| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: ambcomp.c,v 2.26 2014/04/16 20:32:00 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 |
* Declarations of external symbols in ambient.h |
| 12 |
*/ |
| 13 |
|
| 14 |
#include "copyright.h" |
| 15 |
|
| 16 |
#include "ray.h" |
| 17 |
#include "ambient.h" |
| 18 |
#include "random.h" |
| 19 |
|
| 20 |
#ifdef NEWAMB |
| 21 |
|
| 22 |
extern void SDsquare2disk(double ds[2], double seedx, double seedy); |
| 23 |
|
| 24 |
typedef struct { |
| 25 |
RAY *rp; /* originating ray sample */ |
| 26 |
FVECT ux, uy; /* tangent axis unit vectors */ |
| 27 |
int ns; /* number of samples per axis */ |
| 28 |
COLOR acoef; /* division contribution coefficient */ |
| 29 |
struct s_ambsamp { |
| 30 |
COLOR v; /* hemisphere sample value */ |
| 31 |
float p[3]; /* intersection point */ |
| 32 |
} sa[1]; /* sample array (extends struct) */ |
| 33 |
} AMBHEMI; /* ambient sample hemisphere */ |
| 34 |
|
| 35 |
#define ambsamp(h,i,j) (h)->sa[(i)*(h)->ns + (j)] |
| 36 |
|
| 37 |
typedef struct { |
| 38 |
FVECT r_i, r_i1, e_i; |
| 39 |
double nf, I1, I2, J2; |
| 40 |
} FFTRI; /* vectors and coefficients for Hessian calculation */ |
| 41 |
|
| 42 |
|
| 43 |
static AMBHEMI * |
| 44 |
inithemi( /* initialize sampling hemisphere */ |
| 45 |
COLOR ac, |
| 46 |
RAY *r, |
| 47 |
double wt |
| 48 |
) |
| 49 |
{ |
| 50 |
AMBHEMI *hp; |
| 51 |
double d; |
| 52 |
int n, i; |
| 53 |
/* set number of divisions */ |
| 54 |
if (ambacc <= FTINY && |
| 55 |
wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
| 56 |
wt = d; /* avoid ray termination */ |
| 57 |
n = sqrt(ambdiv * wt) + 0.5; |
| 58 |
i = 1 + 5*(ambacc > FTINY); /* minimum number of samples */ |
| 59 |
if (n < i) |
| 60 |
n = i; |
| 61 |
/* allocate sampling array */ |
| 62 |
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + |
| 63 |
sizeof(struct s_ambsamp)*(n*n - 1)); |
| 64 |
if (hp == NULL) |
| 65 |
return(NULL); |
| 66 |
hp->rp = r; |
| 67 |
hp->ns = n; |
| 68 |
/* assign coefficient */ |
| 69 |
copycolor(hp->acoef, ac); |
| 70 |
d = 1.0/(n*n); |
| 71 |
scalecolor(hp->acoef, d); |
| 72 |
/* make tangent axes */ |
| 73 |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
| 74 |
for (i = 0; i < 3; i++) |
| 75 |
if (r->ron[i] < 0.6 && r->ron[i] > -0.6) |
| 76 |
break; |
| 77 |
if (i >= 3) |
| 78 |
error(CONSISTENCY, "bad ray direction in inithemi()"); |
| 79 |
hp->uy[i] = 1.0; |
| 80 |
VCROSS(hp->ux, hp->uy, r->ron); |
| 81 |
normalize(hp->ux); |
| 82 |
VCROSS(hp->uy, r->ron, hp->ux); |
| 83 |
/* we're ready to sample */ |
| 84 |
return(hp); |
| 85 |
} |
| 86 |
|
| 87 |
|
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static int |
| 89 |
ambsample( /* sample an ambient direction */ |
| 90 |
AMBHEMI *hp, |
| 91 |
int i, |
| 92 |
int j |
| 93 |
) |
| 94 |
{ |
| 95 |
struct s_ambsamp *ap = &ambsamp(hp,i,j); |
| 96 |
RAY ar; |
| 97 |
int hlist[3]; |
| 98 |
double spt[2], zd; |
| 99 |
int ii; |
| 100 |
/* ambient coefficient for weight */ |
