1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: ambcomp.c,v 2.85 2019/05/14 17:39:10 greg Exp $"; |
3 |
#endif |
4 |
/* |
5 |
* Routines to compute "ambient" values using Monte Carlo |
6 |
* |
7 |
* 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 |
* 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 |
* Declarations of external symbols in ambient.h |
16 |
*/ |
17 |
|
18 |
#include "copyright.h" |
19 |
|
20 |
#include "ray.h" |
21 |
#include "ambient.h" |
22 |
#include "random.h" |
23 |
|
24 |
#ifndef MINADIV |
25 |
#define MINADIV 7 /* minimum # divisions in each dimension */ |
26 |
#endif |
27 |
|
28 |
extern void SDsquare2disk(double ds[2], double seedx, double seedy); |
29 |
|
30 |
typedef struct { |
31 |
COLOR v; /* hemisphere sample value */ |
32 |
float d; /* reciprocal distance */ |
33 |
FVECT p; /* intersection point */ |
34 |
} AMBSAMP; /* sample value */ |
35 |
|
36 |
typedef struct { |
37 |
RAY *rp; /* originating ray sample */ |
38 |
int ns; /* number of samples per axis */ |
39 |
int sampOK; /* acquired full sample set? */ |
40 |
COLOR acoef; /* division contribution coefficient */ |
41 |
double acol[3]; /* accumulated color */ |
42 |
FVECT ux, uy; /* tangent axis unit vectors */ |
43 |
AMBSAMP sa[1]; /* sample array (extends struct) */ |
44 |
} AMBHEMI; /* ambient sample hemisphere */ |
45 |
|
46 |
#define AI(h,i,j) ((i)*(h)->ns + (j)) |
47 |
#define ambsam(h,i,j) (h)->sa[AI(h,i,j)] |
48 |
|
49 |
typedef struct { |
50 |
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
51 |
double I1, I2; |
52 |
} FFTRI; /* vectors and coefficients for Hessian calculation */ |
53 |
|
54 |
|
55 |
static int |
56 |
ambcollision( /* proposed direciton collides? */ |
57 |
AMBHEMI *hp, |
58 |
int i, |
59 |
int j, |
60 |
FVECT dv |
61 |
) |
62 |
{ |
63 |
double cos_thresh; |
64 |
int ii, jj; |
65 |
/* min. spacing = 1/4th division */ |
66 |
cos_thresh = (PI/4.)/(double)hp->ns; |
67 |
cos_thresh = 1. - .5*cos_thresh*cos_thresh; |
68 |
/* check existing neighbors */ |
69 |
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 |
if (ap->d <= .5/FHUGE) |
81 |
continue; /* no one home */ |
82 |
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 |
return(0); /* nothing to worry about */ |
89 |
} |
90 |
|
91 |
|
92 |
static int |
93 |
ambsample( /* initial ambient division sample */ |
94 |
AMBHEMI *hp, |
95 |
int i, |
96 |
int j, |
97 |
int n |
98 |
) |
99 |
{ |
100 |
AMBSAMP *ap = &ambsam(hp,i,j); |
101 |
RAY ar; |
102 |
int hlist[3], ii; |
103 |
double spt[2], zd; |
104 |
/* generate hemispherical sample */ |
105 |
/* ambient coefficient for weight */ |
106 |
if (ambacc > FTINY) |
107 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
108 |
else |
109 |
copycolor(ar.rcoef, hp->acoef); |
110 |
if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0) |
111 |
return(0); |
112 |
if (ambacc > FTINY) { |
113 |
multcolor(ar.rcoef, hp->acoef); |
114 |
scalecolor(ar.rcoef, 1./AVGREFL); |
115 |
} |
116 |
hlist[0] = hp->rp->rno; |
117 |
hlist[1] = j; |
118 |
hlist[2] = i; |
119 |
multisamp(spt, 2, urand(ilhash(hlist,3)+n)); |
120 |
resample: |
121 |
SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns); |
122 |
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
123 |
for (ii = 3; ii--; ) |
124 |
ar.rdir[ii] = spt[0]*hp->ux[ii] + |
125 |
spt[1]*hp->uy[ii] + |
126 |
zd*hp->rp->ron[ii]; |
127 |
checknorm(ar.rdir); |
128 |
/* avoid coincident samples */ |
129 |
if (!n && ambcollision(hp, i, j, ar.rdir)) { |
130 |
spt[0] = frandom(); spt[1] = frandom(); |
131 |
goto resample; /* reject this sample */ |
132 |
} |
133 |
dimlist[ndims++] = AI(hp,i,j) + 90171; |
134 |
rayvalue(&ar); /* evaluate ray */ |
135 |
ndims--; |
136 |
zd = raydistance(&ar); |
137 |
if (zd <= FTINY) |
138 |
return(0); /* should never happen */ |
139 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
140 |
if (zd*ap->d < 1.0) /* new/closer distance? */ |
141 |
ap->d = 1.0/zd; |
142 |
if (!n) { /* record first vertex & value */ |
