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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.86
Committed: Wed Feb 17 01:29:22 2021 UTC (3 years, 2 months ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.85: +10 -6 lines
Log Message: 
perf: slight increase in ambient sampling accuracy

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.86 static const char RCSid[] = "$Id: ambcomp.c,v 2.85 2019/05/14 17:39:10 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 extern void SDsquare2disk(double ds[2], double seedx, double seedy);
29    
30     typedef struct {
31 greg 2.44 COLOR v; /* hemisphere sample value */
32 greg 2.83 float d; /* reciprocal distance */
33 greg 2.44 FVECT p; /* intersection point */
34     } AMBSAMP; /* sample value */
35    
36     typedef struct {
37 greg 2.26 RAY *rp; /* originating ray sample */
38     int ns; /* number of samples per axis */
39 greg 2.61 int sampOK; /* acquired full sample set? */
40 greg 2.26 COLOR acoef; /* division contribution coefficient */
41 greg 2.61 double acol[3]; /* accumulated color */
42     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     double spt[2], zd;
104 greg 2.61 /* generate hemispherical sample */
105 greg 2.26 /* ambient coefficient for weight */
106     if (ambacc > FTINY)
107 greg 2.61 setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
108 greg 2.26 else
109 greg 2.61 copycolor(ar.rcoef, hp->acoef);
110 greg 2.62 if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0)
111 greg 2.41 return(0);
112 greg 2.26 if (ambacc > FTINY) {
113 greg 2.61 multcolor(ar.rcoef, hp->acoef);
114     scalecolor(ar.rcoef, 1./AVGREFL);
115 greg 2.41 }
116     hlist[0] = hp->rp->rno;
117 greg 2.46 hlist[1] = j;
118     hlist[2] = i;
119 greg 2.41 multisamp(spt, 2, urand(ilhash(hlist,3)+n));
120 greg 2.73 resample:
121 greg 2.46 SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
122 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
123     for (ii = 3; ii--; )
124 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
125 greg 2.26 spt[1]*hp->uy[ii] +
126     zd*hp->rp->ron[ii];
127 greg 2.61 checknorm(ar.rdir);
128 greg 2.73 /* avoid coincident samples */
129     if (!n && ambcollision(hp, i, j, ar.rdir)) {
130     spt[0] = frandom(); spt[1] = frandom();
131 greg 2.75 goto resample; /* reject this sample */
132 greg 2.73 }
133 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
134 greg 2.61 rayvalue(&ar); /* evaluate ray */
135     ndims--;
136 greg 2.83 zd = raydistance(&ar);
137     if (zd <= FTINY)
138 greg 2.61 return(0); /* should never happen */
139     multcolor(ar.rcol, ar.rcoef); /* apply coefficient */
140 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
141     ap->d = 1.0/zd;
142 greg 2.61 if (!n) { /* record first vertex & value */
143 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
144     zd = 10.0*thescene.cusize + 1000.;
145     VSUM(ap->p, ar.rorg, ar.rdir, zd);
146 greg 2.61 copycolor(ap->v, ar.rcol);
147     } else { /* else update recorded value */
148     hp->acol[RED] -= colval(ap->v,RED);
149     hp->acol[GRN] -= colval(ap->v,GRN);
150     hp->acol[BLU] -= colval(ap->v,BLU);
151     zd = 1.0/(double)(n+1);
152     scalecolor(ar.rcol, zd);
153     zd *= (double)n;
154     scalecolor(ap->v, zd);
155     addcolor(ap->v, ar.rcol);
156     }
157     addcolor(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 2.77 const double normf = 1./bright(hp->acoef);
167 greg 2.55 float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
168 greg 2.41 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     b = bright(ap[0].v);
179 greg 2.41 if (i) { /* from above */
180 greg 2.81 b1 = bright(ap[-hp->ns].v);
181 greg 2.82 d2 = b - b1;
182     d2 *= d2*normf/(b + b1);
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 2.81 b1 = bright(ap[-1].v);
189 greg 2.82 d2 = b - b1;
190     d2 *= d2*normf/(b + b1);
191 greg 2.55 ep[0] += d2;
192     ep[-1] += d2;
193     if (!i) continue;
194     /* diagonal */
195 greg 2.81 b1 = bright(ap[-hp->ns-1].v);
196 greg 2.82 d2 = b - b1;
197     d2 *= d2*normf/(b + b1);
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 2.55 earr[0] *= 8./3.;