| 101 |
if (ambacc > FTINY) |
| 102 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
| 103 |
else |
| 104 |
copycolor(ar.rcoef, hp->acoef); |
| 105 |
if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0) { |
| 106 |
setcolor(ap->v, 0., 0., 0.); |
| 107 |
VCOPY(ap->p, hp->rp->rop); |
| 108 |
return(0); /* no sample taken */ |
| 109 |
} |
| 110 |
if (ambacc > FTINY) { |
| 111 |
multcolor(ar.rcoef, hp->acoef); |
| 112 |
scalecolor(ar.rcoef, 1./AVGREFL); |
| 113 |
} |
| 114 |
/* generate hemispherical sample */ |
| 115 |
SDsquare2disk(spt, (i+.1+.8*frandom())/hp->ns, |
| 116 |
(j+.1+.8*frandom())/hp->ns); |
| 117 |
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
| 118 |
for (ii = 3; ii--; ) |
| 119 |
ar.rdir[ii] = spt[0]*hp->ux[ii] + |
| 120 |
spt[1]*hp->uy[ii] + |
| 121 |
zd*hp->rp->ron[ii]; |
| 122 |
checknorm(ar.rdir); |
| 123 |
dimlist[ndims++] = i*hp->ns + j + 90171; |
| 124 |
rayvalue(&ar); /* evaluate ray */ |
| 125 |
ndims--; |
| 126 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
| 127 |
copycolor(ap->v, ar.rcol); |
| 128 |
if (ar.rt > 20.0*maxarad) /* limit vertex distance */ |
| 129 |
ar.rt = 20.0*maxarad; |
| 130 |
VSUM(ap->p, ar.rorg, ar.rdir, ar.rt); |
| 131 |
return(1); |
| 132 |
} |
| 133 |
|
| 134 |
|
| 135 |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
| 136 |
static void |
| 137 |
comp_fftri(FFTRI *ftp, float ap0[3], float ap1[3], FVECT rop) |
| 138 |
{ |
| 139 |
FVECT v1; |
| 140 |
double dot_e, dot_er, dot_r, dot_r1; |
| 141 |
|
| 142 |
VSUB(ftp->r_i, ap0, rop); |
| 143 |
VSUB(ftp->r_i1, ap1, rop); |
| 144 |
VSUB(ftp->e_i, ap1, ap0); |
| 145 |
VCROSS(v1, ftp->e_i, ftp->r_i); |
| 146 |
ftp->nf = 1.0/DOT(v1,v1); |
| 147 |
VCROSS(v1, ftp->r_i, ftp->r_i1); |
| 148 |
ftp->I1 = sqrt(DOT(v1,v1)*ftp->nf); |
| 149 |
dot_e = DOT(ftp->e_i,ftp->e_i); |
| 150 |
dot_er = DOT(ftp->e_i, ftp->r_i); |
| 151 |
dot_r = DOT(ftp->r_i,ftp->r_i); |
| 152 |
dot_r1 = DOT(ftp->r_i1,ftp->r_i1); |
| 153 |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)/dot_r1 - dot_er/dot_r + |
| 154 |
dot_e*ftp->I1 )*0.5*ftp->nf; |
| 155 |
ftp->J2 = 0.25*ftp->nf*( 1.0/dot_r - 1.0/dot_r1 ) - |
| 156 |
dot_er/dot_e*ftp->I2; |
| 157 |
} |
| 158 |
|
| 159 |
|
| 160 |
/* Compose matrix from two vectors */ |
| 161 |
static void |
| 162 |
compose_matrix(FVECT mat[3], FVECT va, FVECT vb) |
| 163 |
{ |
| 164 |
mat[0][0] = 2.0*va[0]*vb[0]; |
| 165 |
mat[1][1] = 2.0*va[1]*vb[1]; |
| 166 |
mat[2][2] = 2.0*va[2]*vb[2]; |
| 167 |
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0]; |
| 168 |
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0]; |
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mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1]; |
| 170 |
} |
| 171 |
|
| 172 |
|
| 173 |
/* Compute partial 3x3 Hessian matrix for edge */ |
| 174 |
static void |
| 175 |
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
| 176 |
{ |
| 177 |
FVECT v1, v2; |
| 178 |
FVECT m1[3], m2[3], m3[3], m4[3]; |
