ViewVC Help
View File | Revision Log | Show Annotations | Download File | Root Listing
root/radiance/ray/src/rt/ambcomp.c
Revision: 2.90
Committed: Wed Nov 15 18:02:52 2023 UTC (17 months, 2 weeks ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.89: +39 -40 lines
Log Message: 
feat(rpict,rtrace,rcontrib,rtpict): Hyperspectral rendering (except photon map)

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.90 static const char RCSid[] = "$Id: ambcomp.c,v 2.89 2022/04/19 00:36:34 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 2.90 SCOLOR acoef; /* division contribution coefficient */
39     SCOLOR acol; /* accumulated color */
40 greg 2.61 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 2.90 setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
107 greg 2.26 else
108 greg 2.90 copyscolor(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 2.90 smultscolor(ar.rcoef, hp->acoef);
113     scalescolor(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 greg 2.90 smultscolor(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 2.90 copyscolor(ap->v, ar.rcol);
146 greg 2.61 } else { /* else update recorded value */
147 greg 2.90 sopscolor(hp->acol, -=, ap->v);
148 greg 2.61 zd = 1.0/(double)(n+1);
149 greg 2.90 scalescolor(ar.rcol, zd);
150 greg 2.61 zd *= (double)n;
151 greg 2.90 scalescolor(ap->v, zd);
152     saddscolor(ap->v, ar.rcol);
153 greg 2.61 }
154 greg 2.90 saddscolor(hp->acol, ap->v); /* add to our sum */
155 greg 2.41 return(1);
156     }
157    
158    
159 greg 2.82 /* Estimate variance based on ambient division differences */
160 greg 2.41 static float *
161     getambdiffs(AMBHEMI *hp)
162     {
163 greg 2.77 const double normf = 1./bright(hp->acoef);
164 greg 2.55 float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
165 greg 2.41 float *ep;
166 greg 2.42 AMBSAMP *ap;
167 greg 2.81 double b, b1, d2;
168 greg 2.41 int i, j;
169    
170     if (earr == NULL) /* out of memory? */
171     return(NULL);
172 greg 2.81 /* sum squared neighbor diffs */
173 greg 2.42 for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
174     for (j = 0; j < hp->ns; j++, ap++, ep++) {
175 greg 2.90 b = pbright(ap[0].v);
176 greg 2.41 if (i) { /* from above */
177 greg 2.90 b1 = pbright(ap[-hp->ns].v);
178 greg 2.82 d2 = b - b1;
179 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
180 greg 2.41 ep[0] += d2;
181     ep[-hp->ns] += d2;
182     }
183 greg 2.55 if (!j) continue;
184     /* from behind */
185 greg 2.90 b1 = pbright(ap[-1].v);
186 greg 2.82 d2 = b - b1;
187 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
188 greg 2.55 ep[0] += d2;
189     ep[-1] += d2;
190     if (!i) continue;
191     /* diagonal */
192 greg 2.90 b1 = pbright(ap[-hp->ns-1].v);
193 greg 2.82 d2 = b - b1;
194 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
195 greg 2.55 ep[0] += d2;
196     ep[-hp->ns-1] += d2;
197 greg 2.41 }
198     /* correct for number of neighbors */
199 greg 2.55 earr[0] *= 8./3.;
200     earr[hp->ns-1] *= 8./3.;
201     earr[(hp->ns-1)*hp->ns] *= 8./3.;
202     earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.;
203 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
204 greg 2.55 earr[i*hp->ns] *= 8./5.;
205     earr[i*hp->ns + hp->ns-1] *= 8./5.;
206 greg 2.41 }
207     for (j = 1; j < hp->ns-1; j++) {
208 greg 2.55 earr[j] *= 8./5.;
209     earr[(hp->ns-1)*hp->ns + j] *= 8./5.;
210 greg 2.41 }
211     return(earr);
212     }
213    
214    
215 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
216 greg 2.41 static void
217 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
218 greg 2.41 {
219     float *earr = getambdiffs(hp);
220 greg 2.54 double e2rem = 0;
221 greg 2.41 float *ep;
222 greg 2.55 int i, j, n, nss;
223 greg 2.41
224     if (earr == NULL) /* just skip calc. if no memory */
225     return;
226 greg 2.54 /* accumulate estimated variances */
227 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
