1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: bsdfrbf.c,v 2.10 2013/10/18 02:49:30 greg Exp $"; |
3 |
#endif |
4 |
/* |
5 |
* Radial basis function representation for BSDF data. |
6 |
* |
7 |
* G. Ward |
8 |
*/ |
9 |
|
10 |
#define _USE_MATH_DEFINES |
11 |
#include <stdio.h> |
12 |
#include <stdlib.h> |
13 |
#include <string.h> |
14 |
#include <math.h> |
15 |
#include "bsdfrep.h" |
16 |
|
17 |
#ifndef MINRSCA |
18 |
#define MINRSCA 1.0 /* minimum radius scaling factor */ |
19 |
#endif |
20 |
#ifndef MAXRSCA |
21 |
#define MAXRSCA 2.7 /* maximum radius scaling factor */ |
22 |
#endif |
23 |
#ifndef VARTHRESH |
24 |
#define VARTHRESH 0.0015 /* culling variance threshold */ |
25 |
#endif |
26 |
#ifndef DIFFMAX2 |
27 |
#define DIFFMAX2 (16.*VARTHRESH) /* maximum ignored sample variance */ |
28 |
#endif |
29 |
#ifndef MAXFRAC |
30 |
#define MAXFRAC 0.5 /* maximum contribution to neighbor */ |
31 |
#endif |
32 |
#ifndef NNEIGH |
33 |
#define NNEIGH 10 /* number of neighbors to consider */ |
34 |
#endif |
35 |
/* our loaded grid for this incident angle */ |
36 |
GRIDVAL dsf_grid[GRIDRES][GRIDRES]; |
37 |
|
38 |
/* Start new DSF input grid */ |
39 |
void |
40 |
new_bsdf_data(double new_theta, double new_phi) |
41 |
{ |
42 |
if (!new_input_direction(new_theta, new_phi)) |
43 |
exit(1); |
44 |
memset(dsf_grid, 0, sizeof(dsf_grid)); |
45 |
} |
46 |
|
47 |
/* Add BSDF data point */ |
48 |
void |
49 |
add_bsdf_data(double theta_out, double phi_out, double val, int isDSF) |
50 |
{ |
51 |
FVECT ovec; |
52 |
int pos[2]; |
53 |
|
54 |
if (!output_orient) /* check output orientation */ |
55 |
output_orient = 1 - 2*(theta_out > 90.); |
56 |
else if (output_orient > 0 ^ theta_out < 90.) { |
57 |
fputs("Cannot handle output angles on both sides of surface\n", |
58 |
stderr); |
59 |
exit(1); |
60 |
} |
61 |
ovec[2] = sin((M_PI/180.)*theta_out); |
62 |
ovec[0] = cos((M_PI/180.)*phi_out) * ovec[2]; |
63 |
ovec[1] = sin((M_PI/180.)*phi_out) * ovec[2]; |
64 |
ovec[2] = sqrt(1. - ovec[2]*ovec[2]); |
65 |
|
66 |
if (val <= 0) /* truncate to zero */ |
67 |
val = 0; |
68 |
else if (!isDSF) |
69 |
val *= ovec[2]; /* convert from BSDF to DSF */ |
70 |
|
71 |
/* update BSDF histogram */ |
72 |
if (val < BSDF2BIG*ovec[2] && val > BSDF2SML*ovec[2]) |
73 |
++bsdf_hist[histndx(val/ovec[2])]; |
74 |
|
75 |
pos_from_vec(pos, ovec); |
76 |
|
77 |
dsf_grid[pos[0]][pos[1]].vsum += val; |
78 |
dsf_grid[pos[0]][pos[1]].nval++; |
79 |
} |
80 |
|
81 |
/* Compute radii for non-empty bins */ |
82 |
/* (distance to furthest empty bin for which non-empty test bin is closest) */ |
83 |
static void |
84 |
