| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: bsdfrbf.c,v 2.9 2013/10/17 19:09:11 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 0.5 /* minimum radius scaling factor */ |
| 19 |
#endif |
| 20 |
#ifndef MAXRSCA |
| 21 |
#define MAXRSCA 2.7 /* maximum radius scaling factor */ |
| 22 |
#endif |
| 23 |
#ifndef DIFFTHRESH |
| 24 |
#define DIFFTHRESH 0.2 /* culling difference threshold */ |
| 25 |
#endif |
| 26 |
#ifndef MAXFRAC |
| 27 |
#define MAXFRAC 0.5 /* maximum contribution to neighbor */ |
| 28 |
#endif |
| 29 |
#ifndef NNEIGH |
| 30 |
#define NNEIGH 10 /* number of neighbors to consider */ |
| 31 |
#endif |
| 32 |
/* our loaded grid for this incident angle */ |
| 33 |
GRIDVAL dsf_grid[GRIDRES][GRIDRES]; |
| 34 |
|
| 35 |
/* Start new DSF input grid */ |
| 36 |
void |
| 37 |
new_bsdf_data(double new_theta, double new_phi) |
| 38 |
{ |
| 39 |
if (!new_input_direction(new_theta, new_phi)) |
| 40 |
exit(1); |
| 41 |
memset(dsf_grid, 0, sizeof(dsf_grid)); |
| 42 |
} |
| 43 |
|
| 44 |
/* Add BSDF data point */ |
| 45 |
void |
| 46 |
add_bsdf_data(double theta_out, double phi_out, double val, int isDSF) |
| 47 |
{ |
| 48 |
FVECT ovec; |
| 49 |
int pos[2]; |
| 50 |
|
| 51 |
if (!output_orient) /* check output orientation */ |
| 52 |
output_orient = 1 - 2*(theta_out > 90.); |
| 53 |
else if (output_orient > 0 ^ theta_out < 90.) { |
| 54 |
fputs("Cannot handle output angles on both sides of surface\n", |
| 55 |
stderr); |
| 56 |
exit(1); |
| 57 |
} |
| 58 |
ovec[2] = sin((M_PI/180.)*theta_out); |
| 59 |
ovec[0] = cos((M_PI/180.)*phi_out) * ovec[2]; |
| 60 |
ovec[1] = sin((M_PI/180.)*phi_out) * ovec[2]; |
| 61 |
ovec[2] = sqrt(1. - ovec[2]*ovec[2]); |
| 62 |
|
| 63 |
if (val <= 0) /* truncate to zero */ |
| 64 |
val = 0; |
| 65 |
else if (!isDSF) |
| 66 |
val *= ovec[2]; /* convert from BSDF to DSF */ |
| 67 |
|
| 68 |
/* update BSDF histogram */ |
| 69 |
if (val < BSDF2BIG*ovec[2] && val > BSDF2SML*ovec[2]) |
| 70 |
++bsdf_hist[histndx(val/ovec[2])]; |
| 71 |
|
| 72 |
pos_from_vec(pos, ovec); |
| 73 |
|
| 74 |
dsf_grid[pos[0]][pos[1]].vsum += val; |
| 75 |
dsf_grid[pos[0]][pos[1]].nval++; |
| 76 |
} |
| 77 |
|
| 78 |
/* Check if the two DSF values are significantly different */ |
| 79 |
static int |
| 80 |
big_diff(double ref, double tst) |
| 81 |
{ |
| 82 |
if (ref > 0) { |
| 83 |
tst = tst/ref - 1.; |
| 84 |
if (tst < 0) tst = -tst; |
| 85 |
} else |
| 86 |
tst *= 50.; |
| 87 |
return(tst > DIFFTHRESH); |
| 88 |
} |
| 89 |
|
| 90 |
/* Compute radii for non-empty bins */ |
| 91 |
