| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: bsdfinterp.c,v 2.7 2012/11/26 07:02:20 greg Exp $"; |
| 3 |
#endif |
| 4 |
/* |
| 5 |
* Interpolate BSDF data from radial basis functions in advection mesh. |
| 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 |
/* Insert vertex in ordered list */ |
| 18 |
static void |
| 19 |
insert_vert(RBFNODE **vlist, RBFNODE *v) |
| 20 |
{ |
| 21 |
int i, j; |
| 22 |
|
| 23 |
for (i = 0; vlist[i] != NULL; i++) { |
| 24 |
if (v == vlist[i]) |
| 25 |
return; |
| 26 |
if (v->ord < vlist[i]->ord) |
| 27 |
break; |
| 28 |
} |
| 29 |
for (j = i; vlist[j] != NULL; j++) |
| 30 |
; |
| 31 |
while (j > i) { |
| 32 |
vlist[j] = vlist[j-1]; |
| 33 |
--j; |
| 34 |
} |
| 35 |
vlist[i] = v; |
| 36 |
} |
| 37 |
|
| 38 |
/* Sort triangle edges in standard order */ |
| 39 |
static int |
| 40 |
order_triangle(MIGRATION *miga[3]) |
| 41 |
{ |
| 42 |
RBFNODE *vert[7]; |
| 43 |
MIGRATION *ord[3]; |
| 44 |
int i; |
| 45 |
/* order vertices, first */ |
| 46 |
memset(vert, 0, sizeof(vert)); |
| 47 |
for (i = 3; i--; ) { |
| 48 |
if (miga[i] == NULL) |
| 49 |
return(0); |
| 50 |
insert_vert(vert, miga[i]->rbfv[0]); |
| 51 |
insert_vert(vert, miga[i]->rbfv[1]); |
| 52 |
} |
| 53 |
/* should be just 3 vertices */ |
| 54 |
if ((vert[2] == NULL) | (vert[3] != NULL)) |
| 55 |
return(0); |
| 56 |
/* identify edge 0 */ |
| 57 |
for (i = 3; i--; ) |
| 58 |
if (miga[i]->rbfv[0] == vert[0] && |
| 59 |
miga[i]->rbfv[1] == vert[1]) { |
| 60 |
ord[0] = miga[i]; |
| 61 |
break; |
| 62 |
} |
| 63 |
if (i < 0) |
| 64 |
return(0); |
| 65 |
/* identify edge 1 */ |
| 66 |
for (i = 3; i--; ) |
| 67 |
if (miga[i]->rbfv[0] == vert[1] && |
| 68 |
miga[i]->rbfv[1] == vert[2]) { |
| 69 |
ord[1] = miga[i]; |
| 70 |
break; |
| 71 |
} |
| 72 |
if (i < 0) |
| 73 |
return(0); |
| 74 |
/* identify edge 2 */ |
| 75 |
for (i = 3; i--; ) |
| 76 |
if (miga[i]->rbfv[0] == vert[0] && |
| 77 |
miga[i]->rbfv[1] == vert[2]) { |
| 78 |
ord[2] = miga[i]; |
| 79 |
break; |
| 80 |
} |
| 81 |
if (i < 0) |
| 82 |
return(0); |
| 83 |
/* reassign order */ |
| 84 |
miga[0] = ord[0]; miga[1] = ord[1]; miga[2] = ord[2]; |
| 85 |
return(1); |
| 86 |
} |
| 87 |
|
| 88 |
/* Determine if we are close enough to an edge */ |
| 89 |
static int |
| 90 |
on_edge(const MIGRATION *ej, const FVECT ivec) |
| 91 |
{ |
| 92 |
double cos_a, cos_b, cos_c, cos_aplusb; |
| 93 |
/* use triangle inequality */ |
| 94 |
cos_a = DOT(ej->rbfv[0]->invec, ivec); |
| 95 |
if (cos_a <= 0) |
| 96 |
return(0); |
| 97 |
|
| 98 |