compute_radii(void) |
85 |
{ |
86 |
const int cradmin = ANG2R(.5*M_PI/GRIDRES); |
87 |
unsigned int fill_grid[GRIDRES][GRIDRES]; |
88 |
unsigned short fill_cnt[GRIDRES][GRIDRES]; |
89 |
FVECT ovec0, ovec1; |
90 |
double ang2, lastang2; |
91 |
int r, i, j, jn, ii, jj, inear, jnear; |
92 |
|
93 |
r = GRIDRES/2; /* proceed in zig-zag */ |
94 |
for (i = 0; i < GRIDRES; i++) |
95 |
for (jn = 0; jn < GRIDRES; jn++) { |
96 |
j = (i&1) ? jn : GRIDRES-1-jn; |
97 |
if (dsf_grid[i][j].nval) /* find empty grid pos. */ |
98 |
continue; |
99 |
ovec_from_pos(ovec0, i, j); |
100 |
inear = jnear = -1; /* find nearest non-empty */ |
101 |
lastang2 = M_PI*M_PI; |
102 |
for (ii = i-r; ii <= i+r; ii++) { |
103 |
if (ii < 0) continue; |
104 |
if (ii >= GRIDRES) break; |
105 |
for (jj = j-r; jj <= j+r; jj++) { |
106 |
if (jj < 0) continue; |
107 |
if (jj >= GRIDRES) break; |
108 |
if (!dsf_grid[ii][jj].nval) |
109 |
continue; |
110 |
ovec_from_pos(ovec1, ii, jj); |
111 |
ang2 = 2. - 2.*DOT(ovec0,ovec1); |
112 |
if (ang2 >= lastang2) |
113 |
continue; |
114 |
lastang2 = ang2; |
115 |
inear = ii; jnear = jj; |
116 |
} |
117 |
} |
118 |
if (inear < 0) { |
119 |
fprintf(stderr, |
120 |
"%s: Could not find non-empty neighbor!\n", |
121 |
progname); |
122 |
exit(1); |
123 |
} |
124 |
ang2 = sqrt(lastang2); |
125 |
r = ANG2R(ang2); /* record if > previous */ |
126 |
if (r > dsf_grid[inear][jnear].crad) |
127 |
dsf_grid[inear][jnear].crad = r; |
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/* next search radius */ |
129 |
r = ang2*(2.*GRIDRES/M_PI) + 3; |
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} |
131 |
for (i = 0; i < GRIDRES; i++) /* grow radii where uniform */ |
132 |
for (j = 0; j < GRIDRES; j++) { |
133 |
double midmean = 0.0; |
134 |
int nsum = 0; |
135 |
if (!dsf_grid[i][j].nval) |
136 |
continue; |
137 |
r = 1; /* avg. immediate neighbors */ |
138 |
for (ii = i-r; ii <= i+r; ii++) { |
139 |
if (ii < 0) continue; |
140 |
if (ii >= GRIDRES) break; |
141 |
for (jj = j-r; jj <= j+r; jj++) { |
142 |
if (jj < 0) continue; |
143 |
if (jj >= GRIDRES) break; |
144 |
midmean += dsf_grid[ii][jj].vsum; |
145 |
nsum += dsf_grid[ii][jj].nval; |
146 |
} |
147 |
} |
148 |
midmean /= (double)nsum; |
149 |
while (++r < GRIDRES) { /* attempt to grow perimeter */ |
150 |
double diff2sum = 0.0; |
151 |
nsum = 0; |
152 |
for (ii = i-r; ii <= i+r; ii++) { |
153 |
int jstep = 1; |
154 |
if (ii < 0) continue; |
155 |
if (ii >= GRIDRES) break; |
156 |
if ((i-r < ii) & (ii < i+r)) |
157 |
jstep = r<<1; |
158 |
for (jj = j-r; jj <= j+r; jj += jstep) { |
159 |
double d2; |
160 |
if (jj < 0) continue; |
161 |
