1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: ambcomp.c,v 2.60 2014/05/17 00:49:17 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 |
#ifdef NEWAMB |
25 |
|
26 |
extern void SDsquare2disk(double ds[2], double seedx, double seedy); |
27 |
|
28 |
typedef struct { |
29 |
COLOR v; /* hemisphere sample value */ |
30 |
float d; /* reciprocal distance (1/rt) */ |
31 |
FVECT p; /* intersection point */ |
32 |
} AMBSAMP; /* sample value */ |
33 |
|
34 |
typedef struct { |
35 |
RAY *rp; /* originating ray sample */ |
36 |
int ns; /* number of samples per axis */ |
37 |
int sampOK; /* acquired full sample set? */ |
38 |
COLOR acoef; /* division contribution coefficient */ |
39 |
double acol[3]; /* accumulated color */ |
40 |
FVECT ux, uy; /* tangent axis unit vectors */ |
41 |
AMBSAMP sa[1]; /* sample array (extends struct) */ |
42 |
} AMBHEMI; /* ambient sample hemisphere */ |
43 |
|
44 |
#define AI(h,i,j) ((i)*(h)->ns + (j)) |
45 |
#define ambsam(h,i,j) (h)->sa[AI(h,i,j)] |
46 |
|
47 |
typedef struct { |
48 |
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
49 |
double I1, I2; |
50 |
} FFTRI; /* vectors and coefficients for Hessian calculation */ |
51 |
|
52 |
|
53 |
static int |
54 |
ambsample( /* initial ambient division sample */ |
55 |
AMBHEMI *hp, |
56 |
int i, |
57 |
int j, |
58 |
int n |
59 |
) |
60 |
{ |
61 |
AMBSAMP *ap = &ambsam(hp,i,j); |
62 |
RAY ar; |
63 |
int hlist[3], ii; |
64 |
double spt[2], zd; |
65 |
/* generate hemispherical sample */ |
66 |
/* ambient coefficient for weight */ |
67 |
if (ambacc > FTINY) |
68 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
69 |
else |
70 |
copycolor(ar.rcoef, hp->acoef); |
71 |
if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0) { |
72 |
if (!n) memset(ap, 0, sizeof(AMBSAMP)); |
73 |
return(0); |
74 |
} |
75 |
if (ambacc > FTINY) { |
76 |
multcolor(ar.rcoef, hp->acoef); |
77 |
scalecolor(ar.rcoef, 1./AVGREFL); |
78 |
} |
79 |
hlist[0] = hp->rp->rno; |
80 |
hlist[1] = j; |
81 |
hlist[2] = i; |
82 |
multisamp(spt, 2, urand(ilhash(hlist,3)+n)); |
83 |
if (!n) { /* avoid border samples for n==0 */ |
84 |
if ((spt[0] < 0.1) | (spt[0] >= 0.9)) |
85 |
spt[0] = 0.1 + 0.8*frandom(); |
86 |
if ((spt[1] < 0.1) | (spt[1] >= 0.9)) |
87 |
spt[1] = 0.1 + 0.8*frandom(); |
88 |
} |
89 |
SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns); |
90 |
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
91 |
for (ii = 3; ii--; ) |
92 |
ar.rdir[ii] = spt[0]*hp->ux[ii] + |
93 |
spt[1]*hp->uy[ii] + |
94 |
zd*hp->rp->ron[ii]; |
95 |
checknorm(ar.rdir); |
96 |
dimlist[ndims++] = AI(hp,i,j) + 90171; |
97 |
rayvalue(&ar); /* evaluate ray */ |
98 |
ndims--; |
99 |
if (ar.rt <= FTINY) |
100 |
return(0); /* should never happen */ |
101 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
102 |
if (!n || ar.rt*ap->d < 1.0) /* new/closer distance? */ |
103 |
ap->d = 1.0/ar.rt; |
104 |
if (!n) { /* record first vertex & value */ |
105 |
if (ar.rt > 10.0*thescene.cusize) |
106 |
ar.rt = 10.0*thescene.cusize; |
107 |
VSUM(ap->p, ar.rorg, ar.rdir, ar.rt); |
108 |
copycolor(ap->v, ar.rcol); |
109 |
} else { /* else update recorded value */ |
110 |
hp->acol[RED] -= colval(ap->v,RED); |
111 |
hp->acol[GRN] -= colval(ap->v,GRN); |
112 |
hp->acol[BLU] -= colval(ap->v,BLU); |
113 |
zd = 1.0/(double)(n+1); |
114 |
scalecolor(ar.rcol, zd); |
115 |
zd *= (double)n; |
116 |
scalecolor(ap->v, zd); |
117 |
addcolor(ap->v, ar.rcol); |
118 |
} |
119 |
addcolor(hp->acol, ap->v); /* add to our sum */ |
120 |
return(1); |
121 |
} |
122 |
|
123 |
|
124 |
/* Estimate errors based on ambient division differences */ |
125 |
static float * |
126 |
getambdiffs(AMBHEMI *hp) |
127 |
{ |
128 |
float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float)); |
129 |
float *ep; |
130 |
AMBSAMP *ap; |
131 |
double b, d2; |
132 |
int i, j; |
133 |
|
134 |
if (earr == NULL) /* out of memory? */ |
135 |
return(NULL); |
136 |
/* compute squared neighbor diffs */ |
137 |
for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++) |
138 |
for (j = 0; j < hp->ns; j++, ap++, ep++) { |
139 |
b = bright(ap[0].v); |
140 |
if (i) { /* from above */ |
141 |
d2 = b - bright(ap[-hp->ns].v); |
142 |
d2 *= d2; |
143 |
ep[0] += d2; |
144 |
ep[-hp->ns] += d2; |
145 |
} |
146 |
if (!j) continue; |
147 |
/* from behind */ |
148 |
d2 = b - bright(ap[-1].v); |
149 |
d2 *= d2; |
150 |
ep[0] += d2; |
151 |
ep[-1] += d2; |
152 |
if (!i) continue; |
153 |
/* diagonal */ |
154 |
d2 = b - bright(ap[-hp->ns-1].v); |
155 |
d2 *= d2; |
156 |
ep[0] += d2; |
157 |
ep[-hp->ns-1] += d2; |
158 |
} |
159 |
/* correct for number of neighbors */ |
160 |