/* (distance to furthest empty bin for which non-empty test bin is closest) */ |
| 92 |
static void |
| 93 |
compute_radii(void) |
| 94 |
{ |
| 95 |
const int cradmin = ANG2R(.5*M_PI/GRIDRES); |
| 96 |
unsigned int fill_grid[GRIDRES][GRIDRES]; |
| 97 |
unsigned short fill_cnt[GRIDRES][GRIDRES]; |
| 98 |
FVECT ovec0, ovec1; |
| 99 |
double ang2, lastang2; |
| 100 |
int r, i, j, jn, ii, jj, inear, jnear; |
| 101 |
|
| 102 |
r = GRIDRES/2; /* proceed in zig-zag */ |
| 103 |
for (i = 0; i < GRIDRES; i++) |
| 104 |
for (jn = 0; jn < GRIDRES; jn++) { |
| 105 |
j = (i&1) ? jn : GRIDRES-1-jn; |
| 106 |
if (dsf_grid[i][j].nval) /* find empty grid pos. */ |
| 107 |
continue; |
| 108 |
ovec_from_pos(ovec0, i, j); |
| 109 |
inear = jnear = -1; /* find nearest non-empty */ |
| 110 |
lastang2 = M_PI*M_PI; |
| 111 |
for (ii = i-r; ii <= i+r; ii++) { |
| 112 |
if (ii < 0) continue; |
| 113 |
if (ii >= GRIDRES) break; |
| 114 |
for (jj = j-r; jj <= j+r; jj++) { |
| 115 |
if (jj < 0) continue; |
| 116 |
if (jj >= GRIDRES) break; |
| 117 |
if (!dsf_grid[ii][jj].nval) |
| 118 |
continue; |
| 119 |
ovec_from_pos(ovec1, ii, jj); |
| 120 |
ang2 = 2. - 2.*DOT(ovec0,ovec1); |
| 121 |
if (ang2 >= lastang2) |
| 122 |
continue; |
| 123 |
lastang2 = ang2; |
| 124 |
inear = ii; jnear = jj; |
| 125 |
} |
| 126 |
} |
| 127 |
if (inear < 0) { |
| 128 |
fprintf(stderr, |
| 129 |
"%s: Could not find non-empty neighbor!\n", |
| 130 |
progname); |
| 131 |
exit(1); |
| 132 |
} |
| 133 |
ang2 = sqrt(lastang2); |
| 134 |
r = ANG2R(ang2); /* record if > previous */ |
| 135 |
if (r > dsf_grid[inear][jnear].crad) |
| 136 |
dsf_grid[inear][jnear].crad = r; |
| 137 |
/* next search radius */ |
| 138 |
r = ang2*(2.*GRIDRES/M_PI) + 3; |
| 139 |
} |
| 140 |
for (i = 0; i < GRIDRES; i++) /* grow radii where uniform */ |
| 141 |
for (j = 0; j < GRIDRES; j++) { |
| 142 |
double midmean; |
| 143 |
if (!dsf_grid[i][j].nval) |
| 144 |
continue; |
| 145 |
midmean = dsf_grid[i][j].vsum / (double)dsf_grid[i][j].nval; |
| 146 |
r = R2ANG(dsf_grid[i][j].crad)*(MAXRSCA*GRIDRES/M_PI); |
| 147 |
while (++r < GRIDRES) { /* attempt to grow perimeter */ |
| 148 |
for (ii = i-r; ii <= i+r; ii++) { |
| 149 |
int jstep = 1; |
| 150 |
if (ii < 0) continue; |
| 151 |
if (ii >= GRIDRES) break; |
| 152 |
if ((i-r < ii) & (ii < i+r)) |
| 153 |
jstep = r<<1; |
| 154 |
for (jj = j-r; jj <= j+r; jj += jstep) { |
| 155 |
if (jj < 0) continue; |
| 156 |
if (jj >= GRIDRES) break; |
| 157 |
if (dsf_grid[ii][jj].nval && big_diff(midmean, |
| 158 |
dsf_grid[ii][jj].vsum / |
| 159 |
(double)dsf_grid[ii][jj].nval)) |