if (jj >= GRIDRES) break; |
162 |
if (!dsf_grid[ii][jj].nval) |
163 |
continue; |
164 |
d2 = midmean - dsf_grid[ii][jj].vsum / |
165 |
(double)dsf_grid[ii][jj].nval; |
166 |
d2 *= d2; |
167 |
if (d2 > DIFFMAX2*midmean*midmean) |
168 |
goto escape; |
169 |
diff2sum += d2; |
170 |
++nsum; |
171 |
} |
172 |
} |
173 |
if (diff2sum > VARTHRESH*midmean*midmean*(double)nsum) |
174 |
break; |
175 |
} |
176 |
escape: --r; |
177 |
r = ANG2R(r*(M_PI/MAXRSCA/GRIDRES)); |
178 |
if (r < cradmin) |
179 |
r = cradmin; |
180 |
if (dsf_grid[i][j].crad < r) |
181 |
dsf_grid[i][j].crad = r; |
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} |
183 |
/* blur radii over hemisphere */ |
184 |
memset(fill_grid, 0, sizeof(fill_grid)); |
185 |
memset(fill_cnt, 0, sizeof(fill_cnt)); |
186 |
for (i = 0; i < GRIDRES; i++) |
187 |
for (j = 0; j < GRIDRES; j++) { |
188 |
if (!dsf_grid[i][j].nval) |
189 |
continue; /* not part of this */ |
190 |
r = R2ANG(dsf_grid[i][j].crad)*(2.*MAXRSCA*GRIDRES/M_PI); |
191 |
for (ii = i-r; ii <= i+r; ii++) { |
192 |
if (ii < 0) continue; |
193 |
if (ii >= GRIDRES) break; |
194 |
for (jj = j-r; jj <= j+r; jj++) { |
195 |
if (jj < 0) continue; |
196 |
if (jj >= GRIDRES) break; |
197 |
if ((ii-i)*(ii-i) + (jj-j)*(jj-j) > r*r) |
198 |
continue; |
199 |
fill_grid[ii][jj] += dsf_grid[i][j].crad; |
200 |
fill_cnt[ii][jj]++; |
201 |
} |
202 |
} |
203 |
} |
204 |
/* copy back blurred radii */ |
205 |
for (i = 0; i < GRIDRES; i++) |
206 |
for (j = 0; j < GRIDRES; j++) |
207 |
if (fill_cnt[i][j]) |
208 |
dsf_grid[i][j].crad = fill_grid[i][j]/fill_cnt[i][j]; |
209 |
} |
210 |
|
211 |
/* Radius comparison for qsort() */ |
212 |
static int |
213 |
radius_cmp(const void *p1, const void *p2) |
214 |
{ |
215 |
return( (int)dsf_grid[0][*(const int *)p1].crad - |
216 |
(int)dsf_grid[0][*(const int *)p2].crad ); |
217 |
} |
218 |
|
219 |
/* Cull points for more uniform distribution, leave all nval 0 or 1 */ |
220 |
static void |
221 |
cull_values(void) |
222 |
{ |
223 |
int indx[GRIDRES*GRIDRES]; |
224 |
FVECT ovec0, ovec1; |
225 |
double maxang, maxang2; |
226 |
int i, j, k, ii, jj, r; |
227 |
/* sort by radius first */ |
228 |
for (k = GRIDRES*GRIDRES; k--; ) |
229 |
indx[k] = k; |
230 |
qsort(indx, GRIDRES*GRIDRES, sizeof(int), &radius_cmp); |
231 |
/* simple greedy algorithm */ |
232 |
for (k = GRIDRES*GRIDRES; k--; ) { |
233 |
i = indx[k]/GRIDRES; /* from biggest radius down */ |
234 |
j = indx[k] - i*GRIDRES; |
235 |
if (!dsf_grid[i][j].nval) |
236 |
continue; |
237 |
if (!dsf_grid[i][j].crad) |
238 |
break; /* shouldn't happen */ |
239 |
ovec_from_pos(ovec0, i, j); |
240 |