203     earr[hp->ns-1] *= 8./3.;
204     earr[(hp->ns-1)*hp->ns] *= 8./3.;
205     earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.;
206 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
207 greg 2.55 earr[i*hp->ns] *= 8./5.;
208     earr[i*hp->ns + hp->ns-1] *= 8./5.;
209 greg 2.41 }
210     for (j = 1; j < hp->ns-1; j++) {
211 greg 2.55 earr[j] *= 8./5.;
212     earr[(hp->ns-1)*hp->ns + j] *= 8./5.;
213 greg 2.41 }
214     return(earr);
215     }
216    
217    
218 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
219 greg 2.41 static void
220 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
221 greg 2.41 {
222     float *earr = getambdiffs(hp);
223 greg 2.54 double e2rem = 0;
224 greg 2.41 float *ep;
225 greg 2.55 int i, j, n, nss;
226 greg 2.41
227     if (earr == NULL) /* just skip calc. if no memory */
228     return;
229 greg 2.54 /* accumulate estimated variances */
230 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
231     e2rem += *--ep;
232 greg 2.41 ep = earr; /* perform super-sampling */
233 greg 2.81 for (i = 0; i < hp->ns; i++)
234     for (j = 0; j < hp->ns; j++) {
235 greg 2.55 if (e2rem <= FTINY)
236     goto done; /* nothing left to do */
237     nss = *ep/e2rem*cnt + frandom();
238 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
239 greg 2.77 if (!--cnt) goto done;
240 greg 2.61 e2rem -= *ep++; /* update remainder */
241 greg 2.41 }
242 greg 2.55 done:
243 greg 2.41 free(earr);
244     }
245    
246    
247 greg 2.61 static AMBHEMI *
248     samp_hemi( /* sample indirect hemisphere */
249     COLOR rcol,
250     RAY *r,
251     double wt
252     )
253     {
254     AMBHEMI *hp;
255     double d;
256     int n, i, j;
257 greg 2.77 /* insignificance check */
258     if (bright(rcol) <= FTINY)
259     return(NULL);
260 greg 2.61 /* set number of divisions */
261     if (ambacc <= FTINY &&
262     wt > (d = 0.8*intens(rcol)*r->rweight/(ambdiv*minweight)))
263     wt = d; /* avoid ray termination */
264     n = sqrt(ambdiv * wt) + 0.5;
265 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
266     if (n < i) /* use minimum number of samples? */
267 greg 2.61 n = i;
268     /* allocate sampling array */
269     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
270     if (hp == NULL)
271     error(SYSTEM, "out of memory in samp_hemi");
272     hp->rp = r;
273     hp->ns = n;
274     hp->acol[RED] = hp->acol[GRN] = hp->acol[BLU] = 0.0;
275 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
276 greg 2.61 hp->sampOK = 0;
277     /* assign coefficient */
278     copycolor(hp->acoef, rcol);
279     d = 1.0/(n*n);
280     scalecolor(hp->acoef, d);
281     /* make tangent plane axes */
282 greg 2.70 if (!getperpendicular(hp->ux, r->ron, 1))
283 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
284     VCROSS(hp->uy, r->ron, hp->ux);
285     /* sample divisions */
286     for (i = hp->ns; i--; )
287     for (j = hp->ns; j--; )
288     hp->sampOK += ambsample(hp, i, j, 0);
289     copycolor(rcol, hp->acol);
290     if (!hp->sampOK) { /* utter failure? */
291     free(hp);
292     return(NULL);
293     }
294     if (hp->sampOK < hp->ns*hp->ns) {
295     hp->sampOK *= -1; /* soft failure */
296     return(hp);
297     }
298 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
299     return(hp); /* don't bother super-sampling */
300 greg 2.61 n = ambssamp*wt + 0.5;
301     if (n > 8) { /* perform super-sampling? */
302     ambsupersamp(hp, n);
303     copycolor(rcol, hp->acol);
304     }
305     return(hp); /* all is well */
306     }
307    
308    
309 greg 2.46 /* Return brightness of farthest ambient sample */
310     static double
311 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
312 greg 2.46 {
313 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
314     if (hp->sa[n1].d <= hp->sa[n3].d)
315     return(colval(hp->sa[n1].v,CIEY));
316     return(colval(hp->sa[n3].v,CIEY));
317     }
318     if (hp->sa[n2].d <= hp->sa[n3].d)
319     return(colval(hp->sa[n2].v,CIEY));
320     return(colval(hp->sa[n3].v,CIEY));
321 greg 2.46 }
322    
323    