| 179 |
double d1, d2, d3, d4; |
| 180 |
double I3, J3, K3; |
| 181 |
int i, j; |
| 182 |
/* compute intermediate coefficients */ |
| 183 |
d1 = 1.0/DOT(ftp->r_i,ftp->r_i); |
| 184 |
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
| 185 |
d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
| 186 |
d4 = DOT(ftp->e_i, ftp->r_i); |
| 187 |
I3 = 0.25*ftp->nf*( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + |
| 188 |
3.0*ftp->I2*d3 ); |
| 189 |
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
| 190 |
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
| 191 |
/* intermediate matrices */ |
| 192 |
VCROSS(v1, nrm, ftp->e_i); |
| 193 |
for (j = 3; j--; ) |
| 194 |
v2[i] = ftp->I2*ftp->r_i[j] + ftp->J2*ftp->e_i[j]; |
| 195 |
compose_matrix(m1, v1, v2); |
| 196 |
compose_matrix(m2, ftp->r_i, ftp->r_i); |
| 197 |
compose_matrix(m3, ftp->e_i, ftp->e_i); |
| 198 |
compose_matrix(m4, ftp->r_i, ftp->e_i); |
| 199 |
VCROSS(v1, ftp->r_i, ftp->e_i); |
| 200 |
d1 = DOT(nrm, v1); |
| 201 |
d2 = -d1*ftp->I2; |
| 202 |
d1 *= 2.0; |
| 203 |
for (i = 3; i--; ) /* final matrix sum */ |
| 204 |
for (j = 3; j--; ) { |
| 205 |
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] + |
| 206 |
2.0*J3*m4[i][j] ); |
| 207 |
hess[i][j] += d2*(i==j); |
| 208 |
hess[i][j] *= -1.0/PI; |
| 209 |
} |
| 210 |
} |
| 211 |
|
| 212 |
|
| 213 |
/* Reverse hessian calculation result for edge in other direction */ |
| 214 |
static void |
| 215 |
rev_hessian(FVECT hess[3]) |
| 216 |
{ |
| 217 |
int i; |
| 218 |
|
| 219 |
for (i = 3; i--; ) { |
| 220 |
hess[i][0] = -hess[i][0]; |
| 221 |
hess[i][1] = -hess[i][1]; |
| 222 |
hess[i][2] = -hess[i][2]; |
| 223 |
} |
| 224 |
} |
| 225 |
|
| 226 |
|
| 227 |
/* Add to radiometric Hessian from the given triangle */ |
| 228 |
static void |
| 229 |
add2hessian(FVECT hess[3], FVECT ehess1[3], |
| 230 |
FVECT ehess2[3], FVECT ehess3[3], COLORV v) |
| 231 |
{ |
| 232 |
int i, j; |
| 233 |
|
| 234 |
for (i = 3; i--; ) |
| 235 |
for (j = 3; j--; ) |
| 236 |
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] ); |
| 237 |
} |
| 238 |
|
| 239 |
|
| 240 |
/* Compute partial displacement form factor gradient for edge */ |
| 241 |
static void |
| 242 |
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
| 243 |
{ |
| 244 |
FVECT vcp; |
| 245 |
double f1; |
| 246 |
int i; |
| 247 |
|
| 248 |
VCROSS(vcp, ftp->r_i, ftp->r_i1); |
| 249 |
f1 = 2.0*DOT(nrm, vcp); |
| 250 |
VCROSS(vcp, nrm, ftp->e_i); |
| 251 |
for (i = 3; i--; ) |
| 252 |
grad[i] = (0.5/PI)*( ftp->I1*vcp[i] + |
| 253 |
f1*(ftp->I2*ftp->r_i[i] + ftp->J2*ftp->e_i[i]) ); |
| 254 |
} |
| 255 |
|
| 256 |
|
| 257 |
/* Reverse gradient calculation result for edge in other direction */ |
| 258 |
static void |
| 259 |
rev_gradient(FVECT grad) |
| 260 |
{ |
| 261 |
grad[0] = -grad[0]; |
| 262 |
grad[1] = -grad[1]; |
| 263 |
grad[2] = -grad[2]; |
| 264 |
} |
| 265 |
|
| 266 |
|
| 267 |
/* Add to displacement gradient from the given triangle */ |
| 268 |