maxang = 2.*R2ANG(dsf_grid[i][j].crad); |
241 |
/* clamp near horizon */ |
242 |
if (maxang > output_orient*ovec0[2]) |
243 |
maxang = output_orient*ovec0[2]; |
244 |
r = maxang*(2.*GRIDRES/M_PI) + 1; |
245 |
maxang2 = maxang*maxang; |
246 |
for (ii = i-r; ii <= i+r; ii++) { |
247 |
if (ii < 0) continue; |
248 |
if (ii >= GRIDRES) break; |
249 |
for (jj = j-r; jj <= j+r; jj++) { |
250 |
if ((ii == i) & (jj == j)) |
251 |
continue; /* don't get self-absorbed */ |
252 |
if (jj < 0) continue; |
253 |
if (jj >= GRIDRES) break; |
254 |
if (!dsf_grid[ii][jj].nval) |
255 |
continue; |
256 |
ovec_from_pos(ovec1, ii, jj); |
257 |
if (2. - 2.*DOT(ovec0,ovec1) >= maxang2) |
258 |
continue; |
259 |
/* absorb sum */ |
260 |
dsf_grid[i][j].vsum += dsf_grid[ii][jj].vsum; |
261 |
dsf_grid[i][j].nval += dsf_grid[ii][jj].nval; |
262 |
/* keep value, though */ |
263 |
dsf_grid[ii][jj].vsum /= (float)dsf_grid[ii][jj].nval; |
264 |
dsf_grid[ii][jj].nval = 0; |
265 |
} |
266 |
} |
267 |
} |
268 |
/* final averaging pass */ |
269 |
for (i = 0; i < GRIDRES; i++) |
270 |
for (j = 0; j < GRIDRES; j++) |
271 |
if (dsf_grid[i][j].nval > 1) { |
272 |
dsf_grid[i][j].vsum /= (float)dsf_grid[i][j].nval; |
273 |
dsf_grid[i][j].nval = 1; |
274 |
} |
275 |
} |
276 |
|
277 |
/* Compute minimum BSDF from histogram (does not clear) */ |
278 |
static void |
279 |
comp_bsdf_min() |
280 |
{ |
281 |
int cnt; |
282 |
int i, target; |
283 |
|
284 |
cnt = 0; |
285 |
for (i = HISTLEN; i--; ) |
286 |
cnt += bsdf_hist[i]; |
287 |
if (!cnt) { /* shouldn't happen */ |
288 |
bsdf_min = 0; |
289 |
return; |
290 |
} |
291 |
target = cnt/100; /* ignore bottom 1% */ |
292 |
cnt = 0; |
293 |
for (i = 0; cnt <= target; i++) |
294 |
cnt += bsdf_hist[i]; |
295 |
bsdf_min = histval(i-1); |
296 |
} |
297 |
|
298 |
/* Find n nearest sub-sampled neighbors to the given grid position */ |
299 |
static int |
300 |
get_neighbors(int neigh[][2], int n, const int i, const int j) |
301 |
{ |
302 |
int k = 0; |
303 |
int r; |
304 |
/* search concentric squares */ |
305 |
for (r = 1; r < GRIDRES; r++) { |
306 |
int ii, jj; |
307 |
for (ii = i-r; ii <= i+r; ii++) { |
308 |
int jstep = 1; |
309 |
if (ii < 0) continue; |
310 |
if (ii >= GRIDRES) break; |
311 |
if ((i-r < ii) & (ii < i+r)) |
312 |
jstep = r<<1; |
313 |
for (jj = j-r; jj <= j+r; jj += jstep) { |
314 |
if (jj < 0) continue; |
315 |
if (jj >= GRIDRES) break; |
316 |
if (dsf_grid[ii][jj].nval) { |
317 |
neigh[k][0] = ii; |
318 |
neigh[k][1] = jj; |
319 |
if (++k >= n) |
320 |
return(n); |
321 |
} |
322 |
} |
323 |
} |
324 |
} |
325 |
return(k); |
326 |
} |
327 |
|
328 |