earr[0] *= 8./3.; |
161 |
earr[hp->ns-1] *= 8./3.; |
162 |
earr[(hp->ns-1)*hp->ns] *= 8./3.; |
163 |
earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.; |
164 |
for (i = 1; i < hp->ns-1; i++) { |
165 |
earr[i*hp->ns] *= 8./5.; |
166 |
earr[i*hp->ns + hp->ns-1] *= 8./5.; |
167 |
} |
168 |
for (j = 1; j < hp->ns-1; j++) { |
169 |
earr[j] *= 8./5.; |
170 |
earr[(hp->ns-1)*hp->ns + j] *= 8./5.; |
171 |
} |
172 |
return(earr); |
173 |
} |
174 |
|
175 |
|
176 |
/* Perform super-sampling on hemisphere (introduces bias) */ |
177 |
static void |
178 |
ambsupersamp(AMBHEMI *hp, int cnt) |
179 |
{ |
180 |
float *earr = getambdiffs(hp); |
181 |
double e2rem = 0; |
182 |
AMBSAMP *ap; |
183 |
RAY ar; |
184 |
float *ep; |
185 |
int i, j, n, nss; |
186 |
|
187 |
if (earr == NULL) /* just skip calc. if no memory */ |
188 |
return; |
189 |
/* accumulate estimated variances */ |
190 |
for (ep = earr + hp->ns*hp->ns; ep > earr; ) |
191 |
e2rem += *--ep; |
192 |
ep = earr; /* perform super-sampling */ |
193 |
for (ap = hp->sa, i = 0; i < hp->ns; i++) |
194 |
for (j = 0; j < hp->ns; j++, ap++) { |
195 |
if (e2rem <= FTINY) |
196 |
goto done; /* nothing left to do */ |
197 |
nss = *ep/e2rem*cnt + frandom(); |
198 |
for (n = 1; n <= nss; n++) |
199 |
cnt -= ambsample(hp, i, j, n); |
200 |
e2rem -= *ep++; /* update remainder */ |
201 |
} |
202 |
done: |
203 |
free(earr); |
204 |
} |
205 |
|
206 |
|
207 |
static AMBHEMI * |
208 |
samp_hemi( /* sample indirect hemisphere */ |
209 |
COLOR rcol, |
210 |
RAY *r, |
211 |
double wt |
212 |
) |
213 |
{ |
214 |
AMBHEMI *hp; |
215 |
double d; |
216 |
int n, i, j; |
217 |
/* set number of divisions */ |
218 |
if (ambacc <= FTINY && |
219 |
wt > (d = 0.8*intens(rcol)*r->rweight/(ambdiv*minweight))) |
220 |
wt = d; /* avoid ray termination */ |
221 |
n = sqrt(ambdiv * wt) + 0.5; |
222 |
i = 1 + 5*(ambacc > FTINY); /* minimum number of samples */ |
223 |
if (n < i) |
224 |
n = i; |
225 |
/* allocate sampling array */ |
226 |
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1)); |
227 |
if (hp == NULL) |
228 |
error(SYSTEM, "out of memory in samp_hemi"); |
229 |
hp->rp = r; |
230 |
hp->ns = n; |
231 |
hp->acol[RED] = hp->acol[GRN] = hp->acol[BLU] = 0.0; |
232 |
hp->sampOK = 0; |
233 |
/* assign coefficient */ |
234 |
copycolor(hp->acoef, rcol); |
235 |
d = 1.0/(n*n); |
236 |
scalecolor(hp->acoef, d); |
237 |
/* make tangent plane axes */ |
238 |
hp->uy[0] = 0.5 - frandom(); |
239 |
hp->uy[1] = 0.5 - frandom(); |
240 |
hp->uy[2] = 0.5 - frandom(); |
241 |
for (i = 3; i--; ) |
242 |
if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6)) |
243 |
break; |
244 |
if (i < 0) |
245 |
error(CONSISTENCY, "bad ray direction in samp_hemi"); |
246 |
hp->uy[i] = 1.0; |
247 |
VCROSS(hp->ux, hp->uy, r->ron); |
248 |
normalize(hp->ux); |
249 |
VCROSS(hp->uy, r->ron, hp->ux); |
250 |
/* sample divisions */ |
251 |
for (i = hp->ns; i--; ) |
252 |
for (j = hp->ns; j--; ) |
253 |
hp->sampOK += ambsample(hp, i, j, 0); |
254 |
copycolor(rcol, hp->acol); |
255 |
if (!hp->sampOK) { /* utter failure? */ |
256 |
free(hp); |
257 |
return(NULL); |
258 |
} |
259 |
if (hp->sampOK < hp->ns*hp->ns) { |
260 |
hp->sampOK *= -1; /* soft failure */ |
261 |
return(hp); |
262 |
} |
263 |
n = ambssamp*wt + 0.5; |
264 |
if (n > 8) { /* perform super-sampling? */ |
265 |
ambsupersamp(hp, n); |
266 |
copycolor(rcol, hp->acol); |
267 |
} |
268 |
return(hp); /* all is well */ |
269 |
} |
270 |
|
271 |
|
272 |
/* Return brightness of farthest ambient sample */ |
273 |
static double |
274 |
back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3) |
275 |
{ |
276 |
if (hp->sa[n1].d <= hp->sa[n2].d) { |
277 |
if (hp->sa[n1].d <= hp->sa[n3].d) |
278 |
return(colval(hp->sa[n1].v,CIEY)); |
279 |
return(colval(hp->sa[n3].v,CIEY)); |
280 |
} |
281 |
if (hp->sa[n2].d <= hp->sa[n3].d) |
282 |
return(colval(hp->sa[n2].v,CIEY)); |
283 |
return(colval(hp->sa[n3].v,CIEY)); |
284 |
} |
285 |
|
286 |
|
287 |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
288 |
static void |
289 |
comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1) |
290 |
{ |
291 |
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2; |
292 |
int ii; |
293 |
|
294 |
VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop); |
295 |
VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop); |
296 |
VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p); |
297 |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
298 |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
299 |
dot_e = DOT(ftp->e_i,ftp->e_i); |
300 |
dot_er = DOT(ftp->e_i, ftp->r_i); |
301 |
rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i); |