324 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
325     static void
326 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
327 greg 2.27 {
328 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
329     int ii;
330    
331     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
332     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
333     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
334 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
335     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
336 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
337     dot_er = DOT(ftp->e_i, ftp->r_i);
338 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
339     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
340     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
341 greg 2.35 sqrt( rdot_cp );
342 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
343 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
344 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
345 greg 2.46 for (ii = 3; ii--; )
346     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
347 greg 2.27 }
348    
349    
350 greg 2.28 /* Compose 3x3 matrix from two vectors */
351 greg 2.27 static void
352     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
353     {
354     mat[0][0] = 2.0*va[0]*vb[0];
355     mat[1][1] = 2.0*va[1]*vb[1];
356     mat[2][2] = 2.0*va[2]*vb[2];
357     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
358     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
359     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
360     }
361    
362    
363     /* Compute partial 3x3 Hessian matrix for edge */
364     static void
365     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
366     {
367 greg 2.35 FVECT ncp;
368 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
369     double d1, d2, d3, d4;
370     double I3, J3, K3;
371     int i, j;
372     /* compute intermediate coefficients */
373     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
374     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
375     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
376     d4 = DOT(ftp->e_i, ftp->r_i);
377 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
378     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
379 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
380     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
381     /* intermediate matrices */
382 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
383     compose_matrix(m1, ncp, ftp->rI2_eJ2);
384 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
385     compose_matrix(m3, ftp->e_i, ftp->e_i);
386     compose_matrix(m4, ftp->r_i, ftp->e_i);
387 greg 2.35 d1 = DOT(nrm, ftp->rcp);
388 greg 2.27 d2 = -d1*ftp->I2;
389     d1 *= 2.0;
390     for (i = 3; i--; ) /* final matrix sum */
391     for (j = 3; j--; ) {
392     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
393     2.0*J3*m4[i][j] );
394     hess[i][j] += d2*(i==j);
395 greg 2.46 hess[i][j] *= -1.0/PI;
396 greg 2.27 }
397     }
398    
399    
400     /* Reverse hessian calculation result for edge in other direction */
401     static void
402     rev_hessian(FVECT hess[3])
403     {
404     int i;
405    
406     for (i = 3; i--; ) {
407     hess[i][0] = -hess[i][0];
408     hess[i][1] = -hess[i][1];
409     hess[i][2] = -hess[i][2];
410     }
411     }
412    
413    
414     /* Add to radiometric Hessian from the given triangle */
415     static void
416     add2hessian(FVECT hess[3], FVECT ehess1[3],
417 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
418 greg 2.27 {
419     int i, j;
420    
421     for (i = 3; i--; )
422     for (j = 3; j--; )
423     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
424     }
425    
426    
427     /* Compute partial displacement form factor gradient for edge */
428     static void
429     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
430     {
431 greg 2.35 FVECT ncp;
432 greg 2.27 double f1;
433     int i;
434    
435 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
436     VCROSS(ncp, nrm, ftp->e_i);