/* Adjust coded radius for the given grid position based on neighborhood */ |
329 |
static int |
330 |
adj_coded_radius(const int i, const int j) |
331 |
{ |
332 |
const double rad0 = R2ANG(dsf_grid[i][j].crad); |
333 |
const double minrad = MINRSCA * rad0; |
334 |
double currad = MAXRSCA * rad0; |
335 |
int neigh[NNEIGH][2]; |
336 |
int n; |
337 |
FVECT our_dir; |
338 |
|
339 |
ovec_from_pos(our_dir, i, j); |
340 |
n = get_neighbors(neigh, NNEIGH, i, j); |
341 |
while (n--) { |
342 |
FVECT their_dir; |
343 |
double max_ratio, rad_ok2; |
344 |
/* check our value at neighbor */ |
345 |
ovec_from_pos(their_dir, neigh[n][0], neigh[n][1]); |
346 |
max_ratio = MAXFRAC * dsf_grid[neigh[n][0]][neigh[n][1]].vsum |
347 |
/ dsf_grid[i][j].vsum; |
348 |
if (max_ratio >= 1) |
349 |
continue; |
350 |
rad_ok2 = (DOT(their_dir,our_dir) - 1.)/log(max_ratio); |
351 |
if (rad_ok2 >= currad*currad) |
352 |
continue; /* value fraction OK */ |
353 |
currad = sqrt(rad_ok2); /* else reduce lobe radius */ |
354 |
if (currad <= minrad) /* limit how small we'll go */ |
355 |
return(ANG2R(minrad)); |
356 |
} |
357 |
return(ANG2R(currad)); /* encode selected radius */ |
358 |
} |
359 |
|
360 |
/* Count up filled nodes and build RBF representation from current grid */ |
361 |
RBFNODE * |
362 |
make_rbfrep(void) |
363 |
{ |
364 |
long cradsum = 0, ocradsum = 0; |
365 |
int niter = 16; |
366 |
double lastVar, thisVar = 100.; |
367 |
int nn; |
368 |
RBFNODE *newnode; |
369 |
RBFVAL *itera; |
370 |
int i, j; |
371 |
|
372 |
#ifdef DEBUG |
373 |
{ |
374 |
int maxcnt = 0, nempty = 0; |
375 |
long cntsum = 0; |
376 |
for (i = 0; i < GRIDRES; i++) |
377 |
for (j = 0; j < GRIDRES; j++) |
378 |
if (!dsf_grid[i][j].nval) { |
379 |
++nempty; |
380 |
} else { |
381 |
if (dsf_grid[i][j].nval > maxcnt) |
382 |
maxcnt = dsf_grid[i][j].nval; |
383 |
cntsum += dsf_grid[i][j].nval; |
384 |
} |
385 |
fprintf(stderr, "Average, maximum bin count: %d, %d (%.1f%% empty)\n", |
386 |
(int)(cntsum/((GRIDRES*GRIDRES)-nempty)), maxcnt, |
387 |
100./(GRIDRES*GRIDRES)*nempty); |
388 |
} |
389 |
#endif |
390 |
/* compute RBF radii */ |
391 |
compute_radii(); |
392 |
/* coagulate lobes */ |
393 |
cull_values(); |
394 |
nn = 0; /* count selected bins */ |
395 |
for (i = 0; i < GRIDRES; i++) |
396 |
for (j = 0; j < GRIDRES; j++) |
397 |
nn += dsf_grid[i][j].nval; |
398 |
/* compute minimum BSDF */ |
399 |
comp_bsdf_min(); |
400 |
/* allocate RBF array */ |
401 |
newnode = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(nn-1)); |
402 |
if (newnode == NULL) |
403 |
goto memerr; |
404 |
newnode->ord = -1; |
405 |
newnode->next = NULL; |
406 |
newnode->ejl = NULL; |