302 |
rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
303 |
ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) * |
304 |
sqrt( rdot_cp ); |
305 |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
306 |
dot_e*ftp->I1 )*0.5*rdot_cp; |
307 |
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
308 |
for (ii = 3; ii--; ) |
309 |
ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii]; |
310 |
} |
311 |
|
312 |
|
313 |
/* Compose 3x3 matrix from two vectors */ |
314 |
static void |
315 |
compose_matrix(FVECT mat[3], FVECT va, FVECT vb) |
316 |
{ |
317 |
mat[0][0] = 2.0*va[0]*vb[0]; |
318 |
mat[1][1] = 2.0*va[1]*vb[1]; |
319 |
mat[2][2] = 2.0*va[2]*vb[2]; |
320 |
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0]; |
321 |
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0]; |
322 |
mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1]; |
323 |
} |
324 |
|
325 |
|
326 |
/* Compute partial 3x3 Hessian matrix for edge */ |
327 |
static void |
328 |
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
329 |
{ |
330 |
FVECT ncp; |
331 |
FVECT m1[3], m2[3], m3[3], m4[3]; |
332 |
double d1, d2, d3, d4; |
333 |
double I3, J3, K3; |
334 |
int i, j; |
335 |
/* compute intermediate coefficients */ |
336 |
d1 = 1.0/DOT(ftp->r_i,ftp->r_i); |
337 |
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
338 |
d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
339 |
d4 = DOT(ftp->e_i, ftp->r_i); |
340 |
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 ) |
341 |
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) ); |
342 |
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
343 |
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
344 |
/* intermediate matrices */ |
345 |
VCROSS(ncp, nrm, ftp->e_i); |
346 |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
347 |
compose_matrix(m2, ftp->r_i, ftp->r_i); |
348 |
compose_matrix(m3, ftp->e_i, ftp->e_i); |
349 |
compose_matrix(m4, ftp->r_i, ftp->e_i); |
350 |
d1 = DOT(nrm, ftp->rcp); |
351 |
d2 = -d1*ftp->I2; |
352 |
d1 *= 2.0; |
353 |
for (i = 3; i--; ) /* final matrix sum */ |
354 |
for (j = 3; j--; ) { |
355 |
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] + |
356 |
2.0*J3*m4[i][j] ); |
357 |
hess[i][j] += d2*(i==j); |
358 |
hess[i][j] *= -1.0/PI; |
359 |
} |
360 |
} |
361 |
|
362 |
|
363 |
/* Reverse hessian calculation result for edge in other direction */ |
364 |
static void |
365 |
rev_hessian(FVECT hess[3]) |
366 |
{ |
367 |
int i; |
368 |
|
369 |
for (i = 3; i--; ) { |
370 |
hess[i][0] = -hess[i][0]; |
371 |
hess[i][1] = -hess[i][1]; |
372 |
hess[i][2] = -hess[i][2]; |
373 |
} |
374 |
} |
375 |
|
376 |
|
377 |
/* Add to radiometric Hessian from the given triangle */ |
378 |
static void |
379 |
add2hessian(FVECT hess[3], FVECT ehess1[3], |
380 |
FVECT ehess2[3], FVECT ehess3[3], double v) |
381 |
{ |
382 |
int i, j; |
383 |
|
384 |
for (i = 3; i--; ) |
385 |
for (j = 3; j--; ) |
386 |
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] ); |
387 |
} |
388 |
|
389 |
|
390 |
/* Compute partial displacement form factor gradient for edge */ |
391 |
static void |
392 |
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
393 |
{ |
394 |
FVECT ncp; |
395 |
double f1; |
396 |
int i; |
397 |
|
398 |
f1 = 2.0*DOT(nrm, ftp->rcp); |
399 |
VCROSS(ncp, nrm, ftp->e_i); |
400 |
for (i = 3; i--; ) |
401 |
grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
402 |
} |
403 |
|
404 |
|
405 |
/* Reverse gradient calculation result for edge in other direction */ |
406 |
static void |
407 |
rev_gradient(FVECT grad) |
408 |
{ |
409 |
grad[0] = -grad[0]; |
410 |
grad[1] = -grad[1]; |
411 |
grad[2] = -grad[2]; |
412 |
} |
413 |
|
414 |
|
415 |
/* Add to displacement gradient from the given triangle */ |
416 |
static void |
417 |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v) |
418 |
{ |
419 |
int i; |
420 |
|
421 |
for (i = 3; i--; ) |
422 |
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] ); |
423 |
} |
424 |
|
425 |
|
426 |
/* Compute anisotropic radii and eigenvector directions */ |
427 |
static void |
428 |
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3]) |
429 |
{ |
430 |
double hess2[2][2]; |
431 |
FVECT a, b; |
432 |
double evalue[2], slope1, xmag1; |
433 |
int i; |
434 |
/* project Hessian to sample plane */ |
435 |
for (i = 3; i--; ) { |
436 |
a[i] = DOT(hessian[i], uv[0]); |
437 |
b[i] = DOT(hessian[i], uv[1]); |
438 |
} |
439 |
hess2[0][0] = DOT(uv[0], a); |
440 |
hess2[0][1] = DOT(uv[0], b); |
441 |
hess2[1][0] = DOT(uv[1], a); |
442 |
hess2[1][1] = DOT(uv[1], b); |
443 |
/* compute eigenvalue(s) */ |
444 |