228     e2rem += *--ep;
229 greg 2.41 ep = earr; /* perform super-sampling */
230 greg 2.81 for (i = 0; i < hp->ns; i++)
231     for (j = 0; j < hp->ns; j++) {
232 greg 2.55 if (e2rem <= FTINY)
233     goto done; /* nothing left to do */
234     nss = *ep/e2rem*cnt + frandom();
235 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
236 greg 2.77 if (!--cnt) goto done;
237 greg 2.61 e2rem -= *ep++; /* update remainder */
238 greg 2.41 }
239 greg 2.55 done:
240 greg 2.41 free(earr);
241     }
242    
243    
244 greg 2.61 static AMBHEMI *
245     samp_hemi( /* sample indirect hemisphere */
246 greg 2.90 SCOLOR rcol,
247 greg 2.61 RAY *r,
248     double wt
249     )
250     {
251     AMBHEMI *hp;
252     double d;
253     int n, i, j;
254 greg 2.77 /* insignificance check */
255 greg 2.90 d = sintens(rcol);
256     if (d <= FTINY)
257 greg 2.77 return(NULL);
258 greg 2.61 /* set number of divisions */
259     if (ambacc <= FTINY &&
260 greg 2.90 wt > (d *= 0.8*r->rweight/(ambdiv*minweight)))
261 greg 2.61 wt = d; /* avoid ray termination */
262     n = sqrt(ambdiv * wt) + 0.5;
263 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
264     if (n < i) /* use minimum number of samples? */
265 greg 2.61 n = i;
266     /* allocate sampling array */
267     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
268     if (hp == NULL)
269     error(SYSTEM, "out of memory in samp_hemi");
270     hp->rp = r;
271     hp->ns = n;
272 greg 2.90 scolorblack(hp->acol);
273 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
274 greg 2.61 hp->sampOK = 0;
275     /* assign coefficient */
276 greg 2.90 copyscolor(hp->acoef, rcol);
277 greg 2.61 d = 1.0/(n*n);
278 greg 2.90 scalescolor(hp->acoef, d);
279 greg 2.61 /* make tangent plane axes */
280 greg 2.70 if (!getperpendicular(hp->ux, r->ron, 1))
281 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
282     VCROSS(hp->uy, r->ron, hp->ux);
283     /* sample divisions */
284     for (i = hp->ns; i--; )
285     for (j = hp->ns; j--; )
286     hp->sampOK += ambsample(hp, i, j, 0);
287 greg 2.90 copyscolor(rcol, hp->acol);
288 greg 2.61 if (!hp->sampOK) { /* utter failure? */
289     free(hp);
290     return(NULL);
291     }
292     if (hp->sampOK < hp->ns*hp->ns) {
293     hp->sampOK *= -1; /* soft failure */
294     return(hp);
295     }
296 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
297     return(hp); /* don't bother super-sampling */
298 greg 2.61 n = ambssamp*wt + 0.5;
299     if (n > 8) { /* perform super-sampling? */
300     ambsupersamp(hp, n);
301 greg 2.90 copyscolor(rcol, hp->acol);
302 greg 2.61 }
303     return(hp); /* all is well */
304     }
305    
306    
307 greg 2.46 /* Return brightness of farthest ambient sample */
308     static double
309 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
310 greg 2.46 {
311 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
312     if (hp->sa[n1].d <= hp->sa[n3].d)
313 greg 2.90 return(hp->sa[n1].v[0]);
314     return(hp->sa[n3].v[0]);
315 greg 2.56 }
316     if (hp->sa[n2].d <= hp->sa[n3].d)
317 greg 2.90 return(hp->sa[n2].v[0]);
318     return(hp->sa[n3].v[0]);
319 greg 2.46 }
320    
321    
322 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
323     static void
324 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
325 greg 2.27 {
326 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
327     int ii;
328    
329     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
330     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
331     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
332 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
333     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
334 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
335     dot_er = DOT(ftp->e_i, ftp->r_i);
336 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
337     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