| 160 |
goto hit_diff; |
| 161 |
} |
| 162 |
} |
| 163 |
} |
| 164 |
hit_diff: --r; |
| 165 |
dsf_grid[i][j].crad = ANG2R(r*(M_PI/MAXRSCA/GRIDRES)); |
| 166 |
if (dsf_grid[i][j].crad < cradmin) |
| 167 |
dsf_grid[i][j].crad = cradmin; |
| 168 |
} |
| 169 |
/* blur radii over hemisphere */ |
| 170 |
memset(fill_grid, 0, sizeof(fill_grid)); |
| 171 |
memset(fill_cnt, 0, sizeof(fill_cnt)); |
| 172 |
for (i = 0; i < GRIDRES; i++) |
| 173 |
for (j = 0; j < GRIDRES; j++) { |
| 174 |
if (!dsf_grid[i][j].nval) |
| 175 |
continue; /* not part of this */ |
| 176 |
r = R2ANG(dsf_grid[i][j].crad)*(2.*MAXRSCA*GRIDRES/M_PI); |
| 177 |
for (ii = i-r; ii <= i+r; ii++) { |
| 178 |
if (ii < 0) continue; |
| 179 |
if (ii >= GRIDRES) break; |
| 180 |
for (jj = j-r; jj <= j+r; jj++) { |
| 181 |
if (jj < 0) continue; |
| 182 |
if (jj >= GRIDRES) break; |
| 183 |
if ((ii-i)*(ii-i) + (jj-j)*(jj-j) > r*r) |
| 184 |
continue; |
| 185 |
fill_grid[ii][jj] += dsf_grid[i][j].crad; |
| 186 |
fill_cnt[ii][jj]++; |
| 187 |
} |
| 188 |
} |
| 189 |
} |
| 190 |
/* copy back blurred radii */ |
| 191 |
for (i = 0; i < GRIDRES; i++) |
| 192 |
for (j = 0; j < GRIDRES; j++) |
| 193 |
if (fill_cnt[i][j]) |
| 194 |
dsf_grid[i][j].crad = fill_grid[i][j]/fill_cnt[i][j]; |
| 195 |
} |
| 196 |
|
| 197 |
/* Cull points for more uniform distribution, leave all nval 0 or 1 */ |
| 198 |
static void |
| 199 |
cull_values(void) |
| 200 |
{ |
| 201 |
FVECT ovec0, ovec1; |
| 202 |
double maxang, maxang2; |
| 203 |
int i, j, ii, jj, r; |
| 204 |
/* simple greedy algorithm */ |
| 205 |
for (i = 0; i < GRIDRES; i++) |
| 206 |
for (j = 0; j < GRIDRES; j++) { |
| 207 |
if (!dsf_grid[i][j].nval) |
| 208 |
continue; |
| 209 |
if (!dsf_grid[i][j].crad) |
| 210 |
continue; /* shouldn't happen */ |
| 211 |
ovec_from_pos(ovec0, i, j); |
| 212 |
maxang = 2.*R2ANG(dsf_grid[i][j].crad); |
| 213 |
/* clamp near horizon */ |
| 214 |
if (maxang > output_orient*ovec0[2]) |
| 215 |
maxang = output_orient*ovec0[2]; |
| 216 |
r = maxang*(2.*GRIDRES/M_PI) + 1; |
| 217 |
maxang2 = maxang*maxang; |
| 218 |
for (ii = i-r; ii <= i+r; ii++) { |
| 219 |
if (ii < 0) continue; |
| 220 |
if (ii >= GRIDRES) break; |
| 221 |
for (jj = j-r; jj <= j+r; jj++) { |
| 222 |
if ((ii == i) & (jj == j)) |
| 223 |
continue; /* don't get self-absorbed */ |
| 224 |
if (jj < 0) continue; |
| 225 |
if (jj >= GRIDRES) break; |
| 226 |
if (!dsf_grid[ii][jj].nval) |
| 227 |
continue; |
| 228 |
ovec_from_pos(ovec1, ii, jj); |
| 229 |
if (2. - 2.*DOT(ovec0,ovec1) >= maxang2) |
| 230 |
continue; |
| 231 |