437 greg 2.27 for (i = 3; i--; )
438 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
439 greg 2.27 }
440    
441    
442     /* Reverse gradient calculation result for edge in other direction */
443     static void
444     rev_gradient(FVECT grad)
445     {
446     grad[0] = -grad[0];
447     grad[1] = -grad[1];
448     grad[2] = -grad[2];
449     }
450    
451    
452     /* Add to displacement gradient from the given triangle */
453     static void
454 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
455 greg 2.27 {
456     int i;
457    
458     for (i = 3; i--; )
459     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
460     }
461    
462    
463     /* Compute anisotropic radii and eigenvector directions */
464 greg 2.53 static void
465 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
466     {
467     double hess2[2][2];
468     FVECT a, b;
469     double evalue[2], slope1, xmag1;
470     int i;
471     /* project Hessian to sample plane */
472     for (i = 3; i--; ) {
473     a[i] = DOT(hessian[i], uv[0]);
474     b[i] = DOT(hessian[i], uv[1]);
475     }
476     hess2[0][0] = DOT(uv[0], a);
477     hess2[0][1] = DOT(uv[0], b);
478     hess2[1][0] = DOT(uv[1], a);
479     hess2[1][1] = DOT(uv[1], b);
480 greg 2.38 /* compute eigenvalue(s) */
481     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
482     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
483     if (i == 1) /* double-root (circle) */
484     evalue[1] = evalue[0];
485     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
486 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
487     ra[0] = ra[1] = maxarad;
488     return;
489     }
490 greg 2.27 if (evalue[0] > evalue[1]) {
491 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
492     ra[1] = sqrt(sqrt(4.0/evalue[1]));
493 greg 2.27 slope1 = evalue[1];
494     } else {
495 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
496     ra[1] = sqrt(sqrt(4.0/evalue[0]));
497 greg 2.27 slope1 = evalue[0];
498     }
499     /* compute unit eigenvectors */
500     if (fabs(hess2[0][1]) <= FTINY)
501     return; /* uv OK as is */
502     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
503     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
504     for (i = 3; i--; ) {
505     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
506     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
507     }
508     VCOPY(uv[0], a);
509     VCOPY(uv[1], b);
510     }
511    
512    
513 greg 2.26 static void
514     ambHessian( /* anisotropic radii & pos. gradient */
515     AMBHEMI *hp,
516     FVECT uv[2], /* returned */
517 greg 2.28 float ra[2], /* returned (optional) */
518     float pg[2] /* returned (optional) */
519 greg 2.26 )
520     {
521 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
522     FVECT (*hessrow)[3] = NULL;
523     FVECT *gradrow = NULL;
524     FVECT hessian[3];
525     FVECT gradient;
526     FFTRI fftr;
527     int i, j;
528     /* be sure to assign unit vectors */
529     VCOPY(uv[0], hp->ux);
530     VCOPY(uv[1], hp->uy);
531     /* clock-wise vertex traversal from sample POV */
532     if (ra != NULL) { /* initialize Hessian row buffer */
533 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
534 greg 2.27 if (hessrow == NULL)
535     error(SYSTEM, memerrmsg);
536     memset(hessian, 0, sizeof(hessian));
537     } else if (pg == NULL) /* bogus call? */
538     return;
539     if (pg != NULL) { /* initialize form factor row buffer */
540 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
541 greg 2.27 if (gradrow == NULL)
542     error(SYSTEM, memerrmsg);
543     memset(gradient, 0, sizeof(gradient));
544     }
545     /* compute first row of edges */
546     for (j = 0; j < hp->ns-1; j++) {
547 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
548 greg 2.27 if (hessrow != NULL)
549     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
550     if (gradrow != NULL)
551     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
552     }
553     /* sum each row of triangles */
554     for (i = 0; i < hp->ns-1; i++) {