i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
445 |
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]); |
446 |
if (i == 1) /* double-root (circle) */ |
447 |
evalue[1] = evalue[0]; |
448 |
if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) | |
449 |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) { |
450 |
ra[0] = ra[1] = maxarad; |
451 |
return; |
452 |
} |
453 |
if (evalue[0] > evalue[1]) { |
454 |
ra[0] = sqrt(sqrt(4.0/evalue[0])); |
455 |
ra[1] = sqrt(sqrt(4.0/evalue[1])); |
456 |
slope1 = evalue[1]; |
457 |
} else { |
458 |
ra[0] = sqrt(sqrt(4.0/evalue[1])); |
459 |
ra[1] = sqrt(sqrt(4.0/evalue[0])); |
460 |
slope1 = evalue[0]; |
461 |
} |
462 |
/* compute unit eigenvectors */ |
463 |
if (fabs(hess2[0][1]) <= FTINY) |
464 |
return; /* uv OK as is */ |
465 |
slope1 = (slope1 - hess2[0][0]) / hess2[0][1]; |
466 |
xmag1 = sqrt(1.0/(1.0 + slope1*slope1)); |
467 |
for (i = 3; i--; ) { |
468 |
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i]; |
469 |
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i]; |
470 |
} |
471 |
VCOPY(uv[0], a); |
472 |
VCOPY(uv[1], b); |
473 |
} |
474 |
|
475 |
|
476 |
static void |
477 |
ambHessian( /* anisotropic radii & pos. gradient */ |
478 |
AMBHEMI *hp, |
479 |
FVECT uv[2], /* returned */ |
480 |
float ra[2], /* returned (optional) */ |
481 |
float pg[2] /* returned (optional) */ |
482 |
) |
483 |
{ |
484 |
static char memerrmsg[] = "out of memory in ambHessian()"; |
485 |
FVECT (*hessrow)[3] = NULL; |
486 |
FVECT *gradrow = NULL; |
487 |
FVECT hessian[3]; |
488 |
FVECT gradient; |
489 |
FFTRI fftr; |
490 |
int i, j; |
491 |
/* be sure to assign unit vectors */ |
492 |
VCOPY(uv[0], hp->ux); |
493 |
VCOPY(uv[1], hp->uy); |
494 |
/* clock-wise vertex traversal from sample POV */ |
495 |
if (ra != NULL) { /* initialize Hessian row buffer */ |
496 |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1)); |
497 |
if (hessrow == NULL) |
498 |
error(SYSTEM, memerrmsg); |
499 |
memset(hessian, 0, sizeof(hessian)); |
500 |
} else if (pg == NULL) /* bogus call? */ |
501 |
return; |
502 |
if (pg != NULL) { /* initialize form factor row buffer */ |
503 |
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1)); |
504 |
if (gradrow == NULL) |
505 |
error(SYSTEM, memerrmsg); |
506 |
memset(gradient, 0, sizeof(gradient)); |
507 |
} |
508 |
/* compute first row of edges */ |
509 |
for (j = 0; j < hp->ns-1; j++) { |
510 |
comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1)); |
511 |
if (hessrow != NULL) |
512 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
513 |
if (gradrow != NULL) |
514 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
515 |
} |
516 |
/* sum each row of triangles */ |
517 |
for (i = 0; i < hp->ns-1; i++) { |
518 |
FVECT hesscol[3]; /* compute first vertical edge */ |
519 |
FVECT gradcol; |
520 |
comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0)); |
521 |
if (hessrow != NULL) |
522 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
523 |
if (gradrow != NULL) |
524 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
525 |
for (j = 0; j < hp->ns-1; j++) { |
526 |
FVECT hessdia[3]; /* compute triangle contributions */ |
527 |
FVECT graddia; |
528 |
double backg; |
529 |
backg = back_ambval(hp, AI(hp,i,j), |
530 |
AI(hp,i,j+1), AI(hp,i+1,j)); |
531 |
/* diagonal (inner) edge */ |
532 |
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j)); |
533 |
if (hessrow != NULL) { |
534 |
comp_hessian(hessdia, &fftr, hp->rp->ron); |
535 |
rev_hessian(hesscol); |
536 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
537 |
} |
538 |
if (gradrow != NULL) { |
539 |
comp_gradient(graddia, &fftr, hp->rp->ron); |
540 |
rev_gradient(gradcol); |
541 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
542 |
} |
543 |
/* initialize edge in next row */ |
544 |
comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j)); |
545 |
if (hessrow != NULL) |
546 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
547 |
if (gradrow != NULL) |
548 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
549 |
/* new column edge & paired triangle */ |
550 |
backg = back_ambval(hp, AI(hp,i+1,j+1), |
551 |
AI(hp,i+1,j), AI(hp,i,j+1)); |
552 |
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1)); |
553 |
if (hessrow != NULL) { |
554 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
555 |
rev_hessian(hessdia); |
556 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
557 |
if (i < hp->ns-2) |
558 |
rev_hessian(hessrow[j]); |
559 |
} |
560 |
if (gradrow != NULL) { |
561 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
562 |
rev_gradient(graddia); |