static void |
| 269 |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, COLORV v) |
| 270 |
{ |
| 271 |
int i; |
| 272 |
|
| 273 |
for (i = 3; i--; ) |
| 274 |
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] ); |
| 275 |
} |
| 276 |
|
| 277 |
|
| 278 |
/* Return brightness of furthest ambient sample */ |
| 279 |
static COLORV |
| 280 |
back_ambval(struct s_ambsamp *ap1, struct s_ambsamp *ap2, |
| 281 |
struct s_ambsamp *ap3, FVECT orig) |
| 282 |
{ |
| 283 |
COLORV vback; |
| 284 |
FVECT vec; |
| 285 |
double d2, d2best; |
| 286 |
|
| 287 |
VSUB(vec, ap1->p, orig); |
| 288 |
d2best = DOT(vec,vec); |
| 289 |
vback = ap1->v[CIEY]; |
| 290 |
VSUB(vec, ap2->p, orig); |
| 291 |
d2 = DOT(vec,vec); |
| 292 |
if (d2 > d2best) { |
| 293 |
d2best = d2; |
| 294 |
vback = ap2->v[CIEY]; |
| 295 |
} |
| 296 |
VSUB(vec, ap3->p, orig); |
| 297 |
d2 = DOT(vec,vec); |
| 298 |
if (d2 > d2best) |
| 299 |
return(ap3->v[CIEY]); |
| 300 |
return(vback); |
| 301 |
} |
| 302 |
|
| 303 |
|
| 304 |
/* Compute anisotropic radii and eigenvector directions */ |
| 305 |
static int |
| 306 |
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3]) |
| 307 |
{ |
| 308 |
double hess2[2][2]; |
| 309 |
FVECT a, b; |
| 310 |
double evalue[2], slope1, xmag1; |
| 311 |
int i; |
| 312 |
/* project Hessian to sample plane */ |
| 313 |
for (i = 3; i--; ) { |
| 314 |
a[i] = DOT(hessian[i], uv[0]); |
| 315 |
b[i] = DOT(hessian[i], uv[1]); |
| 316 |
} |
| 317 |
hess2[0][0] = DOT(uv[0], a); |
| 318 |
hess2[0][1] = DOT(uv[0], b); |
| 319 |
hess2[1][0] = DOT(uv[1], a); |
| 320 |
hess2[1][1] = DOT(uv[1], b); |
| 321 |
/* compute eigenvalues */ |
| 322 |
if (quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
| 323 |
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]) != 2 || |
| 324 |
(evalue[0] = fabs(evalue[0])) <= FTINY*FTINY*FTINY || |
| 325 |
(evalue[1] = fabs(evalue[1])) <= FTINY*FTINY*FTINY) |
| 326 |
error(INTERNAL, "bad eigenvalue calculation"); |
| 327 |
|
| 328 |
if (evalue[0] > evalue[1]) { |
| 329 |
ra[0] = 1.0/sqrt(sqrt(evalue[0])); |
| 330 |
ra[1] = 1.0/sqrt(sqrt(evalue[1])); |
| 331 |
slope1 = evalue[1]; |
| 332 |
} else { |
| 333 |
ra[0] = 1.0/sqrt(sqrt(evalue[1])); |
| 334 |
ra[1] = 1.0/sqrt(sqrt(evalue[0])); |
| 335 |
slope1 = evalue[0]; |
| 336 |
} |
| 337 |
/* compute unit eigenvectors */ |
| 338 |
if (fabs(hess2[0][1]) <= FTINY) |
| 339 |
return; /* uv OK as is */ |
| 340 |
slope1 = (slope1 - hess2[0][0]) / hess2[0][1]; |
| 341 |
xmag1 = sqrt(1.0/(1.0 + slope1*slope1)); |
| 342 |
for (i = 3; i--; ) { |
| 343 |
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i]; |
| 344 |
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i]; |
| 345 |
} |
| 346 |
VCOPY(uv[0], a); |
| 347 |
VCOPY(uv[1], b); |
| 348 |
} |
| 349 |
|
| 350 |
|
| 351 |
static void |
| 352 |
ambHessian( /* anisotropic radii & pos. gradient */ |
| 353 |
AMBHEMI *hp, |
| 354 |
FVECT uv[2], /* returned */ |
| 355 |
float ra[2], /* returned */ |
| 356 |