555     FVECT hesscol[3]; /* compute first vertical edge */
556     FVECT gradcol;
557 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
558 greg 2.27 if (hessrow != NULL)
559     comp_hessian(hesscol, &fftr, hp->rp->ron);
560     if (gradrow != NULL)
561     comp_gradient(gradcol, &fftr, hp->rp->ron);
562     for (j = 0; j < hp->ns-1; j++) {
563     FVECT hessdia[3]; /* compute triangle contributions */
564     FVECT graddia;
565 greg 2.46 double backg;
566 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
567     AI(hp,i,j+1), AI(hp,i+1,j));
568 greg 2.27 /* diagonal (inner) edge */
569 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
570 greg 2.27 if (hessrow != NULL) {
571     comp_hessian(hessdia, &fftr, hp->rp->ron);
572     rev_hessian(hesscol);
573     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
574     }
575 greg 2.39 if (gradrow != NULL) {
576 greg 2.27 comp_gradient(graddia, &fftr, hp->rp->ron);
577     rev_gradient(gradcol);
578     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
579     }
580     /* initialize edge in next row */
581 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
582 greg 2.27 if (hessrow != NULL)
583     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
584     if (gradrow != NULL)
585     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
586     /* new column edge & paired triangle */
587 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
588     AI(hp,i+1,j), AI(hp,i,j+1));
589     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
590 greg 2.27 if (hessrow != NULL) {
591     comp_hessian(hesscol, &fftr, hp->rp->ron);
592     rev_hessian(hessdia);
593     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
594     if (i < hp->ns-2)
595     rev_hessian(hessrow[j]);
596     }
597     if (gradrow != NULL) {
598     comp_gradient(gradcol, &fftr, hp->rp->ron);
599     rev_gradient(graddia);
600     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
601     if (i < hp->ns-2)
602     rev_gradient(gradrow[j]);
603     }
604     }
605     }
606     /* release row buffers */
607     if (hessrow != NULL) free(hessrow);
608     if (gradrow != NULL) free(gradrow);
609    
610     if (ra != NULL) /* extract eigenvectors & radii */
611     eigenvectors(uv, ra, hessian);
612 greg 2.32 if (pg != NULL) { /* tangential position gradient */
613     pg[0] = DOT(gradient, uv[0]);
614     pg[1] = DOT(gradient, uv[1]);
615 greg 2.27 }
616     }
617    
618    
619     /* Compute direction gradient from a hemispherical sampling */
620     static void
621     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
622     {
623 greg 2.41 AMBSAMP *ap;
624     double dgsum[2];
625     int n;
626     FVECT vd;
627     double gfact;
628 greg 2.27
629 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
630 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
631     /* use vector for azimuth + 90deg */
632     VSUB(vd, ap->p, hp->rp->rop);
633 greg 2.29 /* brightness over cosine factor */
634     gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
635 greg 2.40 /* sine = proj_radius/vd_length */
636     dgsum[0] -= DOT(uv[1], vd) * gfact;
637     dgsum[1] += DOT(uv[0], vd) * gfact;
638 greg 2.26 }
639 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
640     dg[1] = dgsum[1] / (hp->ns*hp->ns);
641 greg 2.26 }
642    
643 greg 2.27
644 greg 2.49 /* Compute potential light leak direction flags for cache value */
645     static uint32
646     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
647 greg 2.47 {
648 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
649 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
650     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
651 greg 2.51 double avg_d = 0;
652 greg 2.50 uint32 flgs = 0;
653 greg 2.58 FVECT vec;
654 greg 2.62 double u, v;
655 greg 2.58 double ang, a1;
656 greg 2.50 int i, j;
657 greg 2.52 /* don't bother for a few samples */
658 greg 2.72 if (hp->ns < 8)
659 greg 2.52 return(0);
660     /* check distances overhead */
661 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
662     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