563 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
564 |
if (i < hp->ns-2) |
565 |
rev_gradient(gradrow[j]); |
566 |
} |
567 |
} |
568 |
} |
569 |
/* release row buffers */ |
570 |
if (hessrow != NULL) free(hessrow); |
571 |
if (gradrow != NULL) free(gradrow); |
572 |
|
573 |
if (ra != NULL) /* extract eigenvectors & radii */ |
574 |
eigenvectors(uv, ra, hessian); |
575 |
if (pg != NULL) { /* tangential position gradient */ |
576 |
pg[0] = DOT(gradient, uv[0]); |
577 |
pg[1] = DOT(gradient, uv[1]); |
578 |
} |
579 |
} |
580 |
|
581 |
|
582 |
/* Compute direction gradient from a hemispherical sampling */ |
583 |
static void |
584 |
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2]) |
585 |
{ |
586 |
AMBSAMP *ap; |
587 |
double dgsum[2]; |
588 |
int n; |
589 |
FVECT vd; |
590 |
double gfact; |
591 |
|
592 |
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */ |
593 |
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) { |
594 |
/* use vector for azimuth + 90deg */ |
595 |
VSUB(vd, ap->p, hp->rp->rop); |
596 |
/* brightness over cosine factor */ |
597 |
gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd); |
598 |
/* sine = proj_radius/vd_length */ |
599 |
dgsum[0] -= DOT(uv[1], vd) * gfact; |
600 |
dgsum[1] += DOT(uv[0], vd) * gfact; |
601 |
} |
602 |
dg[0] = dgsum[0] / (hp->ns*hp->ns); |
603 |
dg[1] = dgsum[1] / (hp->ns*hp->ns); |
604 |
} |
605 |
|
606 |
|
607 |
/* Compute potential light leak direction flags for cache value */ |
608 |
static uint32 |
609 |
ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1) |
610 |
{ |
611 |
const double max_d = 1.0/(minarad*ambacc + 0.001); |
612 |
const double ang_res = 0.5*PI/(hp->ns-1); |
613 |
const double ang_step = ang_res/((int)(16/PI*ang_res) + (1+FTINY)); |
614 |
double avg_d = 0; |
615 |
uint32 flgs = 0; |
616 |
FVECT vec; |
617 |
double d, u, v; |
618 |
double ang, a1; |
619 |
int i, j; |
620 |
/* don't bother for a few samples */ |
621 |
if (hp->ns < 12) |
622 |
return(0); |
623 |
/* check distances overhead */ |
624 |
for (i = hp->ns*3/4; i-- > hp->ns>>2; ) |
625 |
for (j = hp->ns*3/4; j-- > hp->ns>>2; ) |
626 |
avg_d += ambsam(hp,i,j).d; |
627 |
avg_d *= 4.0/(hp->ns*hp->ns); |
628 |
if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */ |
629 |
return(0); |
630 |
if (avg_d >= max_d) /* insurance */ |
631 |
return(0); |
632 |
/* else circle around perimeter */ |
633 |
for (i = 0; i < hp->ns; i++) |
634 |
for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) { |
635 |
AMBSAMP *ap = &ambsam(hp,i,j); |
636 |
if ((ap->d <= FTINY) | (ap->d >= max_d)) |
637 |
continue; /* too far or too near */ |
638 |
VSUB(vec, ap->p, hp->rp->rop); |
639 |
d = DOT(vec, hp->rp->ron); |
640 |
d = 1.0/sqrt(DOT(vec,vec) - d*d); |
641 |
u = DOT(vec, uv[0]) * d; |
642 |
v = DOT(vec, uv[1]) * d; |
643 |
if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= 1.0) |
644 |
continue; /* occluder outside ellipse */ |
645 |
ang = atan2a(v, u); /* else set direction flags */ |
646 |
for (a1 = ang-.5*ang_res; a1 <= ang+.5*ang_res; a1 += ang_step) |
647 |
flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0))); |
648 |
} |
649 |
/* add low-angle incident (< 20deg) */ |
650 |
if (fabs(hp->rp->rod) <= 0.342) { |
651 |
u = -DOT(hp->rp->rdir, uv[0]); |
652 |
v = -DOT(hp->rp->rdir, uv[1]); |
653 |
if ((r0*r0*u*u + r1*r1*v*v) > hp->rp->rot*hp->rp->rot) { |
654 |
ang = atan2a(v, u); |
655 |
ang += 2.*PI*(ang < 0); |
656 |
ang *= 16/PI; |
657 |
if ((ang < .5) | (ang >= 31.5)) |
658 |
flgs |= 0x80000001; |
659 |
else |
660 |
flgs |= 3L<<(int)(ang-.5); |
661 |
} |
662 |
} |
663 |
return(flgs); |
664 |
} |
665 |
|
666 |
|
667 |
int |
668 |
doambient( /* compute ambient component */ |
669 |
COLOR rcol, /* input/output color */ |
670 |
RAY *r, |
671 |
double wt, |
672 |
FVECT uv[2], /* returned (optional) */ |
673 |
float ra[2], /* returned (optional) */ |
674 |
float pg[2], /* returned (optional) */ |
675 |
float dg[2], /* returned (optional) */ |
676 |
uint32 *crlp /* returned (optional) */ |
677 |
) |
678 |
{ |
679 |
AMBHEMI *hp = samp_hemi(rcol, r, wt); |
680 |
FVECT my_uv[2]; |
681 |
double d, K; |
682 |
AMBSAMP *ap; |
683 |
int i; |
684 |
/* clear return values */ |
685 |
if (uv != NULL) |
686 |
memset(uv, 0, sizeof(FVECT)*2); |
687 |
if (ra != NULL) |
688 |
ra[0] = ra[1] = 0.0; |
689 |
if (pg != NULL) |
690 |
pg[0] = pg[1] = 0.0; |
691 |
if (dg != NULL) |
692 |
dg[0] = dg[1] = 0.0; |
693 |
if (crlp != NULL) |
694 |
*crlp = 0; |
695 |
if (hp == NULL) /* sampling falure? */ |
696 |
return(0); |
697 |
|
698 |
if ((ra == NULL) & (pg == NULL) & (dg == NULL) || |
699 |
(hp->sampOK < 0) | (hp->ns < 4)) { |
700 |
