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root/radiance/ray/src/rt/ambcomp.c
Revision: 2.96
Committed: Fri Nov 15 20:47:42 2024 UTC (5 months, 2 weeks ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.95: +5 -1 lines
Log Message: 
feat(rpict): Experimental source skipping option with -DSSKIPOPT compile flag

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.96 static const char RCSid[] = "$Id: ambcomp.c,v 2.95 2024/04/19 01:52:50 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 2.90 FVECT p; /* intersection point */
30 greg 2.83 float d; /* reciprocal distance */
31 greg 2.90 SCOLOR v; /* hemisphere sample value */
32 greg 2.44 } AMBSAMP; /* sample value */
33    
34     typedef struct {
35 greg 2.26 RAY *rp; /* originating ray sample */
36     int ns; /* number of samples per axis */
37 greg 2.61 int sampOK; /* acquired full sample set? */
38 greg 2.92 int atyp; /* RAMBIENT or TAMBIENT */
39 greg 2.90 SCOLOR acoef; /* division contribution coefficient */
40     SCOLOR acol; /* accumulated color */
41 greg 2.92 FVECT onrm; /* oriented unperturbed surface normal */
42 greg 2.61 FVECT ux, uy; /* tangent axis unit vectors */
43 greg 2.44 AMBSAMP sa[1]; /* sample array (extends struct) */
44 greg 2.26 } AMBHEMI; /* ambient sample hemisphere */
45    
46 greg 2.56 #define AI(h,i,j) ((i)*(h)->ns + (j))
47     #define ambsam(h,i,j) (h)->sa[AI(h,i,j)]
48 greg 2.26
49 greg 2.27 typedef struct {
50 greg 2.35 FVECT r_i, r_i1, e_i, rcp, rI2_eJ2;
51     double I1, I2;
52 greg 2.27 } FFTRI; /* vectors and coefficients for Hessian calculation */
53    
54 greg 2.26
55 greg 2.61 static int
56 greg 2.73 ambcollision( /* proposed direciton collides? */
57     AMBHEMI *hp,
58     int i,
59     int j,
60     FVECT dv
61     )
62     {
63 greg 2.74 double cos_thresh;
64     int ii, jj;
65 greg 2.75 /* min. spacing = 1/4th division */
66     cos_thresh = (PI/4.)/(double)hp->ns;
67 greg 2.74 cos_thresh = 1. - .5*cos_thresh*cos_thresh;
68     /* check existing neighbors */
69 greg 2.73 for (ii = i-1; ii <= i+1; ii++) {
70     if (ii < 0) continue;
71     if (ii >= hp->ns) break;
72     for (jj = j-1; jj <= j+1; jj++) {
73     AMBSAMP *ap;
74     FVECT avec;
75     double dprod;
76     if (jj < 0) continue;
77     if (jj >= hp->ns) break;
78     if ((ii==i) & (jj==j)) continue;
79     ap = &ambsam(hp,ii,jj);
80 greg 2.74 if (ap->d <= .5/FHUGE)
81     continue; /* no one home */
82 greg 2.73 VSUB(avec, ap->p, hp->rp->rop);
83     dprod = DOT(avec, dv);
84     if (dprod >= cos_thresh*VLEN(avec))
85     return(1); /* collision */
86     }
87     }
88 greg 2.74 return(0); /* nothing to worry about */
89 greg 2.73 }
90    
91    
92     static int
93 greg 2.61 ambsample( /* initial ambient division sample */
94     AMBHEMI *hp,
95     int i,
96     int j,
97     int n
98 greg 2.26 )
99     {
100 greg 2.61 AMBSAMP *ap = &ambsam(hp,i,j);
101     RAY ar;
102 greg 2.41 int hlist[3], ii;
103 greg 2.94 double ss[2];
104 greg 2.88 RREAL spt[2];
105     double zd;
106 greg 2.61 /* generate hemispherical sample */
107 greg 2.26 /* ambient coefficient for weight */
108     if (ambacc > FTINY)
109 greg 2.90 setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
110 greg 2.26 else
111 greg 2.90 copyscolor(ar.rcoef, hp->acoef);
112 greg 2.92 if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0)
113 greg 2.41 return(0);
114 greg 2.26 if (ambacc > FTINY) {
115 greg 2.96 #ifdef SSKIPOPT
116     ar.rsrc = -1; /* protect cache from source opt. */
117     ar.scorr = 1.f;
118     #endif
119 greg 2.90 smultscolor(ar.rcoef, hp->acoef);