float pg[2] /* returned */ |
| 357 |
) |
| 358 |
{ |
| 359 |
static char memerrmsg[] = "out of memory in ambHessian()"; |
| 360 |
FVECT (*hessrow)[3] = NULL; |
| 361 |
FVECT *gradrow = NULL; |
| 362 |
FVECT hessian[3]; |
| 363 |
FVECT gradient; |
| 364 |
FFTRI fftr; |
| 365 |
int i, j; |
| 366 |
/* be sure to assign unit vectors */ |
| 367 |
VCOPY(uv[0], hp->ux); |
| 368 |
VCOPY(uv[1], hp->uy); |
| 369 |
/* clock-wise vertex traversal from sample POV */ |
| 370 |
if (ra != NULL) { /* initialize Hessian row buffer */ |
| 371 |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*hp->ns); |
| 372 |
if (hessrow == NULL) |
| 373 |
error(SYSTEM, memerrmsg); |
| 374 |
memset(hessian, 0, sizeof(hessian)); |
| 375 |
} else if (pg == NULL) /* bogus call? */ |
| 376 |
return; |
| 377 |
if (pg != NULL) { /* initialize form factor row buffer */ |
| 378 |
gradrow = (FVECT *)malloc(sizeof(FVECT)*hp->ns); |
| 379 |
if (gradrow == NULL) |
| 380 |
error(SYSTEM, memerrmsg); |
| 381 |
memset(gradient, 0, sizeof(gradient)); |
| 382 |
} |
| 383 |
/* compute first row of edges */ |
| 384 |
for (j = 0; j < hp->ns-1; j++) { |
| 385 |
comp_fftri(&fftr, ambsamp(hp,0,j).p, |
| 386 |
ambsamp(hp,0,j+1).p, hp->rp->rop); |
| 387 |
if (hessrow != NULL) |
| 388 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
| 389 |
if (gradrow != NULL) |
| 390 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
| 391 |
} |
| 392 |
/* sum each row of triangles */ |
| 393 |
for (i = 0; i < hp->ns-1; i++) { |
| 394 |
FVECT hesscol[3]; /* compute first vertical edge */ |
| 395 |
FVECT gradcol; |
| 396 |
comp_fftri(&fftr, ambsamp(hp,i,0).p, |
| 397 |
ambsamp(hp,i+1,0).p, hp->rp->rop); |
| 398 |
if (hessrow != NULL) |
| 399 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
| 400 |
if (gradrow != NULL) |
| 401 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
| 402 |
for (j = 0; j < hp->ns-1; j++) { |
| 403 |
FVECT hessdia[3]; /* compute triangle contributions */ |
| 404 |
FVECT graddia; |
| 405 |
COLORV backg; |
| 406 |
backg = back_ambval(&ambsamp(hp,i,j), &ambsamp(hp,i,j+1), |
| 407 |
&ambsamp(hp,i+1,j), hp->rp->rop); |
| 408 |
/* diagonal (inner) edge */ |
| 409 |
comp_fftri(&fftr, ambsamp(hp,i,j+1).p, |
| 410 |
ambsamp(hp,i+1,j).p, hp->rp->rop); |
| 411 |
if (hessrow != NULL) { |
| 412 |
comp_hessian(hessdia, &fftr, hp->rp->ron); |
| 413 |
rev_hessian(hesscol); |
| 414 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 415 |
} |
| 416 |
if (gradient != NULL) { |
| 417 |
comp_gradient(graddia, &fftr, hp->rp->ron); |
| 418 |
rev_gradient(gradcol); |
| 419 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 420 |
} |
| 421 |
/* initialize edge in next row */ |
| 422 |
comp_fftri(&fftr, ambsamp(hp,i+1,j+1).p, |
| 423 |
ambsamp(hp,i+1,j).p, hp->rp->rop); |
| 424 |
if (hessrow != NULL) |
| 425 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
| 426 |
if (gradrow != NULL) |
| 427 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
| 428 |