free(hp); /* Hessian not requested/possible */ |
701 |
return(-1); /* value-only return value */ |
702 |
} |
703 |
if ((d = bright(rcol)) > FTINY) { /* normalize Y values */ |
704 |
d = 0.99*(hp->ns*hp->ns)/d; |
705 |
K = 0.01; |
706 |
} else { /* or fall back on geometric Hessian */ |
707 |
K = 1.0; |
708 |
pg = NULL; |
709 |
dg = NULL; |
710 |
crlp = NULL; |
711 |
} |
712 |
ap = hp->sa; /* relative Y channel from here on... */ |
713 |
for (i = hp->ns*hp->ns; i--; ap++) |
714 |
colval(ap->v,CIEY) = bright(ap->v)*d + K; |
715 |
|
716 |
if (uv == NULL) /* make sure we have axis pointers */ |
717 |
uv = my_uv; |
718 |
/* compute radii & pos. gradient */ |
719 |
ambHessian(hp, uv, ra, pg); |
720 |
|
721 |
if (dg != NULL) /* compute direction gradient */ |
722 |
ambdirgrad(hp, uv, dg); |
723 |
|
724 |
if (ra != NULL) { /* scale/clamp radii */ |
725 |
if (pg != NULL) { |
726 |
if (ra[0]*(d = fabs(pg[0])) > 1.0) |
727 |
ra[0] = 1.0/d; |
728 |
if (ra[1]*(d = fabs(pg[1])) > 1.0) |
729 |
ra[1] = 1.0/d; |
730 |
if (ra[0] > ra[1]) |
731 |
ra[0] = ra[1]; |
732 |
} |
733 |
if (ra[0] < minarad) { |
734 |
ra[0] = minarad; |
735 |
if (ra[1] < minarad) |
736 |
ra[1] = minarad; |
737 |
} |
738 |
ra[0] *= d = 1.0/sqrt(wt); |
739 |
if ((ra[1] *= d) > 2.0*ra[0]) |
740 |
ra[1] = 2.0*ra[0]; |
741 |
if (ra[1] > maxarad) { |
742 |
ra[1] = maxarad; |
743 |
if (ra[0] > maxarad) |
744 |
ra[0] = maxarad; |
745 |
} |
746 |
/* flag encroached directions */ |
747 |
if ((wt >= 0.89*AVGREFL) & (crlp != NULL)) |
748 |
*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc); |
749 |
if (pg != NULL) { /* cap gradient if necessary */ |
750 |
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1]; |
751 |
if (d > 1.0) { |
752 |
d = 1.0/sqrt(d); |
753 |
pg[0] *= d; |
754 |
pg[1] *= d; |
755 |
} |
756 |
} |
757 |
} |
758 |
free(hp); /* clean up and return */ |
759 |
return(1); |
760 |
} |
761 |
|
762 |
|
763 |
#else /* ! NEWAMB */ |
764 |
|
765 |
|
766 |
void |
767 |
inithemi( /* initialize sampling hemisphere */ |
768 |
AMBHEMI *hp, |
769 |
COLOR ac, |
770 |
RAY *r, |
771 |
double wt |
772 |
) |
773 |
{ |
774 |
double d; |
775 |
int i; |
776 |
/* set number of divisions */ |
777 |
if (ambacc <= FTINY && |
778 |
wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
779 |
wt = d; /* avoid ray termination */ |
780 |
hp->nt = sqrt(ambdiv * wt / PI) + 0.5; |
781 |
i = ambacc > FTINY ? 3 : 1; /* minimum number of samples */ |
782 |
if (hp->nt < i) |
783 |
hp->nt = i; |
784 |
hp->np = PI * hp->nt + 0.5; |
785 |
/* set number of super-samples */ |
786 |
hp->ns = ambssamp * wt + 0.5; |
787 |
/* assign coefficient */ |
788 |
copycolor(hp->acoef, ac); |
789 |
d = 1.0/(hp->nt*hp->np); |
790 |
scalecolor(hp->acoef, d); |
791 |
/* make axes */ |
792 |
VCOPY(hp->uz, r->ron); |
793 |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
794 |
for (i = 0; i < 3; i++) |
795 |
if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6) |
796 |
break; |
797 |
if (i >= 3) |
798 |
error(CONSISTENCY, "bad ray direction in inithemi"); |
799 |
hp->uy[i] = 1.0; |
800 |
fcross(hp->ux, hp->uy, hp->uz); |
801 |
normalize(hp->ux); |
802 |
fcross(hp->uy, hp->uz, hp->ux); |
803 |
} |
804 |
|
805 |
|
806 |
int |
807 |
divsample( /* sample a division */ |
808 |
AMBSAMP *dp, |
809 |
AMBHEMI *h, |
810 |
RAY *r |
811 |
) |
812 |
{ |
813 |
RAY ar; |
814 |
int hlist[3]; |
815 |
double spt[2]; |
816 |
double xd, yd, zd; |
817 |
double b2; |
818 |
double phi; |
819 |
int i; |
820 |
/* ambient coefficient for weight */ |
821 |
if (ambacc > FTINY) |
822 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
823 |
else |
824 |
copycolor(ar.rcoef, h->acoef); |
825 |
if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0) |
826 |
return(-1); |
827 |
if (ambacc > FTINY) { |
828 |
multcolor(ar.rcoef, h->acoef); |
829 |
scalecolor(ar.rcoef, 1./AVGREFL); |
830 |
} |
831 |
hlist[0] = r->rno; |
832 |
hlist[1] = dp->t; |
833 |
hlist[2] = dp->p; |
834 |
multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n)); |
835 |
zd = sqrt((dp->t + spt[0])/h->nt); |
836 |
phi = 2.0*PI * (dp->p + spt[1])/h->np; |
837 |
xd = tcos(phi) * zd; |
838 |
yd = tsin(phi) * zd; |
839 |
zd = sqrt(1.0 - zd*zd); |
840 |
for (i = 0; i < 3; i++) |
841 |
ar.rdir[i] = xd*h->ux[i] + |
842 |
yd*h->uy[i] + |
843 |
zd*h->uz[i]; |
844 |
checknorm(ar.rdir); |
845 |
dimlist[ndims++] = dp->t*h->np + dp->p + 90171; |
846 |
rayvalue(&ar); |
847 |
ndims--; |
848 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
849 |
addcolor(dp->v, ar.rcol); |
850 |
/* use rt to improve gradient calc */ |
851 |
if (ar.rt > FTINY && ar.rt < FHUGE) |
852 |
dp->r += 1.0/ar.rt; |
853 |
/* (re)initialize error */ |