120     scalescolor(ar.rcoef, 1./AVGREFL);
121 greg 2.41 }
122     hlist[0] = hp->rp->rno;
123 greg 2.94 hlist[1] = AI(hp,i,j);
124     hlist[2] = samplendx;
125     multisamp(ss, 2, urand(ilhash(hlist,3)+n));
126 greg 2.73 resample:
127 greg 2.94 square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns);
128 greg 2.26 zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
129     for (ii = 3; ii--; )
130 greg 2.61 ar.rdir[ii] = spt[0]*hp->ux[ii] +
131 greg 2.26 spt[1]*hp->uy[ii] +
132 greg 2.92 zd*hp->onrm[ii];
133 greg 2.61 checknorm(ar.rdir);
134 greg 2.73 /* avoid coincident samples */
135 greg 2.94 if (!n && hp->ns >= 4 && ambcollision(hp, i, j, ar.rdir)) {
136     ss[0] = frandom(); ss[1] = frandom();
137 greg 2.75 goto resample; /* reject this sample */
138 greg 2.73 }
139 greg 2.56 dimlist[ndims++] = AI(hp,i,j) + 90171;
140 greg 2.61 rayvalue(&ar); /* evaluate ray */
141     ndims--;
142 greg 2.83 zd = raydistance(&ar);
143     if (zd <= FTINY)
144 greg 2.61 return(0); /* should never happen */
145 greg 2.90 smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */
146 greg 2.83 if (zd*ap->d < 1.0) /* new/closer distance? */
147     ap->d = 1.0/zd;
148 greg 2.61 if (!n) { /* record first vertex & value */
149 greg 2.83 if (zd > 10.0*thescene.cusize + 1000.)
150     zd = 10.0*thescene.cusize + 1000.;
151     VSUM(ap->p, ar.rorg, ar.rdir, zd);
152 greg 2.90 copyscolor(ap->v, ar.rcol);
153 greg 2.61 } else { /* else update recorded value */
154 greg 2.90 sopscolor(hp->acol, -=, ap->v);
155 greg 2.61 zd = 1.0/(double)(n+1);
156 greg 2.90 scalescolor(ar.rcol, zd);
157 greg 2.61 zd *= (double)n;
158 greg 2.90 scalescolor(ap->v, zd);
159     saddscolor(ap->v, ar.rcol);
160 greg 2.61 }
161 greg 2.90 saddscolor(hp->acol, ap->v); /* add to our sum */
162 greg 2.41 return(1);
163     }
164    
165    
166 greg 2.82 /* Estimate variance based on ambient division differences */
167 greg 2.41 static float *
168     getambdiffs(AMBHEMI *hp)
169     {
170 greg 2.93 const double normf = 1./(pbright(hp->acoef) + FTINY);
171 greg 2.94 float *earr = (float *)calloc(2*hp->ns*hp->ns, sizeof(float));
172     float *ep;
173 greg 2.42 AMBSAMP *ap;
174 greg 2.81 double b, b1, d2;
175 greg 2.41 int i, j;
176    
177     if (earr == NULL) /* out of memory? */
178     return(NULL);
179 greg 2.81 /* sum squared neighbor diffs */
180 greg 2.95 ap = hp->sa;
181     ep = earr + hp->ns*hp->ns; /* original estimates to scratch */
182     for (i = 0; i < hp->ns; i++)
183 greg 2.42 for (j = 0; j < hp->ns; j++, ap++, ep++) {
184 greg 2.90 b = pbright(ap[0].v);
185 greg 2.41 if (i) { /* from above */
186 greg 2.90 b1 = pbright(ap[-hp->ns].v);
187 greg 2.82 d2 = b - b1;
188 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
189 greg 2.41 ep[0] += d2;
190     ep[-hp->ns] += d2;
191     }
192 greg 2.55 if (!j) continue;
193     /* from behind */
194 greg 2.90 b1 = pbright(ap[-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[-1] += d2;
199     if (!i) continue;
200     /* diagonal */
201 greg 2.90 b1 = pbright(ap[-hp->ns-1].v);
202 greg 2.82 d2 = b - b1;
203 greg 2.89 d2 *= d2*normf/(b + b1 + FTINY);
204 greg 2.55 ep[0] += d2;
205     ep[-hp->ns-1] += d2;
206 greg 2.41 }
207     /* correct for number of neighbors */
208 greg 2.95 ep = earr + hp->ns*hp->ns;
209     ep[0] *= 6./3.;
210     ep[hp->ns-1] *= 6./3.;
211     ep[(hp->ns-1)*hp->ns] *= 6./3.;
212     ep[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.;
213 greg 2.41 for (i = 1; i < hp->ns-1; i++) {
214 greg 2.95 ep[i*hp->ns] *= 6./5.;
215     ep[i*hp->ns + hp->ns-1] *= 6./5.;
216 greg 2.41 }