338     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
339 greg 2.35 sqrt( rdot_cp );
340 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
341 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
342 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
343 greg 2.46 for (ii = 3; ii--; )
344     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
345 greg 2.27 }
346    
347    
348 greg 2.28 /* Compose 3x3 matrix from two vectors */
349 greg 2.27 static void
350     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
351     {
352     mat[0][0] = 2.0*va[0]*vb[0];
353     mat[1][1] = 2.0*va[1]*vb[1];
354     mat[2][2] = 2.0*va[2]*vb[2];
355     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
356     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
357     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
358     }
359    
360    
361     /* Compute partial 3x3 Hessian matrix for edge */
362     static void
363     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
364     {
365 greg 2.35 FVECT ncp;
366 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
367     double d1, d2, d3, d4;
368     double I3, J3, K3;
369     int i, j;
370     /* compute intermediate coefficients */
371     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
372     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
373     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
374     d4 = DOT(ftp->e_i, ftp->r_i);
375 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
376     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
377 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
378     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
379     /* intermediate matrices */
380 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
381     compose_matrix(m1, ncp, ftp->rI2_eJ2);
382 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
383     compose_matrix(m3, ftp->e_i, ftp->e_i);
384     compose_matrix(m4, ftp->r_i, ftp->e_i);
385 greg 2.35 d1 = DOT(nrm, ftp->rcp);
386 greg 2.27 d2 = -d1*ftp->I2;
387     d1 *= 2.0;
388     for (i = 3; i--; ) /* final matrix sum */
389     for (j = 3; j--; ) {
390     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
391     2.0*J3*m4[i][j] );
392     hess[i][j] += d2*(i==j);
393 greg 2.46 hess[i][j] *= -1.0/PI;
394 greg 2.27 }
395     }
396    
397    
398     /* Reverse hessian calculation result for edge in other direction */
399     static void
400     rev_hessian(FVECT hess[3])
401     {
402     int i;
403    
404     for (i = 3; i--; ) {
405     hess[i][0] = -hess[i][0];
406     hess[i][1] = -hess[i][1];
407     hess[i][2] = -hess[i][2];
408     }
409     }
410    
411    
412     /* Add to radiometric Hessian from the given triangle */
413     static void
414     add2hessian(FVECT hess[3], FVECT ehess1[3],
415 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
416 greg 2.27 {
417     int i, j;
418    
419     for (i = 3; i--; )
420     for (j = 3; j--; )
421     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
422     }
423    
424    
425     /* Compute partial displacement form factor gradient for edge */
426     static void
427     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
428     {
429 greg 2.35 FVECT ncp;
430 greg 2.27 double f1;
431     int i;
432    
433 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
434     VCROSS(ncp, nrm, ftp->e_i);
435 greg 2.27 for (i = 3; i--; )
436 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
437 greg 2.27 }
438    
439    
440     /* Reverse gradient calculation result for edge in other direction */
441     static void
442     rev_gradient(FVECT grad)
443     {
444     grad[0] = -grad[0];
445     grad[1] = -grad[1];
446     grad[2] = -grad[2];
447     }
448    
449    
450     /* Add to displacement gradient from the given triangle */
451     static void
452 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
453 greg 2.27 {
454     int i;
455    