/* new column edge & paired triangle */ |
| 429 |
backg = back_ambval(&ambsamp(hp,i,j+1), &ambsamp(hp,i+1,j+1), |
| 430 |
&ambsamp(hp,i+1,j), hp->rp->rop); |
| 431 |
comp_fftri(&fftr, ambsamp(hp,i,j+1).p, ambsamp(hp,i+1,j+1).p, |
| 432 |
hp->rp->rop); |
| 433 |
if (hessrow != NULL) { |
| 434 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
| 435 |
rev_hessian(hessdia); |
| 436 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 437 |
if (i < hp->ns-2) |
| 438 |
rev_hessian(hessrow[j]); |
| 439 |
} |
| 440 |
if (gradrow != NULL) { |
| 441 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
| 442 |
rev_gradient(graddia); |
| 443 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 444 |
if (i < hp->ns-2) |
| 445 |
rev_gradient(gradrow[j]); |
| 446 |
} |
| 447 |
} |
| 448 |
} |
| 449 |
/* release row buffers */ |
| 450 |
if (hessrow != NULL) free(hessrow); |
| 451 |
if (gradrow != NULL) free(gradrow); |
| 452 |
|
| 453 |
if (ra != NULL) /* extract eigenvectors & radii */ |
| 454 |
eigenvectors(uv, ra, hessian); |
| 455 |
if (pg != NULL) { /* project position gradient */ |
| 456 |
pg[0] = DOT(gradient, uv[0]); |
| 457 |
pg[1] = DOT(gradient, uv[1]); |
| 458 |
} |
| 459 |
} |
| 460 |
|
| 461 |
|
| 462 |
/* Compute direction gradient from a hemispherical sampling */ |
| 463 |
static void |
| 464 |
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2]) |
| 465 |
{ |
| 466 |
struct s_ambsamp *ap; |
| 467 |
int n; |
| 468 |
|
| 469 |
dg[0] = dg[1] = 0; |
| 470 |
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) { |
| 471 |
FVECT vd; |
| 472 |
double gfact; |
| 473 |
/* use vector for azimuth + 90deg */ |
| 474 |
VSUB(vd, ap->p, hp->rp->rop); |
| 475 |
/* brightness with tangent factor */ |
| 476 |
gfact = ap->v[CIEY] / DOT(hp->rp->ron, vd); |
| 477 |
/* sine = proj_radius/vd_length */ |
| 478 |
dg[0] -= DOT(uv[1], vd) * gfact ; |
| 479 |
dg[1] += DOT(uv[0], vd) * gfact; |
| 480 |
} |
| 481 |
} |
| 482 |
|
| 483 |
|
| 484 |
int |
| 485 |
doambient( /* compute ambient component */ |
| 486 |
COLOR rcol, /* input/output color */ |
| 487 |
RAY *r, |
| 488 |
double wt, |
| 489 |
FVECT uv[2], /* returned (optional) */ |
| 490 |
float ra[2], /* returned (optional) */ |
| 491 |
float pg[2], /* returned (optional) */ |
| 492 |
float dg[2] /* returned (optional) */ |
| 493 |
) |
| 494 |
{ |
| 495 |
int cnt = 0; |
| 496 |
FVECT my_uv[2]; |
| 497 |
AMBHEMI *hp; |
| 498 |
double d, acol[3]; |
| 499 |
struct s_ambsamp *ap; |
| 500 |
int i, j; |
| 501 |
/* initialize */ |
| 502 |
if ((hp = inithemi(rcol, r, wt)) == NULL) |
| 503 |
return(0); |
| 504 |
if (uv != NULL) |
| 505 |
memset(uv, 0, sizeof(FVECT)*2); |
| 506 |
if (ra != NULL) |
| 507 |
ra[0] = ra[1] = 0.0; |
| 508 |
if (pg != NULL) |
| 509 |
pg[0] = pg[1] = 0.0; |
| 510 |
if (dg != NULL) |
| 511 |
dg[0] = dg[1] = 0.0; |
| 512 |
/* sample the hemisphere */ |
| 513 |
acol[0] = acol[1] = acol[2] = 0.0; |
| 514 |
for (i = hp->ns; i--; ) |
| 515 |
for (j = hp->ns; j--; ) |
| 516 |