217     for (j = 1; j < hp->ns-1; j++) {
218 greg 2.95 ep[j] *= 6./5.;
219     ep[(hp->ns-1)*hp->ns + j] *= 6./5.;
220 greg 2.93 }
221 greg 2.95 /* blur final map to reduce bias */
222 greg 2.93 for (i = 0; i < hp->ns-1; i++) {
223 greg 2.94 float *ep2;
224 greg 2.93 ep = earr + i*hp->ns;
225 greg 2.94 ep2 = ep + hp->ns*hp->ns;
226     for (j = 0; j < hp->ns-1; j++, ep++, ep2++) {
227 greg 2.95 ep[0] += .5*ep2[0] + .125*(ep2[1] + ep2[hp->ns]);
228 greg 2.94 ep[1] += .125*ep2[0];
229     ep[hp->ns] += .125*ep2[0];
230 greg 2.93 }
231 greg 2.41 }
232     return(earr);
233     }
234    
235    
236 greg 2.43 /* Perform super-sampling on hemisphere (introduces bias) */
237 greg 2.41 static void
238 greg 2.61 ambsupersamp(AMBHEMI *hp, int cnt)
239 greg 2.41 {
240     float *earr = getambdiffs(hp);
241 greg 2.54 double e2rem = 0;
242 greg 2.41 float *ep;
243 greg 2.55 int i, j, n, nss;
244 greg 2.41
245     if (earr == NULL) /* just skip calc. if no memory */
246     return;
247 greg 2.54 /* accumulate estimated variances */
248 greg 2.55 for (ep = earr + hp->ns*hp->ns; ep > earr; )
249     e2rem += *--ep;
250 greg 2.41 ep = earr; /* perform super-sampling */
251 greg 2.81 for (i = 0; i < hp->ns; i++)
252     for (j = 0; j < hp->ns; j++) {
253 greg 2.55 if (e2rem <= FTINY)
254     goto done; /* nothing left to do */
255     nss = *ep/e2rem*cnt + frandom();
256 greg 2.62 for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
257 greg 2.77 if (!--cnt) goto done;
258 greg 2.61 e2rem -= *ep++; /* update remainder */
259 greg 2.41 }
260 greg 2.55 done:
261 greg 2.41 free(earr);
262     }
263    
264    
265 greg 2.61 static AMBHEMI *
266     samp_hemi( /* sample indirect hemisphere */
267 greg 2.90 SCOLOR rcol,
268 greg 2.61 RAY *r,
269     double wt
270     )
271     {
272 greg 2.92 int backside = (wt < 0);
273 greg 2.61 AMBHEMI *hp;
274     double d;
275     int n, i, j;
276 greg 2.77 /* insignificance check */
277 greg 2.90 d = sintens(rcol);
278     if (d <= FTINY)
279 greg 2.77 return(NULL);
280 greg 2.61 /* set number of divisions */
281 greg 2.92 if (backside) wt = -wt;
282 greg 2.61 if (ambacc <= FTINY &&
283 greg 2.94 wt > (d *= 0.8*r->rweight/(ambdiv*minweight + 1e-20)))
284 greg 2.61 wt = d; /* avoid ray termination */
285     n = sqrt(ambdiv * wt) + 0.5;
286 greg 2.86 i = 1 + (MINADIV-1)*(ambacc > FTINY);
287     if (n < i) /* use minimum number of samples? */
288 greg 2.61 n = i;
289     /* allocate sampling array */
290     hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
291     if (hp == NULL)
292     error(SYSTEM, "out of memory in samp_hemi");
293 greg 2.92
294     if (backside) {
295     hp->atyp = TAMBIENT;
296     hp->onrm[0] = -r->ron[0];
297     hp->onrm[1] = -r->ron[1];
298     hp->onrm[2] = -r->ron[2];
299     } else {
300     hp->atyp = RAMBIENT;
301     VCOPY(hp->onrm, r->ron);
302     }
303 greg 2.61 hp->rp = r;
304     hp->ns = n;
305 greg 2.90 scolorblack(hp->acol);
306 greg 2.62 memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
307 greg 2.61 hp->sampOK = 0;
308     /* assign coefficient */
309 greg 2.90 copyscolor(hp->acoef, rcol);
310 greg 2.61 d = 1.0/(n*n);
311 greg 2.90 scalescolor(hp->acoef, d);
312 greg 2.61 /* make tangent plane axes */
313 greg 2.92 if (!getperpendicular(hp->ux, hp->onrm, 1))
314 greg 2.61 error(CONSISTENCY, "bad ray direction in samp_hemi");
315 greg 2.92 VCROSS(hp->uy, hp->onrm, hp->ux);
316 greg 2.61 /* sample divisions */
317     for (i = hp->ns; i--; )
318     for (j = hp->ns; j--; )
319     hp->sampOK += ambsample(hp, i, j, 0);
320 greg 2.90 copyscolor(rcol, hp->acol);