456     for (i = 3; i--; )
457     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
458     }
459    
460    
461     /* Compute anisotropic radii and eigenvector directions */
462 greg 2.53 static void
463 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
464     {
465     double hess2[2][2];
466     FVECT a, b;
467     double evalue[2], slope1, xmag1;
468     int i;
469     /* project Hessian to sample plane */
470     for (i = 3; i--; ) {
471     a[i] = DOT(hessian[i], uv[0]);
472     b[i] = DOT(hessian[i], uv[1]);
473     }
474     hess2[0][0] = DOT(uv[0], a);
475     hess2[0][1] = DOT(uv[0], b);
476     hess2[1][0] = DOT(uv[1], a);
477     hess2[1][1] = DOT(uv[1], b);
478 greg 2.38 /* compute eigenvalue(s) */
479     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
480     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
481     if (i == 1) /* double-root (circle) */
482     evalue[1] = evalue[0];
483     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
484 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
485     ra[0] = ra[1] = maxarad;
486     return;
487     }
488 greg 2.27 if (evalue[0] > evalue[1]) {
489 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
490     ra[1] = sqrt(sqrt(4.0/evalue[1]));
491 greg 2.27 slope1 = evalue[1];
492     } else {
493 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
494     ra[1] = sqrt(sqrt(4.0/evalue[0]));
495 greg 2.27 slope1 = evalue[0];
496     }
497     /* compute unit eigenvectors */
498     if (fabs(hess2[0][1]) <= FTINY)
499     return; /* uv OK as is */
500     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
501     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
502     for (i = 3; i--; ) {
503     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
504     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
505     }
506     VCOPY(uv[0], a);
507     VCOPY(uv[1], b);
508     }
509    
510    
511 greg 2.26 static void
512     ambHessian( /* anisotropic radii & pos. gradient */
513     AMBHEMI *hp,
514     FVECT uv[2], /* returned */
515 greg 2.28 float ra[2], /* returned (optional) */
516     float pg[2] /* returned (optional) */
517 greg 2.26 )
518     {
519 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
520     FVECT (*hessrow)[3] = NULL;
521     FVECT *gradrow = NULL;
522     FVECT hessian[3];
523     FVECT gradient;
524     FFTRI fftr;
525     int i, j;
526     /* be sure to assign unit vectors */
527     VCOPY(uv[0], hp->ux);
528     VCOPY(uv[1], hp->uy);
529     /* clock-wise vertex traversal from sample POV */
530     if (ra != NULL) { /* initialize Hessian row buffer */
531 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
532 greg 2.27 if (hessrow == NULL)
533     error(SYSTEM, memerrmsg);
534     memset(hessian, 0, sizeof(hessian));
535     } else if (pg == NULL) /* bogus call? */
536     return;
537     if (pg != NULL) { /* initialize form factor row buffer */
538 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
539 greg 2.27 if (gradrow == NULL)
540     error(SYSTEM, memerrmsg);
541     memset(gradient, 0, sizeof(gradient));
542     }
543     /* compute first row of edges */
544     for (j = 0; j < hp->ns-1; j++) {
545 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
546 greg 2.27 if (hessrow != NULL)
547     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
548     if (gradrow != NULL)
549     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
550     }
551     /* sum each row of triangles */
552     for (i = 0; i < hp->ns-1; i++) {
553     FVECT hesscol[3]; /* compute first vertical edge */
554     FVECT gradcol;
555 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
556 greg 2.27 if (hessrow != NULL)
557     comp_hessian(hesscol, &fftr, hp->rp->ron);
558     if (gradrow != NULL)
559     comp_gradient(gradcol, &fftr, hp->rp->ron);
560     for (j = 0; j < hp->ns-1; j++) {
561     FVECT hessdia[3]; /* compute triangle contributions */