cos_b = DOT(ej->rbfv[1]->invec, ivec); |
| 99 |
if (cos_b <= 0) |
| 100 |
return(0); |
| 101 |
|
| 102 |
cos_aplusb = cos_a*cos_b - sqrt((1.-cos_a*cos_a)*(1.-cos_b*cos_b)); |
| 103 |
if (cos_aplusb <= 0) |
| 104 |
return(0); |
| 105 |
|
| 106 |
cos_c = DOT(ej->rbfv[0]->invec, ej->rbfv[1]->invec); |
| 107 |
|
| 108 |
return(cos_c - cos_aplusb < .001); |
| 109 |
} |
| 110 |
|
| 111 |
/* Determine if we are inside the given triangle */ |
| 112 |
static int |
| 113 |
in_tri(const RBFNODE *v1, const RBFNODE *v2, const RBFNODE *v3, const FVECT p) |
| 114 |
{ |
| 115 |
FVECT vc; |
| 116 |
int sgn1, sgn2, sgn3; |
| 117 |
/* signed volume test */ |
| 118 |
VCROSS(vc, v1->invec, v2->invec); |
| 119 |
sgn1 = (DOT(p, vc) > 0); |
| 120 |
VCROSS(vc, v2->invec, v3->invec); |
| 121 |
sgn2 = (DOT(p, vc) > 0); |
| 122 |
if (sgn1 != sgn2) |
| 123 |
return(0); |
| 124 |
VCROSS(vc, v3->invec, v1->invec); |
| 125 |
sgn3 = (DOT(p, vc) > 0); |
| 126 |
return(sgn2 == sgn3); |
| 127 |
} |
| 128 |
|
| 129 |
/* Test (and set) bitmap for edge */ |
| 130 |
static int |
| 131 |
check_edge(unsigned char *emap, int nedges, const MIGRATION *mig, int mark) |
| 132 |
{ |
| 133 |
int ejndx, bit2check; |
| 134 |
|
| 135 |
if (mig->rbfv[0]->ord > mig->rbfv[1]->ord) |
| 136 |
ejndx = mig->rbfv[1]->ord + (nedges-1)*mig->rbfv[0]->ord; |
| 137 |
else |
| 138 |
ejndx = mig->rbfv[0]->ord + (nedges-1)*mig->rbfv[1]->ord; |
| 139 |
|
| 140 |
bit2check = 1<<(ejndx&07); |
| 141 |
|
| 142 |
if (emap[ejndx>>3] & bit2check) |
| 143 |
return(0); |
| 144 |
if (mark) |
| 145 |
emap[ejndx>>3] |= bit2check; |
| 146 |
return(1); |
| 147 |
} |
| 148 |
|
| 149 |
/* Compute intersection with the given position over remaining mesh */ |
| 150 |
static int |
| 151 |
in_mesh(MIGRATION *miga[3], unsigned char *emap, int nedges, |
| 152 |
const FVECT ivec, MIGRATION *mig) |
| 153 |
{ |
| 154 |
MIGRATION *ej1, *ej2; |
| 155 |
RBFNODE *tv; |
| 156 |
/* check visitation record */ |
| 157 |
if (!check_edge(emap, nedges, mig, 1)) |
| 158 |
return(0); |
| 159 |
if (on_edge(mig, ivec)) { |
| 160 |
miga[0] = mig; /* close enough to edge */ |
| 161 |
return(1); |
| 162 |
} |
| 163 |
/* do triangles either side */ |
| 164 |
for (ej1 = mig->rbfv[0]->ejl; ej1 != NULL; |
| 165 |
ej1 = nextedge(mig->rbfv[0],ej1)) { |
| 166 |
if (ej1 == mig) |
| 167 |
continue; |
| 168 |
tv = opp_rbf(mig->rbfv[0],ej1); |
| 169 |
for (ej2 = tv->ejl; ej2 != NULL; ej2 = nextedge(tv,ej2)) |
| 170 |
if (opp_rbf(tv,ej2) == mig->rbfv[1]) { |
| 171 |
int do_ej1 = check_edge(emap, nedges, ej1, 0); |