321 greg 2.61 if (!hp->sampOK) { /* utter failure? */
322     free(hp);
323     return(NULL);
324     }
325     if (hp->sampOK < hp->ns*hp->ns) {
326     hp->sampOK *= -1; /* soft failure */
327     return(hp);
328     }
329 greg 2.86 if (hp->sampOK <= MINADIV*MINADIV)
330     return(hp); /* don't bother super-sampling */
331 greg 2.61 n = ambssamp*wt + 0.5;
332 greg 2.94 if (n >= 4*hp->ns) { /* perform super-sampling? */
333 greg 2.61 ambsupersamp(hp, n);
334 greg 2.90 copyscolor(rcol, hp->acol);
335 greg 2.61 }
336     return(hp); /* all is well */
337     }
338    
339    
340 greg 2.46 /* Return brightness of farthest ambient sample */
341     static double
342 greg 2.56 back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
343 greg 2.46 {
344 greg 2.56 if (hp->sa[n1].d <= hp->sa[n2].d) {
345     if (hp->sa[n1].d <= hp->sa[n3].d)
346 greg 2.90 return(hp->sa[n1].v[0]);
347     return(hp->sa[n3].v[0]);
348 greg 2.56 }
349     if (hp->sa[n2].d <= hp->sa[n3].d)
350 greg 2.90 return(hp->sa[n2].v[0]);
351     return(hp->sa[n3].v[0]);
352 greg 2.46 }
353    
354    
355 greg 2.27 /* Compute vectors and coefficients for Hessian/gradient calcs */
356     static void
357 greg 2.56 comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
358 greg 2.27 {
359 greg 2.56 double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
360     int ii;
361    
362     VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
363     VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
364     VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
365 greg 2.35 VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
366     rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
367 greg 2.27 dot_e = DOT(ftp->e_i,ftp->e_i);
368     dot_er = DOT(ftp->e_i, ftp->r_i);
369 greg 2.32 rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
370     rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
371     ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
372 greg 2.35 sqrt( rdot_cp );
373 greg 2.32 ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
374 greg 2.35 dot_e*ftp->I1 )*0.5*rdot_cp;
375 greg 2.32 J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
376 greg 2.46 for (ii = 3; ii--; )
377     ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
378 greg 2.27 }
379    
380    
381 greg 2.28 /* Compose 3x3 matrix from two vectors */
382 greg 2.27 static void
383     compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
384     {
385     mat[0][0] = 2.0*va[0]*vb[0];
386     mat[1][1] = 2.0*va[1]*vb[1];
387     mat[2][2] = 2.0*va[2]*vb[2];
388     mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
389     mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
390     mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
391     }
392    
393    
394     /* Compute partial 3x3 Hessian matrix for edge */
395     static void
396     comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
397     {
398 greg 2.35 FVECT ncp;
399 greg 2.27 FVECT m1[3], m2[3], m3[3], m4[3];
400     double d1, d2, d3, d4;
401     double I3, J3, K3;
402     int i, j;
403     /* compute intermediate coefficients */
404     d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
405     d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
406     d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
407     d4 = DOT(ftp->e_i, ftp->r_i);
408 greg 2.35 I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
409     / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
410 greg 2.27 J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