/* absorb sum */ |
| 232 |
dsf_grid[i][j].vsum += dsf_grid[ii][jj].vsum; |
| 233 |
dsf_grid[i][j].nval += dsf_grid[ii][jj].nval; |
| 234 |
/* keep value, though */ |
| 235 |
dsf_grid[ii][jj].vsum /= (float)dsf_grid[ii][jj].nval; |
| 236 |
dsf_grid[ii][jj].nval = 0; |
| 237 |
} |
| 238 |
} |
| 239 |
} |
| 240 |
/* final averaging pass */ |
| 241 |
for (i = 0; i < GRIDRES; i++) |
| 242 |
for (j = 0; j < GRIDRES; j++) |
| 243 |
if (dsf_grid[i][j].nval > 1) { |
| 244 |
dsf_grid[i][j].vsum /= (float)dsf_grid[i][j].nval; |
| 245 |
dsf_grid[i][j].nval = 1; |
| 246 |
} |
| 247 |
} |
| 248 |
|
| 249 |
/* Compute minimum BSDF from histogram and clear it */ |
| 250 |
static void |
| 251 |
comp_bsdf_min() |
| 252 |
{ |
| 253 |
int cnt; |
| 254 |
int i, target; |
| 255 |
|
| 256 |
cnt = 0; |
| 257 |
for (i = HISTLEN; i--; ) |
| 258 |
cnt += bsdf_hist[i]; |
| 259 |
if (!cnt) { /* shouldn't happen */ |
| 260 |
bsdf_min = 0; |
| 261 |
return; |
| 262 |
} |
| 263 |
target = cnt/100; /* ignore bottom 1% */ |
| 264 |
cnt = 0; |
| 265 |
for (i = 0; cnt <= target; i++) |
| 266 |
cnt += bsdf_hist[i]; |
| 267 |
bsdf_min = histval(i-1); |
| 268 |
memset(bsdf_hist, 0, sizeof(bsdf_hist)); |
| 269 |
} |
| 270 |
|
| 271 |
/* Find n nearest sub-sampled neighbors to the given grid position */ |
| 272 |
static int |
| 273 |
get_neighbors(int neigh[][2], int n, const int i, const int j) |
| 274 |
{ |
| 275 |
int k = 0; |
| 276 |
int r; |
| 277 |
/* search concentric squares */ |
| 278 |
for (r = 1; r < GRIDRES; r++) { |
| 279 |
int ii, jj; |
| 280 |
for (ii = i-r; ii <= i+r; ii++) { |
| 281 |
int jstep = 1; |
| 282 |
if (ii < 0) continue; |
| 283 |
if (ii >= GRIDRES) break; |
| 284 |
if ((i-r < ii) & (ii < i+r)) |
| 285 |
jstep = r<<1; |
| 286 |
for (jj = j-r; jj <= j+r; jj += jstep) { |
| 287 |
if (jj < 0) continue; |
| 288 |
if (jj >= GRIDRES) break; |
| 289 |
if (dsf_grid[ii][jj].nval) { |
| 290 |
neigh[k][0] = ii; |
| 291 |
neigh[k][1] = jj; |
| 292 |
if (++k >= n) |
| 293 |
return(n); |
| 294 |
} |
| 295 |
} |
| 296 |
} |
| 297 |
} |
| 298 |
return(k); |
| 299 |
} |
| 300 |
|
| 301 |
/* Adjust coded radius for the given grid position based on neighborhood */ |
| 302 |
static int |
| 303 |
adj_coded_radius(const int i, const int j) |
| 304 |
{ |
| 305 |
const double rad0 = R2ANG(dsf_grid[i][j].crad); |
| 306 |
const double minrad = MINRSCA * rad0; |
| 307 |
double currad = MAXRSCA * rad0; |
| 308 |
int neigh[NNEIGH][2]; |
| 309 |
int n; |
| 310 |
FVECT our_dir; |
| 311 |
|
| 312 |
ovec_from_pos(our_dir, i, j); |
| 313 |