| 172 |
int do_ej2 = check_edge(emap, nedges, ej2, 0); |
| 173 |
if (do_ej1 && in_mesh(miga, emap, nedges, ivec, ej1)) |
| 174 |
return(1); |
| 175 |
if (do_ej2 && in_mesh(miga, emap, nedges, ivec, ej2)) |
| 176 |
return(1); |
| 177 |
/* check just once */ |
| 178 |
if (do_ej1 & do_ej2 && in_tri(mig->rbfv[0], |
| 179 |
mig->rbfv[1], tv, ivec)) { |
| 180 |
miga[0] = mig; |
| 181 |
miga[1] = ej1; |
| 182 |
miga[2] = ej2; |
| 183 |
return(1); |
| 184 |
} |
| 185 |
} |
| 186 |
} |
| 187 |
return(0); /* not near this edge */ |
| 188 |
} |
| 189 |
|
| 190 |
/* Find edge(s) for interpolating the given vector, applying symmetry */ |
| 191 |
int |
| 192 |
get_interp(MIGRATION *miga[3], FVECT invec) |
| 193 |
{ |
| 194 |
miga[0] = miga[1] = miga[2] = NULL; |
| 195 |
if (single_plane_incident) { /* isotropic BSDF? */ |
| 196 |
RBFNODE *rbf; /* find edge we're on */ |
| 197 |
for (rbf = dsf_list; rbf != NULL; rbf = rbf->next) { |
| 198 |
if (input_orient*rbf->invec[2] < input_orient*invec[2]) |
| 199 |
break; |
| 200 |
if (rbf->next != NULL && |
| 201 |
input_orient*rbf->next->invec[2] < |
| 202 |
input_orient*invec[2]) { |
| 203 |
for (miga[0] = rbf->ejl; miga[0] != NULL; |
| 204 |
miga[0] = nextedge(rbf,miga[0])) |
| 205 |
if (opp_rbf(rbf,miga[0]) == rbf->next) { |
| 206 |
double nf = 1.-rbf->invec[2]*rbf->invec[2]; |
| 207 |
if (nf > FTINY) { |
| 208 |
nf = sqrt((1.-invec[2]*invec[2])/nf); |
| 209 |
invec[0] = nf*rbf->invec[0]; |
| 210 |
invec[1] = nf*rbf->invec[1]; |
| 211 |
} |
| 212 |
return(0); |
| 213 |
} |
| 214 |
break; |
| 215 |
} |
| 216 |
} |
| 217 |
return(-1); /* outside range! */ |
| 218 |
} |
| 219 |
{ /* else use triangle mesh */ |
| 220 |
int sym = use_symmetry(invec); |
| 221 |
int nedges = 0; |
| 222 |
MIGRATION *mep; |
| 223 |
unsigned char *emap; |
| 224 |
/* clear visitation map */ |
| 225 |
for (mep = mig_list; mep != NULL; mep = mep->next) |
| 226 |
++nedges; |
| 227 |
emap = (unsigned char *)calloc((nedges*(nedges-1) + 7)>>3, 1); |
| 228 |
if (emap == NULL) { |
| 229 |
fprintf(stderr, "%s: Out of memory in get_interp()\n", |
| 230 |
progname); |
| 231 |
exit(1); |
| 232 |
} |
| 233 |
/* identify intersection */ |
| 234 |
if (!in_mesh(miga, emap, nedges, invec, mig_list)) |
| 235 |
sym = -1; /* outside mesh */ |
| 236 |
else if (miga[1] != NULL && |
| 237 |
(miga[2] == NULL || !order_triangle(miga))) { |
| 238 |
#ifdef DEBUG |
| 239 |
fputs("Munged triangle in get_interp()\n", stderr); |
| 240 |
#endif |
| 241 |
sym = -1; |
| 242 |
} |