411     K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
412     /* intermediate matrices */
413 greg 2.35 VCROSS(ncp, nrm, ftp->e_i);
414     compose_matrix(m1, ncp, ftp->rI2_eJ2);
415 greg 2.27 compose_matrix(m2, ftp->r_i, ftp->r_i);
416     compose_matrix(m3, ftp->e_i, ftp->e_i);
417     compose_matrix(m4, ftp->r_i, ftp->e_i);
418 greg 2.35 d1 = DOT(nrm, ftp->rcp);
419 greg 2.27 d2 = -d1*ftp->I2;
420     d1 *= 2.0;
421     for (i = 3; i--; ) /* final matrix sum */
422     for (j = 3; j--; ) {
423     hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
424     2.0*J3*m4[i][j] );
425     hess[i][j] += d2*(i==j);
426 greg 2.46 hess[i][j] *= -1.0/PI;
427 greg 2.27 }
428     }
429    
430    
431     /* Reverse hessian calculation result for edge in other direction */
432     static void
433     rev_hessian(FVECT hess[3])
434     {
435     int i;
436    
437     for (i = 3; i--; ) {
438     hess[i][0] = -hess[i][0];
439     hess[i][1] = -hess[i][1];
440     hess[i][2] = -hess[i][2];
441     }
442     }
443    
444    
445     /* Add to radiometric Hessian from the given triangle */
446     static void
447     add2hessian(FVECT hess[3], FVECT ehess1[3],
448 greg 2.46 FVECT ehess2[3], FVECT ehess3[3], double v)
449 greg 2.27 {
450     int i, j;
451    
452     for (i = 3; i--; )
453     for (j = 3; j--; )
454     hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
455     }
456    
457    
458     /* Compute partial displacement form factor gradient for edge */
459     static void
460     comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
461     {
462 greg 2.35 FVECT ncp;
463 greg 2.27 double f1;
464     int i;
465    
466 greg 2.35 f1 = 2.0*DOT(nrm, ftp->rcp);
467     VCROSS(ncp, nrm, ftp->e_i);
468 greg 2.27 for (i = 3; i--; )
469 greg 2.46 grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
470 greg 2.27 }
471    
472    
473     /* Reverse gradient calculation result for edge in other direction */
474     static void
475     rev_gradient(FVECT grad)
476     {
477     grad[0] = -grad[0];
478     grad[1] = -grad[1];
479     grad[2] = -grad[2];
480     }
481    
482    
483     /* Add to displacement gradient from the given triangle */
484     static void
485 greg 2.46 add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
486 greg 2.27 {
487     int i;
488    
489     for (i = 3; i--; )
490     grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
491     }
492    
493    
494     /* Compute anisotropic radii and eigenvector directions */
495 greg 2.53 static void
496 greg 2.27 eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
497     {
498     double hess2[2][2];
499     FVECT a, b;
500     double evalue[2], slope1, xmag1;
501     int i;
502     /* project Hessian to sample plane */
503     for (i = 3; i--; ) {
504     a[i] = DOT(hessian[i], uv[0]);
505     b[i] = DOT(hessian[i], uv[1]);
506     }
507     hess2[0][0] = DOT(uv[0], a);
508     hess2[0][1] = DOT(uv[0], b);
509     hess2[1][0] = DOT(uv[1], a);
510     hess2[1][1] = DOT(uv[1], b);
511 greg 2.38 /* compute eigenvalue(s) */
512     i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
513     hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
514     if (i == 1) /* double-root (circle) */
515     evalue[1] = evalue[0];
516     if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
517 greg 2.53 ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
518     ra[0] = ra[1] = maxarad;
519     return;
520     }
521 greg 2.27 if (evalue[0] > evalue[1]) {
522 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[0]));
523     ra[1] = sqrt(sqrt(4.0/evalue[1]));