n = get_neighbors(neigh, NNEIGH, i, j); |
| 314 |
while (n--) { |
| 315 |
FVECT their_dir; |
| 316 |
double max_ratio, rad_ok2; |
| 317 |
/* check our value at neighbor */ |
| 318 |
ovec_from_pos(their_dir, neigh[n][0], neigh[n][1]); |
| 319 |
max_ratio = MAXFRAC * dsf_grid[neigh[n][0]][neigh[n][1]].vsum |
| 320 |
/ dsf_grid[i][j].vsum; |
| 321 |
if (max_ratio >= 1) |
| 322 |
continue; |
| 323 |
rad_ok2 = (DOT(their_dir,our_dir) - 1.)/log(max_ratio); |
| 324 |
if (rad_ok2 >= currad*currad) |
| 325 |
continue; /* value fraction OK */ |
| 326 |
currad = sqrt(rad_ok2); /* else reduce lobe radius */ |
| 327 |
if (currad <= minrad) /* limit how small we'll go */ |
| 328 |
return(ANG2R(minrad)); |
| 329 |
} |
| 330 |
return(ANG2R(currad)); /* encode selected radius */ |
| 331 |
} |
| 332 |
|
| 333 |
/* Count up filled nodes and build RBF representation from current grid */ |
| 334 |
RBFNODE * |
| 335 |
make_rbfrep(void) |
| 336 |
{ |
| 337 |
long cradsum = 0, ocradsum = 0; |
| 338 |
int niter = 16; |
| 339 |
double lastVar, thisVar = 100.; |
| 340 |
int nn; |
| 341 |
RBFNODE *newnode; |
| 342 |
RBFVAL *itera; |
| 343 |
int i, j; |
| 344 |
|
| 345 |
#ifdef DEBUG |
| 346 |
{ |
| 347 |
int maxcnt = 0, nempty = 0; |
| 348 |
long cntsum = 0; |
| 349 |
for (i = 0; i < GRIDRES; i++) |
| 350 |
for (j = 0; j < GRIDRES; j++) |
| 351 |
if (!dsf_grid[i][j].nval) { |
| 352 |
++nempty; |
| 353 |
} else { |
| 354 |
if (dsf_grid[i][j].nval > maxcnt) |
| 355 |
maxcnt = dsf_grid[i][j].nval; |
| 356 |
cntsum += dsf_grid[i][j].nval; |
| 357 |
} |
| 358 |
fprintf(stderr, "Average, maximum bin count: %d, %d (%.1f%% empty)\n", |
| 359 |
(int)(cntsum/((GRIDRES*GRIDRES)-nempty)), maxcnt, |
| 360 |
100./(GRIDRES*GRIDRES)*nempty); |
| 361 |
} |
| 362 |
#endif |
| 363 |
/* compute RBF radii */ |
| 364 |
compute_radii(); |
| 365 |
/* coagulate lobes */ |
| 366 |
cull_values(); |
| 367 |
nn = 0; /* count selected bins */ |
| 368 |
for (i = 0; i < GRIDRES; i++) |
| 369 |
for (j = 0; j < GRIDRES; j++) |
| 370 |
nn += dsf_grid[i][j].nval; |
| 371 |
/* compute minimum BSDF */ |
| 372 |
comp_bsdf_min(); |
| 373 |
/* allocate RBF array */ |
| 374 |
newnode = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(nn-1)); |
| 375 |
if (newnode == NULL) |
| 376 |
goto memerr; |
| 377 |
newnode->ord = -1; |
| 378 |
newnode->next = NULL; |
| 379 |
newnode->ejl = NULL; |
| 380 |
newnode->invec[2] = sin((M_PI/180.)*theta_in_deg); |
| 381 |
newnode->invec[0] = cos((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
| 382 |
newnode->invec[1] = sin((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