| 243 |
free(emap); |
| 244 |
return(sym); /* return in standard order */ |
| 245 |
} |
| 246 |
} |
| 247 |
|
| 248 |
/* Advect and allocate new RBF along edge */ |
| 249 |
static RBFNODE * |
| 250 |
e_advect_rbf(const MIGRATION *mig, const FVECT invec) |
| 251 |
{ |
| 252 |
RBFNODE *rbf; |
| 253 |
int n, i, j; |
| 254 |
double t, full_dist; |
| 255 |
/* get relative position */ |
| 256 |
t = acos(DOT(invec, mig->rbfv[0]->invec)); |
| 257 |
if (t < M_PI/grid_res) { /* near first DSF */ |
| 258 |
n = sizeof(RBFNODE) + sizeof(RBFVAL)*(mig->rbfv[0]->nrbf-1); |
| 259 |
rbf = (RBFNODE *)malloc(n); |
| 260 |
if (rbf == NULL) |
| 261 |
goto memerr; |
| 262 |
memcpy(rbf, mig->rbfv[0], n); /* just duplicate */ |
| 263 |
rbf->next = NULL; rbf->ejl = NULL; |
| 264 |
return(rbf); |
| 265 |
} |
| 266 |
full_dist = acos(DOT(mig->rbfv[0]->invec, mig->rbfv[1]->invec)); |
| 267 |
if (t > full_dist-M_PI/grid_res) { /* near second DSF */ |
| 268 |
n = sizeof(RBFNODE) + sizeof(RBFVAL)*(mig->rbfv[1]->nrbf-1); |
| 269 |
rbf = (RBFNODE *)malloc(n); |
| 270 |
if (rbf == NULL) |
| 271 |
goto memerr; |
| 272 |
memcpy(rbf, mig->rbfv[1], n); /* just duplicate */ |
| 273 |
rbf->next = NULL; rbf->ejl = NULL; |
| 274 |
return(rbf); |
| 275 |
} |
| 276 |
t /= full_dist; |
| 277 |
n = 0; /* count migrating particles */ |
| 278 |
for (i = 0; i < mtx_nrows(mig); i++) |
| 279 |
for (j = 0; j < mtx_ncols(mig); j++) |
| 280 |
n += (mtx_coef(mig,i,j) > FTINY); |
| 281 |
#ifdef DEBUG |
| 282 |
fprintf(stderr, "Input RBFs have %d, %d nodes -> output has %d\n", |
| 283 |
mig->rbfv[0]->nrbf, mig->rbfv[1]->nrbf, n); |
| 284 |
#endif |
| 285 |
rbf = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(n-1)); |
| 286 |
if (rbf == NULL) |
| 287 |
goto memerr; |
| 288 |
rbf->next = NULL; rbf->ejl = NULL; |
| 289 |
VCOPY(rbf->invec, invec); |
| 290 |
rbf->nrbf = n; |
| 291 |
rbf->vtotal = 1.-t + t*mig->rbfv[1]->vtotal/mig->rbfv[0]->vtotal; |
| 292 |
n = 0; /* advect RBF lobes */ |
| 293 |
for (i = 0; i < mtx_nrows(mig); i++) { |
| 294 |
const RBFVAL *rbf0i = &mig->rbfv[0]->rbfa[i]; |
| 295 |
const float peak0 = rbf0i->peak; |
| 296 |
const double rad0 = R2ANG(rbf0i->crad); |
| 297 |
FVECT v0; |
| 298 |
float mv; |
| 299 |
ovec_from_pos(v0, rbf0i->gx, rbf0i->gy); |
| 300 |
for (j = 0; j < mtx_ncols(mig); j++) |
| 301 |
if ((mv = mtx_coef(mig,i,j)) > FTINY) { |
| 302 |
const RBFVAL *rbf1j = &mig->rbfv[1]->rbfa[j]; |
| 303 |
double rad1 = R2ANG(rbf1j->crad); |
| 304 |
FVECT v; |
| 305 |
int pos[2]; |
| 306 |