562     FVECT graddia;
563 greg 2.46 double backg;
564 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
565     AI(hp,i,j+1), AI(hp,i+1,j));
566 greg 2.27 /* diagonal (inner) edge */
567 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
568 greg 2.27 if (hessrow != NULL) {
569     comp_hessian(hessdia, &fftr, hp->rp->ron);
570     rev_hessian(hesscol);
571     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
572     }
573 greg 2.39 if (gradrow != NULL) {
574 greg 2.27 comp_gradient(graddia, &fftr, hp->rp->ron);
575     rev_gradient(gradcol);
576     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
577     }
578     /* initialize edge in next row */
579 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
580 greg 2.27 if (hessrow != NULL)
581     comp_hessian(hessrow[j], &fftr, hp->rp->ron);
582     if (gradrow != NULL)
583     comp_gradient(gradrow[j], &fftr, hp->rp->ron);
584     /* new column edge & paired triangle */
585 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
586     AI(hp,i+1,j), AI(hp,i,j+1));
587     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
588 greg 2.27 if (hessrow != NULL) {
589     comp_hessian(hesscol, &fftr, hp->rp->ron);
590     rev_hessian(hessdia);
591     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
592     if (i < hp->ns-2)
593     rev_hessian(hessrow[j]);
594     }
595     if (gradrow != NULL) {
596     comp_gradient(gradcol, &fftr, hp->rp->ron);
597     rev_gradient(graddia);
598     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
599     if (i < hp->ns-2)
600     rev_gradient(gradrow[j]);
601     }
602     }
603     }
604     /* release row buffers */
605     if (hessrow != NULL) free(hessrow);
606     if (gradrow != NULL) free(gradrow);
607    
608     if (ra != NULL) /* extract eigenvectors & radii */
609     eigenvectors(uv, ra, hessian);
610 greg 2.32 if (pg != NULL) { /* tangential position gradient */
611     pg[0] = DOT(gradient, uv[0]);
612     pg[1] = DOT(gradient, uv[1]);
613 greg 2.27 }
614     }
615    
616    
617     /* Compute direction gradient from a hemispherical sampling */
618     static void
619     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
620     {
621 greg 2.41 AMBSAMP *ap;
622     double dgsum[2];
623     int n;
624     FVECT vd;
625     double gfact;
626 greg 2.27
627 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
628 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
629     /* use vector for azimuth + 90deg */
630     VSUB(vd, ap->p, hp->rp->rop);
631 greg 2.29 /* brightness over cosine factor */
632 greg 2.90 gfact = ap->v[0] / DOT(hp->rp->ron, vd);
633 greg 2.40 /* sine = proj_radius/vd_length */
634     dgsum[0] -= DOT(uv[1], vd) * gfact;
635     dgsum[1] += DOT(uv[0], vd) * gfact;
636 greg 2.26 }
637 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
638     dg[1] = dgsum[1] / (hp->ns*hp->ns);
639 greg 2.26 }
640    
641 greg 2.27
642 greg 2.49 /* Compute potential light leak direction flags for cache value */
643     static uint32
644     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
645 greg 2.47 {
646 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
647 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
648     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
649 greg 2.51 double avg_d = 0;
650 greg 2.50 uint32 flgs = 0;
651 greg 2.58 FVECT vec;
652 greg 2.62 double u, v;
653 greg 2.58 double ang, a1;
654 greg 2.50 int i, j;
655 greg 2.52 /* don't bother for a few samples */
656 greg 2.72 if (hp->ns < 8)
657 greg 2.52 return(0);
658     /* check distances overhead */
659 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
660     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
661     avg_d += ambsam(hp,i,j).d;
662     avg_d *= 4.0/(hp->ns*hp->ns);
663 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
664     return(0);
665     if (avg_d >= max_d) /* insurance */
666 greg 2.51 return(0);