854 |
if (dp->n++) { |
855 |
b2 = bright(dp->v)/dp->n - bright(ar.rcol); |
856 |
b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1)); |
857 |
dp->k = b2/(dp->n*dp->n); |
858 |
} else |
859 |
dp->k = 0.0; |
860 |
return(0); |
861 |
} |
862 |
|
863 |
|
864 |
static int |
865 |
ambcmp( /* decreasing order */ |
866 |
const void *p1, |
867 |
const void *p2 |
868 |
) |
869 |
{ |
870 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
871 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
872 |
|
873 |
if (d1->k < d2->k) |
874 |
return(1); |
875 |
if (d1->k > d2->k) |
876 |
return(-1); |
877 |
return(0); |
878 |
} |
879 |
|
880 |
|
881 |
static int |
882 |
ambnorm( /* standard order */ |
883 |
const void *p1, |
884 |
const void *p2 |
885 |
) |
886 |
{ |
887 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
888 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
889 |
int c; |
890 |
|
891 |
if ( (c = d1->t - d2->t) ) |
892 |
return(c); |
893 |
return(d1->p - d2->p); |
894 |
} |
895 |
|
896 |
|
897 |
double |
898 |
doambient( /* compute ambient component */ |
899 |
COLOR rcol, |
900 |
RAY *r, |
901 |
double wt, |
902 |
FVECT pg, |
903 |
FVECT dg |
904 |
) |
905 |
{ |
906 |
double b, d=0; |
907 |
AMBHEMI hemi; |
908 |
AMBSAMP *div; |
909 |
AMBSAMP dnew; |
910 |
double acol[3]; |
911 |
AMBSAMP *dp; |
912 |
double arad; |
913 |
int divcnt; |
914 |
int i, j; |
915 |
/* initialize hemisphere */ |
916 |
inithemi(&hemi, rcol, r, wt); |
917 |
divcnt = hemi.nt * hemi.np; |
918 |
/* initialize */ |
919 |
if (pg != NULL) |
920 |
pg[0] = pg[1] = pg[2] = 0.0; |
921 |
if (dg != NULL) |
922 |
dg[0] = dg[1] = dg[2] = 0.0; |
923 |
setcolor(rcol, 0.0, 0.0, 0.0); |
924 |
if (divcnt == 0) |
925 |
return(0.0); |
926 |
/* allocate super-samples */ |
927 |
if (hemi.ns > 0 || pg != NULL || dg != NULL) { |
928 |
div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP)); |
929 |
if (div == NULL) |
930 |
error(SYSTEM, "out of memory in doambient"); |
931 |
} else |
932 |
div = NULL; |
933 |
/* sample the divisions */ |
934 |
arad = 0.0; |
935 |
acol[0] = acol[1] = acol[2] = 0.0; |
936 |
if ((dp = div) == NULL) |
937 |
dp = &dnew; |
938 |
divcnt = 0; |
939 |
for (i = 0; i < hemi.nt; i++) |
940 |
for (j = 0; j < hemi.np; j++) { |
941 |
dp->t = i; dp->p = j; |
942 |
setcolor(dp->v, 0.0, 0.0, 0.0); |
943 |
dp->r = 0.0; |
944 |
dp->n = 0; |
945 |
if (divsample(dp, &hemi, r) < 0) { |
946 |
if (div != NULL) |
947 |
dp++; |
948 |
continue; |
949 |
} |
950 |
arad += dp->r; |
951 |
divcnt++; |
952 |
if (div != NULL) |
953 |
dp++; |
954 |
else |
955 |
addcolor(acol, dp->v); |
956 |
} |
957 |
if (!divcnt) { |
958 |
if (div != NULL) |
959 |
free((void *)div); |
960 |
return(0.0); /* no samples taken */ |
961 |
} |
962 |
if (divcnt < hemi.nt*hemi.np) { |
963 |
pg = dg = NULL; /* incomplete sampling */ |
964 |
hemi.ns = 0; |
965 |
} else if (arad > FTINY && divcnt/arad < minarad) { |
966 |
hemi.ns = 0; /* close enough */ |
967 |
} else if (hemi.ns > 0) { /* else perform super-sampling? */ |
968 |
comperrs(div, &hemi); /* compute errors */ |
969 |
qsort(div, divcnt, sizeof(AMBSAMP), ambcmp); /* sort divs */ |
970 |
/* super-sample */ |
971 |
for (i = hemi.ns; i > 0; i--) { |
972 |
dnew = *div; |
973 |
if (divsample(&dnew, &hemi, r) < 0) { |
974 |
dp++; |
975 |
continue; |
976 |
} |
977 |
dp = div; /* reinsert */ |
978 |
j = divcnt < i ? divcnt : i; |
979 |
while (--j > 0 && dnew.k < dp[1].k) { |
980 |
*dp = *(dp+1); |
981 |
dp++; |
982 |
} |
983 |
*dp = dnew; |
984 |
} |
985 |
if (pg != NULL || dg != NULL) /* restore order */ |
986 |
qsort(div, divcnt, sizeof(AMBSAMP), ambnorm); |
987 |
} |
988 |
/* compute returned values */ |
989 |
if (div != NULL) { |
990 |
arad = 0.0; /* note: divcnt may be < nt*np */ |
991 |
for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) { |
992 |
arad += dp->r; |
993 |
if (dp->n > 1) { |
994 |
b = 1.0/dp->n; |
995 |
scalecolor(dp->v, b); |
996 |
dp->r *= b; |
997 |
dp->n = 1; |
998 |
} |
999 |
addcolor(acol, dp->v); |
1000 |
} |
1001 |
b = bright(acol); |
1002 |
if (b > FTINY) { |
1003 |
b = 1.0/b; /* compute & normalize gradient(s) */ |
1004 |
if (pg != NULL) { |
1005 |
posgradient(pg, div, &hemi); |
1006 |
for (i = 0; i < 3; i++) |
1007 |
pg[i] *= b; |
1008 |
} |
1009 |
if (dg != NULL) { |
1010 |
dirgradient(dg, div, &hemi); |
1011 |
for (i = 0; i < 3; i++) |
1012 |
dg[i] *= b; |
1013 |
} |
1014 |
} |
1015 |
free((void *)div); |
1016 |
} |
1017 |
copycolor(rcol, acol); |
1018 |
if (arad <= FTINY) |
1019 |
arad = maxarad; |
1020 |
else |
1021 |
arad = (divcnt+hemi.ns)/arad; |
1022 |
if (pg != NULL) { /* reduce radius if gradient large */ |