rbf->rbfa[n].peak = peak0 * mv * rbf->vtotal; |
| 307 |
rbf->rbfa[n].crad = ANG2R(sqrt(rad0*rad0*(1.-t) + |
| 308 |
rad1*rad1*t)); |
| 309 |
ovec_from_pos(v, rbf1j->gx, rbf1j->gy); |
| 310 |
geodesic(v, v0, v, t, GEOD_REL); |
| 311 |
pos_from_vec(pos, v); |
| 312 |
rbf->rbfa[n].gx = pos[0]; |
| 313 |
rbf->rbfa[n].gy = pos[1]; |
| 314 |
++n; |
| 315 |
} |
| 316 |
} |
| 317 |
rbf->vtotal *= mig->rbfv[0]->vtotal; /* turn ratio into actual */ |
| 318 |
return(rbf); |
| 319 |
memerr: |
| 320 |
fprintf(stderr, "%s: Out of memory in e_advect_rbf()\n", progname); |
| 321 |
exit(1); |
| 322 |
return(NULL); /* pro forma return */ |
| 323 |
} |
| 324 |
|
| 325 |
/* Partially advect between recorded incident angles and allocate new RBF */ |
| 326 |
RBFNODE * |
| 327 |
advect_rbf(const FVECT invec) |
| 328 |
{ |
| 329 |
FVECT sivec; |
| 330 |
MIGRATION *miga[3]; |
| 331 |
RBFNODE *rbf; |
| 332 |
int sym; |
| 333 |
float mbfact, mcfact; |
| 334 |
int n, i, j, k; |
| 335 |
FVECT v0, v1, v2; |
| 336 |
double s, t; |
| 337 |
|
| 338 |
VCOPY(sivec, invec); /* find triangle/edge */ |
| 339 |
sym = get_interp(miga, sivec); |
| 340 |
if (sym < 0) /* can't interpolate? */ |
| 341 |
return(NULL); |
| 342 |
if (miga[1] == NULL) { /* advect along edge? */ |
| 343 |
rbf = e_advect_rbf(miga[0], sivec); |
| 344 |
if (single_plane_incident) |
| 345 |
rotate_rbf(rbf, invec); |
| 346 |
else |
| 347 |
rev_rbf_symmetry(rbf, sym); |
| 348 |
return(rbf); |
| 349 |
} |
| 350 |
#ifdef DEBUG |
| 351 |
if (miga[0]->rbfv[0] != miga[2]->rbfv[0] | |
| 352 |
miga[0]->rbfv[1] != miga[1]->rbfv[0] | |
| 353 |
miga[1]->rbfv[1] != miga[2]->rbfv[1]) { |
| 354 |
fprintf(stderr, "%s: Triangle vertex screw-up!\n", progname); |
| 355 |
exit(1); |
| 356 |
} |
| 357 |
#endif |
| 358 |
/* figure out position */ |
| 359 |
fcross(v0, miga[2]->rbfv[0]->invec, miga[2]->rbfv[1]->invec); |
| 360 |
normalize(v0); |
| 361 |
fcross(v2, miga[1]->rbfv[0]->invec, miga[1]->rbfv[1]->invec); |
| 362 |
normalize(v2); |
| 363 |
fcross(v1, sivec, miga[1]->rbfv[1]->invec); |
| 364 |
normalize(v1); |
| 365 |
s = acos(DOT(v0,v1)) / acos(DOT(v0,v2)); |
| 366 |
geodesic(v1, miga[0]->rbfv[0]->invec, miga[0]->rbfv[1]->invec, |
| 367 |
s, GEOD_REL); |
| 368 |
t = acos(DOT(v1,sivec)) / acos(DOT(v1,miga[1]->rbfv[1]->invec)); |
| 369 |
n = 0; /* count migrating particles */ |
| 370 |
for (i = 0; i < mtx_nrows(miga[0]); i++) |
| 371 |
for (j = 0; j < mtx_ncols(miga[0]); j++) |
| 372 |
for (k = (mtx_coef(miga[0],i,j) > FTINY) * |
| 373 |
mtx_ncols(miga[2]); k--; ) |
| 374 |