143 |
if (zd > 10.0*thescene.cusize + 1000.) |
144 |
zd = 10.0*thescene.cusize + 1000.; |
145 |
VSUM(ap->p, ar.rorg, ar.rdir, zd); |
146 |
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 |
return(1); |
159 |
} |
160 |
|
161 |
|
162 |
/* Estimate variance based on ambient division differences */ |
163 |
static float * |
164 |
getambdiffs(AMBHEMI *hp) |
165 |
{ |
166 |
const double normf = 1./bright(hp->acoef); |
167 |
float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float)); |
168 |
float *ep; |
169 |
AMBSAMP *ap; |
170 |
double b, b1, d2; |
171 |
int i, j; |
172 |
|
173 |
if (earr == NULL) /* out of memory? */ |
174 |
return(NULL); |
175 |
/* sum squared neighbor diffs */ |
176 |
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 |
if (i) { /* from above */ |
180 |
b1 = bright(ap[-hp->ns].v); |
181 |
d2 = b - b1; |
182 |
d2 *= d2*normf/(b + b1); |
183 |
ep[0] += d2; |
184 |
ep[-hp->ns] += d2; |
185 |
} |
186 |
if (!j) continue; |
187 |
/* from behind */ |
188 |
b1 = bright(ap[-1].v); |
189 |
d2 = b - b1; |
190 |
d2 *= d2*normf/(b + b1); |
191 |
ep[0] += d2; |
192 |
ep[-1] += d2; |
193 |
if (!i) continue; |
194 |
/* diagonal */ |
195 |
b1 = bright(ap[-hp->ns-1].v); |
196 |
d2 = b - b1; |
197 |
d2 *= d2*normf/(b + b1); |
198 |
ep[0] += d2; |
199 |
ep[-hp->ns-1] += d2; |
200 |
} |
201 |
/* correct for number of neighbors */ |
202 |
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 |
for (i = 1; i < hp->ns-1; i++) { |
207 |
earr[i*hp->ns] *= 8./5.; |
208 |
earr[i*hp->ns + hp->ns-1] *= 8./5.; |
209 |
} |
210 |
for (j = 1; j < hp->ns-1; j++) { |
211 |
earr[j] *= 8./5.; |
212 |
earr[(hp->ns-1)*hp->ns + j] *= 8./5.; |
213 |
} |
214 |
return(earr); |
215 |
} |
216 |
|
217 |
|
218 |
/* Perform super-sampling on hemisphere (introduces bias) */ |
219 |
static void |
220 |
ambsupersamp(AMBHEMI *hp, int cnt) |
221 |
{ |
222 |
float *earr = getambdiffs(hp); |
223 |
double e2rem = 0; |
224 |
float *ep; |
225 |
int i, j, n, nss; |
226 |
|
227 |
if (earr == NULL) /* just skip calc. if no memory */ |
228 |
return; |
229 |
/* accumulate estimated variances */ |
230 |
for (ep = earr + hp->ns*hp->ns; ep > earr; ) |
231 |
e2rem += *--ep; |
232 |
ep = earr; /* perform super-sampling */ |
233 |
for (i = 0; i < hp->ns; i++) |
234 |
for (j = 0; j < hp->ns; j++) { |
235 |
if (e2rem <= FTINY) |
236 |
goto done; /* nothing left to do */ |
237 |
nss = *ep/e2rem*cnt + frandom(); |
238 |
for (n = 1; n <= nss && ambsample(hp,i,j,n); n++) |
239 |
if (!--cnt) goto done; |
240 |
e2rem -= *ep++; /* update remainder */ |
241 |
} |
242 |
done: |
243 |
free(earr); |
244 |
} |
245 |
|
246 |
|
247 |
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 |
/* insignificance check */ |
258 |
if (bright(rcol) <= FTINY) |
259 |
return(NULL); |
260 |
/* 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 |
i = 1 + (MINADIV-1)*(ambacc > FTINY); |
266 |
if (n < i) /* use minimum number of samples? */ |
267 |
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 |
memset(hp->sa, 0, sizeof(AMBSAMP)*n*n); |
276 |
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 |
if (!getperpendicular(hp->ux, r->ron, 1)) |
283 |
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 |
if (hp->sampOK <= MINADIV*MINADIV) |
299 |
return(hp); /* don't bother super-sampling */ |
300 |
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 |
/* Return brightness of farthest ambient sample */ |
310 |
static double |
311 |
back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3) |
312 |
{ |
313 |
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 |
} |
322 |
|
323 |
|
324 |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
325 |
static void |
326 |
comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1) |
327 |
{ |
328 |
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 |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
335 |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
336 |
dot_e = DOT(ftp->e_i,ftp->e_i); |