667     /* else circle around perimeter */
668 greg 2.47 for (i = 0; i < hp->ns; i++)
669     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
670     AMBSAMP *ap = &ambsam(hp,i,j);
671 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
672     continue; /* too far or too near */
673 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
674 greg 2.62 u = DOT(vec, uv[0]);
675     v = DOT(vec, uv[1]);
676     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
677 greg 2.49 continue; /* occluder outside ellipse */
678     ang = atan2a(v, u); /* else set direction flags */
679 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
680 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
681 greg 2.47 }
682 greg 2.49 return(flgs);
683 greg 2.47 }
684    
685    
686 greg 2.26 int
687     doambient( /* compute ambient component */
688 greg 2.90 SCOLOR rcol, /* input/output color */
689 greg 2.26 RAY *r,
690     double wt,
691 greg 2.27 FVECT uv[2], /* returned (optional) */
692     float ra[2], /* returned (optional) */
693     float pg[2], /* returned (optional) */
694 greg 2.49 float dg[2], /* returned (optional) */
695     uint32 *crlp /* returned (optional) */
696 greg 2.26 )
697     {
698 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
699 greg 2.41 FVECT my_uv[2];
700 greg 2.61 double d, K;
701 greg 2.41 AMBSAMP *ap;
702 greg 2.61 int i;
703     /* clear return values */
704 greg 2.26 if (uv != NULL)
705     memset(uv, 0, sizeof(FVECT)*2);
706     if (ra != NULL)
707     ra[0] = ra[1] = 0.0;
708     if (pg != NULL)
709     pg[0] = pg[1] = 0.0;
710     if (dg != NULL)
711     dg[0] = dg[1] = 0.0;
712 greg 2.49 if (crlp != NULL)
713     *crlp = 0;
714 greg 2.61 if (hp == NULL) /* sampling falure? */
715     return(0);
716    
717     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
718 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
719 greg 2.61 free(hp); /* Hessian not requested/possible */
720     return(-1); /* value-only return value */
721 greg 2.26 }
722 greg 2.90 if ((d = scolor_photopic(rcol)) > FTINY) {
723     d = 0.99*(hp->ns*hp->ns)/d; /* normalize Y values */
724 greg 2.38 K = 0.01;
725 greg 2.45 } else { /* or fall back on geometric Hessian */
726 greg 2.38 K = 1.0;
727     pg = NULL;
728     dg = NULL;
729 greg 2.53 crlp = NULL;
730 greg 2.38 }
731 greg 2.90 ap = hp->sa; /* single channel from here on... */
732 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
733 greg 2.90 ap->v[0] = scolor_mean(ap->v)*d + K;
734 greg 2.26
735     if (uv == NULL) /* make sure we have axis pointers */
736     uv = my_uv;
737     /* compute radii & pos. gradient */
738     ambHessian(hp, uv, ra, pg);
739 greg 2.29
740 greg 2.26 if (dg != NULL) /* compute direction gradient */
741     ambdirgrad(hp, uv, dg);
742 greg 2.29
743 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
744 greg 2.35 if (pg != NULL) {
745     if (ra[0]*(d = fabs(pg[0])) > 1.0)
746     ra[0] = 1.0/d;
747     if (ra[1]*(d = fabs(pg[1])) > 1.0)
748     ra[1] = 1.0/d;
749 greg 2.48 if (ra[0] > ra[1])
750     ra[0] = ra[1];
751 greg 2.35 }
752 greg 2.29 if (ra[0] < minarad) {
753     ra[0] = minarad;
754     if (ra[1] < minarad)
755     ra[1] = minarad;
756     }
757 greg 2.60 ra[0] *= d = 1.0/sqrt(wt);
758 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
759     ra[1] = 2.0*ra[0];
760 greg 2.28 if (ra[1] > maxarad) {
761     ra[1] = maxarad;
762     if (ra[0] > maxarad)
763     ra[0] = maxarad;
764     }
765 greg 2.53 /* flag encroached directions */
766 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
767 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
768 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
769     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
770     if (d > 1.0) {
771     d = 1.0/sqrt(d);
772     pg[0] *= d;
773     pg[1] *= d;
774     }
775     }
776 greg 2.26 }
777     free(hp); /* clean up and return */
778     return(1);
779     }