n += (mtx_coef(miga[2],i,k) > FTINY || |
| 375 |
mtx_coef(miga[1],j,k) > FTINY); |
| 376 |
#ifdef DEBUG |
| 377 |
fprintf(stderr, "Input RBFs have %d, %d, %d nodes -> output has %d\n", |
| 378 |
miga[0]->rbfv[0]->nrbf, miga[0]->rbfv[1]->nrbf, |
| 379 |
miga[2]->rbfv[1]->nrbf, n); |
| 380 |
#endif |
| 381 |
rbf = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(n-1)); |
| 382 |
if (rbf == NULL) { |
| 383 |
fprintf(stderr, "%s: Out of memory in advect_rbf()\n", progname); |
| 384 |
exit(1); |
| 385 |
} |
| 386 |
rbf->next = NULL; rbf->ejl = NULL; |
| 387 |
VCOPY(rbf->invec, sivec); |
| 388 |
rbf->nrbf = n; |
| 389 |
n = 0; /* compute RBF lobes */ |
| 390 |
mbfact = s * miga[0]->rbfv[1]->vtotal/miga[0]->rbfv[0]->vtotal * |
| 391 |
(1.-t + t*miga[1]->rbfv[1]->vtotal/miga[1]->rbfv[0]->vtotal); |
| 392 |
mcfact = (1.-s) * |
| 393 |
(1.-t + t*miga[2]->rbfv[1]->vtotal/miga[2]->rbfv[0]->vtotal); |
| 394 |
for (i = 0; i < mtx_nrows(miga[0]); i++) { |
| 395 |
const RBFVAL *rbf0i = &miga[0]->rbfv[0]->rbfa[i]; |
| 396 |
const float w0i = rbf0i->peak; |
| 397 |
const double rad0i = R2ANG(rbf0i->crad); |
| 398 |
ovec_from_pos(v0, rbf0i->gx, rbf0i->gy); |
| 399 |
for (j = 0; j < mtx_ncols(miga[0]); j++) { |
| 400 |
const float ma = mtx_coef(miga[0],i,j); |
| 401 |
const RBFVAL *rbf1j; |
| 402 |
double rad1j, srad2; |
| 403 |
if (ma <= FTINY) |
| 404 |
continue; |
| 405 |
rbf1j = &miga[0]->rbfv[1]->rbfa[j]; |
| 406 |
rad1j = R2ANG(rbf1j->crad); |
| 407 |
srad2 = (1.-s)*(1.-t)*rad0i*rad0i + s*(1.-t)*rad1j*rad1j; |
| 408 |
ovec_from_pos(v1, rbf1j->gx, rbf1j->gy); |
| 409 |
geodesic(v1, v0, v1, s, GEOD_REL); |
| 410 |
for (k = 0; k < mtx_ncols(miga[2]); k++) { |
| 411 |
float mb = mtx_coef(miga[1],j,k); |
| 412 |
float mc = mtx_coef(miga[2],i,k); |
| 413 |
const RBFVAL *rbf2k; |
| 414 |
double rad2k; |
| 415 |
int pos[2]; |
| 416 |
if ((mb <= FTINY) & (mc <= FTINY)) |
| 417 |
continue; |
| 418 |
rbf2k = &miga[2]->rbfv[1]->rbfa[k]; |
| 419 |
rbf->rbfa[n].peak = w0i * ma * (mb*mbfact + mc*mcfact); |
| 420 |
rad2k = R2ANG(rbf2k->crad); |
| 421 |
rbf->rbfa[n].crad = ANG2R(sqrt(srad2 + t*rad2k*rad2k)); |
| 422 |
ovec_from_pos(v2, rbf2k->gx, rbf2k->gy); |
| 423 |
geodesic(v2, v1, v2, t, GEOD_REL); |
| 424 |
pos_from_vec(pos, v2); |
| 425 |
rbf->rbfa[n].gx = pos[0]; |
| 426 |
rbf->rbfa[n].gy = pos[1]; |
| 427 |
++n; |
| 428 |
} |
| 429 |
} |
| 430 |
} |
| 431 |
rbf->vtotal = miga[0]->rbfv[0]->vtotal * (mbfact + mcfact); |
| 432 |
rev_rbf_symmetry(rbf, sym); |
| 433 |
return(rbf); |
| 434 |
} |