524 greg 2.27 slope1 = evalue[1];
525     } else {
526 greg 2.29 ra[0] = sqrt(sqrt(4.0/evalue[1]));
527     ra[1] = sqrt(sqrt(4.0/evalue[0]));
528 greg 2.27 slope1 = evalue[0];
529     }
530     /* compute unit eigenvectors */
531     if (fabs(hess2[0][1]) <= FTINY)
532     return; /* uv OK as is */
533     slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
534     xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
535     for (i = 3; i--; ) {
536     b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
537     a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
538     }
539     VCOPY(uv[0], a);
540     VCOPY(uv[1], b);
541     }
542    
543    
544 greg 2.26 static void
545     ambHessian( /* anisotropic radii & pos. gradient */
546     AMBHEMI *hp,
547     FVECT uv[2], /* returned */
548 greg 2.28 float ra[2], /* returned (optional) */
549     float pg[2] /* returned (optional) */
550 greg 2.26 )
551     {
552 greg 2.27 static char memerrmsg[] = "out of memory in ambHessian()";
553     FVECT (*hessrow)[3] = NULL;
554     FVECT *gradrow = NULL;
555     FVECT hessian[3];
556     FVECT gradient;
557     FFTRI fftr;
558     int i, j;
559     /* be sure to assign unit vectors */
560     VCOPY(uv[0], hp->ux);
561     VCOPY(uv[1], hp->uy);
562     /* clock-wise vertex traversal from sample POV */
563     if (ra != NULL) { /* initialize Hessian row buffer */
564 greg 2.28 hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
565 greg 2.27 if (hessrow == NULL)
566     error(SYSTEM, memerrmsg);
567     memset(hessian, 0, sizeof(hessian));
568     } else if (pg == NULL) /* bogus call? */
569     return;
570     if (pg != NULL) { /* initialize form factor row buffer */
571 greg 2.28 gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
572 greg 2.27 if (gradrow == NULL)
573     error(SYSTEM, memerrmsg);
574     memset(gradient, 0, sizeof(gradient));
575     }
576     /* compute first row of edges */
577     for (j = 0; j < hp->ns-1; j++) {
578 greg 2.56 comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
579 greg 2.27 if (hessrow != NULL)
580 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
581 greg 2.27 if (gradrow != NULL)
582 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
583 greg 2.27 }
584     /* sum each row of triangles */
585     for (i = 0; i < hp->ns-1; i++) {
586     FVECT hesscol[3]; /* compute first vertical edge */
587     FVECT gradcol;
588 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
589 greg 2.27 if (hessrow != NULL)
590 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
591 greg 2.27 if (gradrow != NULL)
592 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
593 greg 2.27 for (j = 0; j < hp->ns-1; j++) {
594     FVECT hessdia[3]; /* compute triangle contributions */
595     FVECT graddia;
596 greg 2.46 double backg;
597 greg 2.56 backg = back_ambval(hp, AI(hp,i,j),
598     AI(hp,i,j+1), AI(hp,i+1,j));
599 greg 2.27 /* diagonal (inner) edge */
600 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
601 greg 2.27 if (hessrow != NULL) {
602 greg 2.92 comp_hessian(hessdia, &fftr, hp->onrm);
603 greg 2.27 rev_hessian(hesscol);
604     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
605     }
606 greg 2.39 if (gradrow != NULL) {
607 greg 2.92 comp_gradient(graddia, &fftr, hp->onrm);
608 greg 2.27 rev_gradient(gradcol);
609     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
610     }
611     /* initialize edge in next row */
612 greg 2.56 comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
613 greg 2.27 if (hessrow != NULL)
614 greg 2.92 comp_hessian(hessrow[j], &fftr, hp->onrm);