337 |
dot_er = DOT(ftp->e_i, ftp->r_i); |
338 |
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 |
sqrt( rdot_cp ); |
342 |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
343 |
dot_e*ftp->I1 )*0.5*rdot_cp; |
344 |
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
345 |
for (ii = 3; ii--; ) |
346 |
ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii]; |
347 |
} |
348 |
|
349 |
|
350 |
/* Compose 3x3 matrix from two vectors */ |
351 |
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 |
FVECT ncp; |
368 |
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 |
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 |
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 |
VCROSS(ncp, nrm, ftp->e_i); |
383 |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
384 |
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 |
d1 = DOT(nrm, ftp->rcp); |
388 |
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 |
hess[i][j] *= -1.0/PI; |
396 |
} |
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 |
FVECT ehess2[3], FVECT ehess3[3], double v) |
418 |
{ |
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 |
FVECT ncp; |
432 |
double f1; |
433 |
int i; |
434 |
|
435 |
f1 = 2.0*DOT(nrm, ftp->rcp); |
436 |
VCROSS(ncp, nrm, ftp->e_i); |
437 |
for (i = 3; i--; ) |
438 |
grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
439 |
} |
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 |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v) |
455 |
{ |
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 |
static void |
465 |
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 |
/* 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 |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) { |
487 |
ra[0] = ra[1] = maxarad; |
488 |
return; |
489 |
} |
490 |
if (evalue[0] > evalue[1]) { |
491 |
ra[0] = sqrt(sqrt(4.0/evalue[0])); |
492 |
ra[1] = sqrt(sqrt(4.0/evalue[1])); |
493 |
slope1 = evalue[1]; |
494 |
} else { |
495 |
ra[0] = sqrt(sqrt(4.0/evalue[1])); |
496 |
ra[1] = sqrt(sqrt(4.0/evalue[0])); |
497 |
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 |
static void |
514 |
ambHessian( /* anisotropic radii & pos. gradient */ |
515 |
AMBHEMI *hp, |
516 |
FVECT uv[2], /* returned */ |
517 |
float ra[2], /* returned (optional) */ |
518 |
float pg[2] /* returned (optional) */ |
519 |
) |
520 |
{ |
521 |
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 |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1)); |
534 |
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 |
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1)); |
541 |
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 |
comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1)); |
548 |
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 |
comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0)); |
558 |
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 |
double backg; |
566 |
backg = back_ambval(hp, AI(hp,i,j), |
567 |
AI(hp,i,j+1), AI(hp,i+1,j)); |
568 |
/* diagonal (inner) edge */ |
569 |
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j)); |
570 |
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 |
if (gradrow != NULL) { |
576 |
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 |
comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j)); |
582 |
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 |
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 |
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 |
if (pg != NULL) { /* tangential position gradient */ |
613 |
pg[0] = DOT(gradient, uv[0]); |
614 |
pg[1] = DOT(gradient, uv[1]); |
615 |
} |
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 |
AMBSAMP *ap; |
624 |
double dgsum[2]; |
625 |
int n; |
626 |
FVECT vd; |
627 |
double gfact; |
628 |
|
629 |
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */ |
630 |
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 |
/* brightness over cosine factor */ |