407 |
newnode->invec[2] = sin((M_PI/180.)*theta_in_deg); |
408 |
newnode->invec[0] = cos((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
409 |
newnode->invec[1] = sin((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
410 |
newnode->invec[2] = input_orient*sqrt(1. - newnode->invec[2]*newnode->invec[2]); |
411 |
newnode->vtotal = 0; |
412 |
newnode->nrbf = nn; |
413 |
nn = 0; /* fill RBF array */ |
414 |
for (i = 0; i < GRIDRES; i++) |
415 |
for (j = 0; j < GRIDRES; j++) |
416 |
if (dsf_grid[i][j].nval) { |
417 |
newnode->rbfa[nn].peak = dsf_grid[i][j].vsum; |
418 |
ocradsum += dsf_grid[i][j].crad; |
419 |
cradsum += |
420 |
newnode->rbfa[nn].crad = adj_coded_radius(i, j); |
421 |
newnode->rbfa[nn].gx = i; |
422 |
newnode->rbfa[nn].gy = j; |
423 |
++nn; |
424 |
} |
425 |
#ifdef DEBUG |
426 |
fprintf(stderr, |
427 |
"Average radius reduced from %.2f to %.2f degrees for %d lobes\n", |
428 |
180./M_PI*MAXRSCA*R2ANG(ocradsum/newnode->nrbf), |
429 |
180./M_PI*R2ANG(cradsum/newnode->nrbf), newnode->nrbf); |
430 |
#endif |
431 |
/* iterate to improve interpolation accuracy */ |
432 |
itera = (RBFVAL *)malloc(sizeof(RBFVAL)*newnode->nrbf); |
433 |
if (itera == NULL) |
434 |
goto memerr; |
435 |
memcpy(itera, newnode->rbfa, sizeof(RBFVAL)*newnode->nrbf); |
436 |
do { |
437 |
double dsum = 0, dsum2 = 0; |
438 |
nn = 0; |
439 |
for (i = 0; i < GRIDRES; i++) |
440 |
for (j = 0; j < GRIDRES; j++) |
441 |
if (dsf_grid[i][j].nval) { |
442 |
FVECT odir; |
443 |
double corr; |
444 |
ovec_from_pos(odir, i, j); |
445 |
itera[nn++].peak *= corr = |
446 |
dsf_grid[i][j].vsum / |
447 |
eval_rbfrep(newnode, odir); |
448 |
dsum += 1. - corr; |
449 |
dsum2 += (1.-corr)*(1.-corr); |
450 |
} |
451 |
memcpy(newnode->rbfa, itera, sizeof(RBFVAL)*newnode->nrbf); |
452 |
lastVar = thisVar; |
453 |
thisVar = dsum2/(double)nn; |
454 |
#ifdef DEBUG |
455 |
fprintf(stderr, "Avg., RMS error: %.1f%% %.1f%%\n", |
456 |
100.*dsum/(double)nn, |
457 |
100.*sqrt(thisVar)); |
458 |
#endif |
459 |
} while (--niter > 0 && lastVar-thisVar > 0.02*lastVar); |
460 |
|
461 |
free(itera); |
462 |
nn = 0; /* compute sum for normalization */ |
463 |
while (nn < newnode->nrbf) |
464 |
newnode->vtotal += rbf_volume(&newnode->rbfa[nn++]); |
465 |
#ifdef DEBUG |
466 |
fprintf(stderr, "Integrated DSF at (%.1f,%.1f) deg. is %.2f\n", |
467 |
get_theta180(newnode->invec), get_phi360(newnode->invec), |
468 |
newnode->vtotal); |
469 |
#endif |
470 |
insert_dsf(newnode); |
471 |
|
472 |
return(newnode); |
473 |
memerr: |
474 |
fprintf(stderr, "%s: Out of memory in make_rbfrep()\n", progname); |
475 |
exit(1); |
476 |
} |