615 greg 2.27 if (gradrow != NULL)
616 greg 2.92 comp_gradient(gradrow[j], &fftr, hp->onrm);
617 greg 2.27 /* new column edge & paired triangle */
618 greg 2.56 backg = back_ambval(hp, AI(hp,i+1,j+1),
619     AI(hp,i+1,j), AI(hp,i,j+1));
620     comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
621 greg 2.27 if (hessrow != NULL) {
622 greg 2.92 comp_hessian(hesscol, &fftr, hp->onrm);
623 greg 2.27 rev_hessian(hessdia);
624     add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
625     if (i < hp->ns-2)
626     rev_hessian(hessrow[j]);
627     }
628     if (gradrow != NULL) {
629 greg 2.92 comp_gradient(gradcol, &fftr, hp->onrm);
630 greg 2.27 rev_gradient(graddia);
631     add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
632     if (i < hp->ns-2)
633     rev_gradient(gradrow[j]);
634     }
635     }
636     }
637     /* release row buffers */
638     if (hessrow != NULL) free(hessrow);
639     if (gradrow != NULL) free(gradrow);
640    
641     if (ra != NULL) /* extract eigenvectors & radii */
642     eigenvectors(uv, ra, hessian);
643 greg 2.32 if (pg != NULL) { /* tangential position gradient */
644     pg[0] = DOT(gradient, uv[0]);
645     pg[1] = DOT(gradient, uv[1]);
646 greg 2.27 }
647     }
648    
649    
650     /* Compute direction gradient from a hemispherical sampling */
651     static void
652     ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
653     {
654 greg 2.41 AMBSAMP *ap;
655     double dgsum[2];
656     int n;
657     FVECT vd;
658     double gfact;
659 greg 2.27
660 greg 2.29 dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
661 greg 2.27 for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
662     /* use vector for azimuth + 90deg */
663     VSUB(vd, ap->p, hp->rp->rop);
664 greg 2.29 /* brightness over cosine factor */
665 greg 2.92 gfact = ap->v[0] / DOT(hp->onrm, vd);
666 greg 2.40 /* sine = proj_radius/vd_length */
667     dgsum[0] -= DOT(uv[1], vd) * gfact;
668     dgsum[1] += DOT(uv[0], vd) * gfact;
669 greg 2.26 }
670 greg 2.29 dg[0] = dgsum[0] / (hp->ns*hp->ns);
671     dg[1] = dgsum[1] / (hp->ns*hp->ns);
672 greg 2.26 }
673    
674 greg 2.27
675 greg 2.49 /* Compute potential light leak direction flags for cache value */
676     static uint32
677     ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
678 greg 2.47 {
679 greg 2.50 const double max_d = 1.0/(minarad*ambacc + 0.001);
680 greg 2.66 const double ang_res = 0.5*PI/hp->ns;
681     const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
682 greg 2.51 double avg_d = 0;
683 greg 2.50 uint32 flgs = 0;
684 greg 2.58 FVECT vec;
685 greg 2.62 double u, v;
686 greg 2.58 double ang, a1;
687 greg 2.50 int i, j;
688 greg 2.52 /* don't bother for a few samples */
689 greg 2.72 if (hp->ns < 8)
690 greg 2.52 return(0);
691     /* check distances overhead */
692 greg 2.51 for (i = hp->ns*3/4; i-- > hp->ns>>2; )
693     for (j = hp->ns*3/4; j-- > hp->ns>>2; )
694     avg_d += ambsam(hp,i,j).d;
695     avg_d *= 4.0/(hp->ns*hp->ns);
696 greg 2.52 if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
697     return(0);
698     if (avg_d >= max_d) /* insurance */
699 greg 2.51 return(0);
700     /* else circle around perimeter */
701 greg 2.47 for (i = 0; i < hp->ns; i++)
702     for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
703     AMBSAMP *ap = &ambsam(hp,i,j);
704 greg 2.50 if ((ap->d <= FTINY) | (ap->d >= max_d))
705     continue; /* too far or too near */
706 greg 2.47 VSUB(vec, ap->p, hp->rp->rop);
707 greg 2.62 u = DOT(vec, uv[0]);
708     v = DOT(vec, uv[1]);