1023 |
d = DOT(pg,pg); |
1024 |
if (d*arad*arad > 1.0) |
1025 |
arad = 1.0/sqrt(d); |
1026 |
} |
1027 |
if (arad < minarad) { |
1028 |
arad = minarad; |
1029 |
if (pg != NULL && d*arad*arad > 1.0) { /* cap gradient */ |
1030 |
d = 1.0/arad/sqrt(d); |
1031 |
for (i = 0; i < 3; i++) |
1032 |
pg[i] *= d; |
1033 |
} |
1034 |
} |
1035 |
if ((arad /= sqrt(wt)) > maxarad) |
1036 |
arad = maxarad; |
1037 |
return(arad); |
1038 |
} |
1039 |
|
1040 |
|
1041 |
void |
1042 |
comperrs( /* compute initial error estimates */ |
1043 |
AMBSAMP *da, /* assumes standard ordering */ |
1044 |
AMBHEMI *hp |
1045 |
) |
1046 |
{ |
1047 |
double b, b2; |
1048 |
int i, j; |
1049 |
AMBSAMP *dp; |
1050 |
/* sum differences from neighbors */ |
1051 |
dp = da; |
1052 |
for (i = 0; i < hp->nt; i++) |
1053 |
for (j = 0; j < hp->np; j++) { |
1054 |
#ifdef DEBUG |
1055 |
if (dp->t != i || dp->p != j) |
1056 |
error(CONSISTENCY, |
1057 |
"division order in comperrs"); |
1058 |
#endif |
1059 |
b = bright(dp[0].v); |
1060 |
if (i > 0) { /* from above */ |
1061 |
b2 = bright(dp[-hp->np].v) - b; |
1062 |
b2 *= b2 * 0.25; |
1063 |
dp[0].k += b2; |
1064 |
dp[-hp->np].k += b2; |
1065 |
} |
1066 |
if (j > 0) { /* from behind */ |
1067 |
b2 = bright(dp[-1].v) - b; |
1068 |
b2 *= b2 * 0.25; |
1069 |
dp[0].k += b2; |
1070 |
dp[-1].k += b2; |
1071 |
} else { /* around */ |
1072 |
b2 = bright(dp[hp->np-1].v) - b; |
1073 |
b2 *= b2 * 0.25; |
1074 |
dp[0].k += b2; |
1075 |
dp[hp->np-1].k += b2; |
1076 |
} |
1077 |
dp++; |
1078 |
} |
1079 |
/* divide by number of neighbors */ |
1080 |
dp = da; |
1081 |
for (j = 0; j < hp->np; j++) /* top row */ |
1082 |
(dp++)->k *= 1.0/3.0; |
1083 |
if (hp->nt < 2) |
1084 |
return; |
1085 |
for (i = 1; i < hp->nt-1; i++) /* central region */ |
1086 |
for (j = 0; j < hp->np; j++) |
1087 |
(dp++)->k *= 0.25; |
1088 |
for (j = 0; j < hp->np; j++) /* bottom row */ |
1089 |
(dp++)->k *= 1.0/3.0; |
1090 |
} |
1091 |
|
1092 |
|
1093 |
void |
1094 |
posgradient( /* compute position gradient */ |
1095 |
FVECT gv, |
1096 |
AMBSAMP *da, /* assumes standard ordering */ |
1097 |
AMBHEMI *hp |
1098 |
) |
1099 |
{ |
1100 |
int i, j; |
1101 |
double nextsine, lastsine, b, d; |
1102 |
double mag0, mag1; |
1103 |
double phi, cosp, sinp, xd, yd; |
1104 |
AMBSAMP *dp; |
1105 |
|
1106 |
xd = yd = 0.0; |
1107 |
for (j = 0; j < hp->np; j++) { |
1108 |
dp = da + j; |
1109 |
mag0 = mag1 = 0.0; |
1110 |
lastsine = 0.0; |
1111 |
for (i = 0; i < hp->nt; i++) { |
1112 |
#ifdef DEBUG |
1113 |
if (dp->t != i || dp->p != j) |
1114 |
error(CONSISTENCY, |
1115 |
"division order in posgradient"); |
1116 |
#endif |
1117 |
b = bright(dp->v); |
1118 |
if (i > 0) { |
1119 |
d = dp[-hp->np].r; |
1120 |
if (dp[0].r > d) d = dp[0].r; |
1121 |
/* sin(t)*cos(t)^2 */ |
1122 |
d *= lastsine * (1.0 - (double)i/hp->nt); |
1123 |
mag0 += d*(b - bright(dp[-hp->np].v)); |
1124 |
} |
1125 |
nextsine = sqrt((double)(i+1)/hp->nt); |
1126 |
if (j > 0) { |
1127 |
d = dp[-1].r; |
1128 |
if (dp[0].r > d) d = dp[0].r; |
1129 |
mag1 += d * (nextsine - lastsine) * |
1130 |
(b - bright(dp[-1].v)); |
1131 |
} else { |
1132 |
d = dp[hp->np-1].r; |
1133 |
if (dp[0].r > d) d = dp[0].r; |
1134 |
mag1 += d * (nextsine - lastsine) * |
1135 |
(b - bright(dp[hp->np-1].v)); |
1136 |
} |
1137 |
dp += hp->np; |
1138 |
lastsine = nextsine; |
1139 |
} |
1140 |
mag0 *= 2.0*PI / hp->np; |
1141 |
phi = 2.0*PI * (double)j/hp->np; |
1142 |
cosp = tcos(phi); sinp = tsin(phi); |
1143 |
xd += mag0*cosp - mag1*sinp; |
1144 |
yd += mag0*sinp + mag1*cosp; |
1145 |
} |
1146 |
for (i = 0; i < 3; i++) |
1147 |
gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI; |
1148 |
} |
1149 |
|
1150 |
|
1151 |
void |
1152 |
dirgradient( /* compute direction gradient */ |
1153 |
FVECT gv, |
1154 |
AMBSAMP *da, /* assumes standard ordering */ |
1155 |
AMBHEMI *hp |
1156 |
) |
1157 |
{ |
1158 |
int i, j; |
1159 |
double mag; |
1160 |
double phi, xd, yd; |
1161 |
AMBSAMP *dp; |
1162 |
|
1163 |
xd = yd = 0.0; |
1164 |
for (j = 0; j < hp->np; j++) { |
1165 |
dp = da + j; |
1166 |
mag = 0.0; |
1167 |
for (i = 0; i < hp->nt; i++) { |
1168 |
#ifdef DEBUG |
1169 |
if (dp->t != i || dp->p != j) |
1170 |
error(CONSISTENCY, |
1171 |
"division order in dirgradient"); |
1172 |
#endif |
1173 |
/* tan(t) */ |
1174 |
mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0); |
1175 |
dp += hp->np; |
1176 |
} |
1177 |
phi = 2.0*PI * (j+.5)/hp->np + PI/2.0; |
1178 |
xd += mag * tcos(phi); |
1179 |
yd += mag * tsin(phi); |
1180 |
} |
1181 |
for (i = 0; i < 3; i++) |
1182 |
gv[i] = xd*hp->ux[i] + yd*hp->uy[i]; |
1183 |
} |
1184 |
|
1185 |
#endif /* ! NEWAMB */ |