| 383 |
newnode->invec[2] = input_orient*sqrt(1. - newnode->invec[2]*newnode->invec[2]); |
| 384 |
newnode->vtotal = 0; |
| 385 |
newnode->nrbf = nn; |
| 386 |
nn = 0; /* fill RBF array */ |
| 387 |
for (i = 0; i < GRIDRES; i++) |
| 388 |
for (j = 0; j < GRIDRES; j++) |
| 389 |
if (dsf_grid[i][j].nval) { |
| 390 |
newnode->rbfa[nn].peak = dsf_grid[i][j].vsum; |
| 391 |
ocradsum += dsf_grid[i][j].crad; |
| 392 |
cradsum += |
| 393 |
newnode->rbfa[nn].crad = adj_coded_radius(i, j); |
| 394 |
newnode->rbfa[nn].gx = i; |
| 395 |
newnode->rbfa[nn].gy = j; |
| 396 |
++nn; |
| 397 |
} |
| 398 |
#ifdef DEBUG |
| 399 |
fprintf(stderr, |
| 400 |
"Average radius reduced from %.2f to %.2f degrees for %d lobes\n", |
| 401 |
180./M_PI*MAXRSCA*R2ANG(ocradsum/newnode->nrbf), |
| 402 |
180./M_PI*R2ANG(cradsum/newnode->nrbf), newnode->nrbf); |
| 403 |
#endif |
| 404 |
/* iterate to improve interpolation accuracy */ |
| 405 |
itera = (RBFVAL *)malloc(sizeof(RBFVAL)*newnode->nrbf); |
| 406 |
if (itera == NULL) |
| 407 |
goto memerr; |
| 408 |
memcpy(itera, newnode->rbfa, sizeof(RBFVAL)*newnode->nrbf); |
| 409 |
do { |
| 410 |
double dsum = 0, dsum2 = 0; |
| 411 |
nn = 0; |
| 412 |
for (i = 0; i < GRIDRES; i++) |
| 413 |
for (j = 0; j < GRIDRES; j++) |
| 414 |
if (dsf_grid[i][j].nval) { |
| 415 |
FVECT odir; |
| 416 |
double corr; |
| 417 |
ovec_from_pos(odir, i, j); |
| 418 |
itera[nn++].peak *= corr = |
| 419 |
dsf_grid[i][j].vsum / |
| 420 |
eval_rbfrep(newnode, odir); |
| 421 |
dsum += 1. - corr; |
| 422 |
dsum2 += (1.-corr)*(1.-corr); |
| 423 |
} |
| 424 |
memcpy(newnode->rbfa, itera, sizeof(RBFVAL)*newnode->nrbf); |
| 425 |
lastVar = thisVar; |
| 426 |
thisVar = dsum2/(double)nn; |
| 427 |
#ifdef DEBUG |
| 428 |
fprintf(stderr, "Avg., RMS error: %.1f%% %.1f%%\n", |
| 429 |
100.*dsum/(double)nn, |
| 430 |
100.*sqrt(thisVar)); |
| 431 |
#endif |
| 432 |
} while (--niter > 0 && lastVar-thisVar > 0.02*lastVar); |
| 433 |
|
| 434 |
free(itera); |
| 435 |
nn = 0; /* compute sum for normalization */ |
| 436 |
while (nn < newnode->nrbf) |
| 437 |
newnode->vtotal += rbf_volume(&newnode->rbfa[nn++]); |
| 438 |
#ifdef DEBUG |
| 439 |
fprintf(stderr, "Integrated DSF at (%.1f,%.1f) deg. is %.2f\n", |
| 440 |
get_theta180(newnode->invec), get_phi360(newnode->invec), |
| 441 |
newnode->vtotal); |
| 442 |
#endif |
| 443 |
insert_dsf(newnode); |
| 444 |
|
| 445 |
return(newnode); |
| 446 |
memerr: |
| 447 |
fprintf(stderr, "%s: Out of memory in make_rbfrep()\n", progname); |
| 448 |
exit(1); |
| 449 |
} |