709     if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
710 greg 2.49 continue; /* occluder outside ellipse */
711     ang = atan2a(v, u); /* else set direction flags */
712 greg 2.66 for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
713 greg 2.50 flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
714 greg 2.47 }
715 greg 2.49 return(flgs);
716 greg 2.47 }
717    
718    
719 greg 2.26 int
720     doambient( /* compute ambient component */
721 greg 2.90 SCOLOR rcol, /* input/output color */
722 greg 2.26 RAY *r,
723 greg 2.92 double wt, /* negative for back side */
724 greg 2.27 FVECT uv[2], /* returned (optional) */
725     float ra[2], /* returned (optional) */
726     float pg[2], /* returned (optional) */
727 greg 2.49 float dg[2], /* returned (optional) */
728     uint32 *crlp /* returned (optional) */
729 greg 2.26 )
730     {
731 greg 2.61 AMBHEMI *hp = samp_hemi(rcol, r, wt);
732 greg 2.41 FVECT my_uv[2];
733 greg 2.61 double d, K;
734 greg 2.41 AMBSAMP *ap;
735 greg 2.61 int i;
736     /* clear return values */
737 greg 2.26 if (uv != NULL)
738     memset(uv, 0, sizeof(FVECT)*2);
739     if (ra != NULL)
740     ra[0] = ra[1] = 0.0;
741     if (pg != NULL)
742     pg[0] = pg[1] = 0.0;
743     if (dg != NULL)
744     dg[0] = dg[1] = 0.0;
745 greg 2.49 if (crlp != NULL)
746     *crlp = 0;
747 greg 2.61 if (hp == NULL) /* sampling falure? */
748     return(0);
749    
750     if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
751 greg 2.86 (hp->sampOK < 0) | (hp->ns < MINADIV)) {
752 greg 2.61 free(hp); /* Hessian not requested/possible */
753     return(-1); /* value-only return value */
754 greg 2.26 }
755 greg 2.91 if ((d = scolor_mean(rcol)) > FTINY) {
756     d = 0.99*(hp->ns*hp->ns)/d; /* normalize avg. values */
757 greg 2.38 K = 0.01;
758 greg 2.45 } else { /* or fall back on geometric Hessian */
759 greg 2.38 K = 1.0;
760     pg = NULL;
761     dg = NULL;
762 greg 2.53 crlp = NULL;
763 greg 2.38 }
764 greg 2.90 ap = hp->sa; /* single channel from here on... */
765 greg 2.26 for (i = hp->ns*hp->ns; i--; ap++)
766 greg 2.90 ap->v[0] = scolor_mean(ap->v)*d + K;
767 greg 2.26
768     if (uv == NULL) /* make sure we have axis pointers */
769     uv = my_uv;
770     /* compute radii & pos. gradient */
771     ambHessian(hp, uv, ra, pg);
772 greg 2.29
773 greg 2.26 if (dg != NULL) /* compute direction gradient */
774     ambdirgrad(hp, uv, dg);
775 greg 2.29
776 greg 2.28 if (ra != NULL) { /* scale/clamp radii */
777 greg 2.35 if (pg != NULL) {
778     if (ra[0]*(d = fabs(pg[0])) > 1.0)
779     ra[0] = 1.0/d;
780     if (ra[1]*(d = fabs(pg[1])) > 1.0)
781     ra[1] = 1.0/d;
782 greg 2.48 if (ra[0] > ra[1])
783     ra[0] = ra[1];
784 greg 2.35 }
785 greg 2.29 if (ra[0] < minarad) {
786     ra[0] = minarad;
787     if (ra[1] < minarad)
788     ra[1] = minarad;
789     }
790 greg 2.92 ra[0] *= d = 1.0/sqrt(fabs(wt));
791 greg 2.26 if ((ra[1] *= d) > 2.0*ra[0])
792     ra[1] = 2.0*ra[0];
793 greg 2.28 if (ra[1] > maxarad) {
794     ra[1] = maxarad;
795     if (ra[0] > maxarad)
796     ra[0] = maxarad;
797     }
798 greg 2.53 /* flag encroached directions */
799 greg 2.87 if (crlp != NULL) /* XXX doesn't update with changes to ambacc */
800 greg 2.49 *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
801 greg 2.35 if (pg != NULL) { /* cap gradient if necessary */
802     d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
803     if (d > 1.0) {
804     d = 1.0/sqrt(d);
805     pg[0] *= d;
806     pg[1] *= d;
807     }
808     }
809 greg 2.26 }
810     free(hp); /* clean up and return */
811     return(1);
812     }