663     avg_d += ambsam(hp,i,j).d;
664     avg_d *= 4.0/(hp->ns*hp->ns);
665 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
666     return(0);
667     if (avg_d >= max_d) /* insurance */
668 greg 2.51 return(0);
669     /* else circle around perimeter */
670 greg 2.47 for (i = 0; i < hp->ns; i++)
671     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
672     AMBSAMP *ap = &ambsam(hp,i,j);
673 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
674     continue; /* too far or too near */
675 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
676 greg 2.62 u = DOT(vec, uv[0]);
677     v = DOT(vec, uv[1]);
678     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
679 greg 2.49 continue; /* occluder outside ellipse */
680     ang = atan2a(v, u); /* else set direction flags */
681 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
682 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
683 greg 2.47 }
684 greg 2.49 return(flgs);
685 greg 2.47 }
686    
687    
688 greg 2.26 int
689     doambient( /* compute ambient component */
690     COLOR rcol, /* input/output color */
691     RAY *r,
692     double wt,
693 greg 2.27 FVECT uv[2], /* returned (optional) */
694     float ra[2], /* returned (optional) */
695     float pg[2], /* returned (optional) */
696 greg 2.49 float dg[2], /* returned (optional) */
697     uint32 *crlp /* returned (optional) */
698 greg 2.26 )
699     {
700 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
701 greg 2.41 FVECT my_uv[2];
702 greg 2.61 double d, K;
703 greg 2.41 AMBSAMP *ap;
704 greg 2.61 int i;
705     /* clear return values */
706 greg 2.26 if (uv != NULL)
707     memset(uv, 0, sizeof(FVECT)*2);
708     if (ra != NULL)
709     ra[0] = ra[1] = 0.0;
710     if (pg != NULL)
711     pg[0] = pg[1] = 0.0;
712     if (dg != NULL)
713     dg[0] = dg[1] = 0.0;
714 greg 2.49 if (crlp != NULL)
715     *crlp = 0;
716 greg 2.61 if (hp == NULL) /* sampling falure? */
717     return(0);
718    
719     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
720 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
721 greg 2.61 free(hp); /* Hessian not requested/possible */
722     return(-1); /* value-only return value */
723 greg 2.26 }
724 greg 2.61 if ((d = bright(rcol)) > FTINY) { /* normalize Y values */
725 greg 2.45 d = 0.99*(hp->ns*hp->ns)/d;
726 greg 2.38 K = 0.01;
727 greg 2.45 } else { /* or fall back on geometric Hessian */
728 greg 2.38 K = 1.0;
729     pg = NULL;
730     dg = NULL;
731 greg 2.53 crlp = NULL;
732 greg 2.38 }
733 greg 2.29 ap = hp->sa; /* relative Y channel from here on... */
734 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
735 greg 2.38 colval(ap->v,CIEY) = bright(ap->v)*d + K;
736 greg 2.26
737     if (uv == NULL) /* make sure we have axis pointers */
738     uv = my_uv;
739     /* compute radii & pos. gradient */
740     ambHessian(hp, uv, ra, pg);
741 greg 2.29
742 greg 2.26 if (dg != NULL) /* compute direction gradient */
743     ambdirgrad(hp, uv, dg);
744 greg 2.29
745 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
746 greg 2.35 if (pg != NULL) {
747     if (ra[0]*(d = fabs(pg[0])) > 1.0)
748     ra[0] = 1.0/d;
749     if (ra[1]*(d = fabs(pg[1])) > 1.0)
750     ra[1] = 1.0/d;
751 greg 2.48 if (ra[0] > ra[1])
752     ra[0] = ra[1];
753 greg 2.35 }
754 greg 2.29 if (ra[0] < minarad) {
755     ra[0] = minarad;
756     if (ra[1] < minarad)
757     ra[1] = minarad;
758     }
759 greg 2.60 ra[0] *= d = 1.0/sqrt(wt);
760 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
761     ra[1] = 2.0*ra[0];
762 greg 2.28 if (ra[1] > maxarad) {
763     ra[1] = maxarad;
764     if (ra[0] > maxarad)
765     ra[0] = maxarad;
766     }
767 greg 2.53 /* flag encroached directions */
768 greg 2.71 if (crlp != NULL)
769 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
770 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
771     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
772     if (d > 1.0) {
773     d = 1.0/sqrt(d);
774     pg[0] *= d;
775     pg[1] *= d;
776     }
777     }
778 greg 2.26 }
779     free(hp); /* clean up and return */
780     return(1);
781     }
782