradient(graddia, &fftr, hp->onrm);
615 greg 2.27 rev_gradient(gradcol);
616     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
617     }
618     /* initialize edge in next row */
619 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
620 greg 2.27 if (hessrow != NULL)
621 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
622 greg 2.27 if (gradrow != NULL)
623 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
624 greg 2.27 /* new column edge & paired triangle */
625 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
626     AI(hp,i+1,j), AI(hp,i,j+1));
627     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
628 greg 2.27 if (hessrow != NULL) {
629 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
630 greg 2.27 rev_hessian(hessdia);
631     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
632     if (i < hp->ns-2)
633     rev_hessian(hessrow[j]);
634     }
635     if (gradrow != NULL) {
636 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
637 greg 2.27 rev_gradient(graddia);
638     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
639     if (i < hp->ns-2)
640     rev_gradient(gradrow[j]);
641     }
642     }
643     }
644     /* release row buffers */
645     if (hessrow != NULL) free(hessrow);
646     if (gradrow != NULL) free(gradrow);
647    
648     if (ra != NULL) /* extract eigenvectors & radii */
649     eigenvectors(uv, ra, hessian);
650 greg 2.32 if (pg != NULL) { /* tangential position gradient */
651     pg[0] = DOT(gradient, uv[0]);
652     pg[1] = DOT(gradient, uv[1]);
653 greg 2.27 }
654     }
655    
656    
657     /* Compute direction gradient from a hemispherical sampling */
658     static void
659     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
660     {
661 greg 2.41 AMBSAMP *ap;
662     double dgsum[2];
663     int n;
664     FVECT vd;
665     double gfact;
666 greg 2.27
667 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
668 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
669     /* use vector for azimuth + 90deg */
670     VSUB(vd, ap->p, hp->rp->rop);
671 greg 2.29 /* brightness over cosine factor */
672 greg 2.92 gfact = ap->v[0] / DOT(hp->onrm, vd);
673 greg 2.40 /* sine = proj_radius/vd_length */
674     dgsum[0] -= DOT(uv[1], vd) * gfact;
675     dgsum[1] += DOT(uv[0], vd) * gfact;
676 greg 2.26 }
677 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
678     dg[1] = dgsum[1] / (hp->ns*hp->ns);
679 greg 2.26 }
680    
681 greg 2.27
682 greg 2.49 /* Compute potential light leak direction flags for cache value */
683     static uint32
684     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
685 greg 2.47 {
686 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
687 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
688     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
689 greg 2.51 double avg_d = 0;
690 greg 2.50 uint32 flgs = 0;
691 greg 2.58 FVECT vec;
692 greg 2.62 double u, v;
693 greg 2.58 double ang, a1;
694 greg 2.50 int i, j;
695 greg 2.52 /* don't bother for a few samples */
696 greg 2.72 if (hp->ns < 8)
697 greg 2.52 return(0);
698     /* check distances overhead */
699 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
700     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
701     avg_d += ambsam(hp,i,j).d;
702     avg_d *= 4.0/(hp->ns*hp->ns);
703 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
704     return(0);
705     if (avg_d >= max_d) /* insurance */
706 greg 2.51 return(0);
707     /* else circle around perimeter */
708 greg 2.47 for (i = 0; i < hp->ns; i++)
709     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
710     AMBSAMP *ap = &ambsam(hp,i,j);
711 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
712     continue; /* too far or too near */
713 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
714 greg 2.62 u = DOT(vec, uv[0]);
715     v = DOT(vec, uv[1]);
716     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
717 greg 2.49 continue; /* occluder outside ellipse */
718     ang = atan2a(v, u); /* else set direction flags */
719 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
720 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
721 greg 2.47 }
722 greg 2.49 return(flgs);
723 greg 2.47 }
724    
725    
726 greg 2.26 int
727     doambient( /* compute ambient component */
728 greg 2.90 SCOLOR rcol, /* input/output color */
729 greg 2.26 RAY *r,
730 greg 2.92 double wt, /* negative for back side */
731 greg 2.27 FVECT uv[2], /* returned (optional) */
732     float ra[2], /* returned (optional) */
733     float pg[2], /* returned (optional) */
734 greg 2.49 float dg[2], /* returned (optional) */
735     uint32 *crlp /* returned (optional) */
736 greg 2.26 )
737     {
738 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
739 greg 2.41 FVECT my_uv[2];
740 greg 2.61 double d, K;
741 greg 2.41 AMBSAMP *ap;
742 greg 2.61 int i;
743     /* clear return values */
744 greg 2.26 if (uv != NULL)
745     memset(uv, 0, sizeof(FVECT)*2);
746     if (ra != NULL)
747     ra[0] = ra[1] = 0.0;
748     if (pg != NULL)
749     pg[0] = pg[1] = 0.0;
750     if (dg != NULL)
751     dg[0] = dg[1] = 0.0;
752 greg 2.49 if (crlp != NULL)
753     *crlp = 0;
754 greg 2.61 if (hp == NULL) /* sampling falure? */
755     return(0);
756    
757     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
758 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
759 greg 2.61 free(hp); /* Hessian not requested/possible */
760     return(-1); /* value-only return value */
761 greg 2.26 }
762 greg 2.91 if ((d = scolor_mean(rcol)) > FTINY) {
763     d = 0.99*(hp->ns*hp->ns)/d; /* normalize avg. values */
764 greg 2.38 K = 0.01;
765 greg 2.45 } else { /* or fall back on geometric Hessian */
766 greg 2.38 K = 1.0;
767     pg = NULL;
768     dg = NULL;
769 greg 2.53 crlp = NULL;
770 greg 2.38 }
771 greg 2.90 ap = hp->sa; /* single channel from here on... */
772 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
773 greg 2.90 ap->v[0] = scolor_mean(ap->v)*d + K;
774 greg 2.26
775     if (uv == NULL) /* make sure we have axis pointers */
776     uv = my_uv;
777     /* compute radii & pos. gradient */
778     ambHessian(hp, uv, ra, pg);
779 greg 2.29
780 greg 2.26 if (dg != NULL) /* compute direction gradient */
781     ambdirgrad(hp, uv, dg);
782 greg 2.29
783 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
784 greg 2.35 if (pg != NULL) {
785     if (ra[0]*(d = fabs(pg[0])) > 1.0)
786     ra[0] = 1.0/d;
787     if (ra[1]*(d = fabs(pg[1])) > 1.0)
788     ra[1] = 1.0/d;
789 greg 2.48 if (ra[0] > ra[1])
790     ra[0] = ra[1];
791 greg 2.35 }
792 greg 2.29 if (ra[0] < minarad) {
793     ra[0] = minarad;
794     if (ra[1] < minarad)
795     ra[1] = minarad;
796     }
797 greg 2.92 ra[0] *= d = 1.0/sqrt(fabs(wt));
798 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
799     ra[1] = 2.0*ra[0];
800 greg 2.28 if (ra[1] > maxarad) {
801     ra[1] = maxarad;
802     if (ra[0] > maxarad)
803     ra[0] = maxarad;
804     }
805 greg 2.53 /* flag encroached directions */
806 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
807 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
808 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
809     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
810     if (d > 1.0) {
811     d = 1.0/sqrt(d);
812     pg[0] *= d;
813     pg[1] *= d;
814     }
815     }
816 greg 2.26 }
817     free(hp); /* clean up and return */
818     return(1);
819     }