634 |
gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd); |
635 |
/* sine = proj_radius/vd_length */ |
636 |
dgsum[0] -= DOT(uv[1], vd) * gfact; |
637 |
dgsum[1] += DOT(uv[0], vd) * gfact; |
638 |
} |
639 |
dg[0] = dgsum[0] / (hp->ns*hp->ns); |
640 |
dg[1] = dgsum[1] / (hp->ns*hp->ns); |
641 |
} |
642 |
|
643 |
|
644 |
/* 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 |
{ |
648 |
const double max_d = 1.0/(minarad*ambacc + 0.001); |
649 |
const double ang_res = 0.5*PI/hp->ns; |
650 |
const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01); |
651 |
double avg_d = 0; |
652 |
uint32 flgs = 0; |
653 |
FVECT vec; |
654 |
double u, v; |
655 |
double ang, a1; |
656 |
int i, j; |
657 |
/* don't bother for a few samples */ |
658 |
if (hp->ns < 8) |
659 |
return(0); |
660 |
/* check distances overhead */ |
661 |
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 |
if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */ |
666 |
return(0); |
667 |
if (avg_d >= max_d) /* insurance */ |
668 |
return(0); |
669 |
/* else circle around perimeter */ |
670 |
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 |
if ((ap->d <= FTINY) | (ap->d >= max_d)) |
674 |
continue; /* too far or too near */ |
675 |
VSUB(vec, ap->p, hp->rp->rop); |
676 |
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 |
continue; /* occluder outside ellipse */ |
680 |
ang = atan2a(v, u); /* else set direction flags */ |
681 |
for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step) |
682 |
flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0))); |
683 |
} |
684 |
return(flgs); |
685 |
} |
686 |
|
687 |
|
688 |
int |
689 |
doambient( /* compute ambient component */ |
690 |
COLOR rcol, /* input/output color */ |
691 |
RAY *r, |
692 |
double wt, |
693 |
FVECT uv[2], /* returned (optional) */ |
694 |
float ra[2], /* returned (optional) */ |
695 |
float pg[2], /* returned (optional) */ |
696 |
float dg[2], /* returned (optional) */ |
697 |
uint32 *crlp /* returned (optional) */ |
698 |
) |
699 |
{ |
700 |
AMBHEMI *hp = samp_hemi(rcol, r, wt); |
701 |
FVECT my_uv[2]; |
702 |
double d, K; |
703 |
AMBSAMP *ap; |
704 |
int i; |
705 |
/* clear return values */ |
706 |
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 |
if (crlp != NULL) |
715 |
*crlp = 0; |
716 |
if (hp == NULL) /* sampling falure? */ |
717 |
return(0); |
718 |
|
719 |
if ((ra == NULL) & (pg == NULL) & (dg == NULL) || |
720 |
(hp->sampOK < 0) | (hp->ns < MINADIV)) { |
721 |
free(hp); /* Hessian not requested/possible */ |
722 |
return(-1); /* value-only return value */ |
723 |
} |
724 |
if ((d = bright(rcol)) > FTINY) { /* normalize Y values */ |
725 |
d = 0.99*(hp->ns*hp->ns)/d; |
726 |
K = 0.01; |
727 |
} else { /* or fall back on geometric Hessian */ |
728 |
K = 1.0; |
729 |
pg = NULL; |
730 |
dg = NULL; |
731 |
crlp = NULL; |
732 |
} |
733 |
ap = hp->sa; /* relative Y channel from here on... */ |
734 |
for (i = hp->ns*hp->ns; i--; ap++) |
735 |
colval(ap->v,CIEY) = bright(ap->v)*d + K; |
736 |
|
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 |
|
742 |
if (dg != NULL) /* compute direction gradient */ |
743 |
ambdirgrad(hp, uv, dg); |
744 |
|
745 |
if (ra != NULL) { /* scale/clamp radii */ |
746 |
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 |
if (ra[0] > ra[1]) |
752 |
ra[0] = ra[1]; |
753 |
} |
754 |
if (ra[0] < minarad) { |
755 |
ra[0] = minarad; |
756 |
if (ra[1] < minarad) |
757 |
ra[1] = minarad; |
758 |
} |
759 |
ra[0] *= d = 1.0/sqrt(wt); |
760 |
if ((ra[1] *= d) > 2.0*ra[0]) |
761 |
ra[1] = 2.0*ra[0]; |
762 |
if (ra[1] > maxarad) { |
763 |
ra[1] = maxarad; |
764 |
if (ra[0] > maxarad) |
765 |
ra[0] = maxarad; |
766 |
} |
767 |
/* flag encroached directions */ |
768 |
if (crlp != NULL) |
769 |
*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc); |
770 |
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 |
} |
779 |
free(hp); /* clean up and return */ |
780 |
return(1); |
781 |
} |
782 |
|