if (ambsample(hp, i, j)) { |
| 517 |
ap = &ambsamp(hp,i,j); |
| 518 |
addcolor(acol, ap->v); |
| 519 |
++cnt; |
| 520 |
} |
| 521 |
if (!cnt) { |
| 522 |
setcolor(rcol, 0.0, 0.0, 0.0); |
| 523 |
free(hp); |
| 524 |
return(0); /* no valid samples */ |
| 525 |
} |
| 526 |
d = 1.0 / cnt; /* final indirect irradiance/PI */ |
| 527 |
acol[0] *= d; acol[1] *= d; acol[2] *= d; |
| 528 |
copycolor(rcol, acol); |
| 529 |
if (cnt < hp->ns*hp->ns || /* incomplete sampling? */ |
| 530 |
(ra == NULL) & (pg == NULL) & (dg == NULL)) { |
| 531 |
free(hp); |
| 532 |
return(-1); /* no radius or gradient calc. */ |
| 533 |
} |
| 534 |
d = 0.01 * bright(rcol); /* add in 1% before Hessian comp. */ |
| 535 |
if (d < FTINY) d = FTINY; |
| 536 |
ap = hp->sa; /* using Y channel from here on... */ |
| 537 |
for (i = hp->ns*hp->ns; i--; ap++) |
| 538 |
colval(ap->v,CIEY) = bright(ap->v) + d; |
| 539 |
|
| 540 |
if (uv == NULL) /* make sure we have axis pointers */ |
| 541 |
uv = my_uv; |
| 542 |
/* compute radii & pos. gradient */ |
| 543 |
ambHessian(hp, uv, ra, pg); |
| 544 |
if (dg != NULL) /* compute direction gradient */ |
| 545 |
ambdirgrad(hp, uv, dg); |
| 546 |
if (ra != NULL) { /* adjust/clamp radii */ |
| 547 |
d = sqrt(sqrt((4.0/PI)*bright(rcol)/wt)); |
| 548 |
if ((ra[0] *= d) > maxarad) |
| 549 |
ra[0] = maxarad; |
| 550 |
if ((ra[1] *= d) > 2.0*ra[0]) |
| 551 |
ra[1] = 2.0*ra[0]; |
| 552 |
} |
| 553 |
free(hp); /* clean up and return */ |
| 554 |
return(1); |
| 555 |
} |
| 556 |
|
| 557 |
|
| 558 |
#else /* ! NEWAMB */ |
| 559 |
|
| 560 |
|
| 561 |
void |
| 562 |
inithemi( /* initialize sampling hemisphere */ |
| 563 |
AMBHEMI *hp, |
| 564 |
COLOR ac, |
| 565 |
RAY *r, |
| 566 |
double wt |
| 567 |
) |
| 568 |
{ |
| 569 |
double d; |
| 570 |
int i; |
| 571 |
/* set number of divisions */ |
| 572 |
if (ambacc <= FTINY && |
| 573 |
wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
| 574 |
wt = d; /* avoid ray termination */ |
| 575 |
hp->nt = sqrt(ambdiv * wt / PI) + 0.5; |
| 576 |
i = ambacc > FTINY ? 3 : 1; /* minimum number of samples */ |
| 577 |
if (hp->nt < i) |
| 578 |
hp->nt = i; |
| 579 |
hp->np = PI * hp->nt + 0.5; |
| 580 |
/* set number of super-samples */ |
| 581 |
hp->ns = ambssamp * wt + 0.5; |
| 582 |
/* assign coefficient */ |
| 583 |
copycolor(hp->acoef, ac); |
| 584 |
d = 1.0/(hp->nt*hp->np); |
| 585 |
scalecolor(hp->acoef, d); |
| 586 |
/* make axes */ |
| 587 |
VCOPY(hp->uz, r->ron); |
| 588 |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
| 589 |
for (i = 0; i < 3; i++) |
| 590 |
if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6) |
| 591 |
break; |
| 592 |
if (i >= 3) |
| 593 |
error(CONSISTENCY, "bad ray direction in inithemi"); |
| 594 |
hp->uy[i] = 1.0; |
| 595 |
fcross(hp->ux, hp->uy, hp->uz); |
| 596 |
normalize(hp->ux); |
| 597 |
fcross(hp->uy, hp->uz, hp->ux); |
| 598 |
} |
| 599 |
|
| 600 |
|
| 601 |
int |
| 602 |
divsample( /* sample a division */ |
| 603 |
AMBSAMP *dp, |
| 604 |
AMBHEMI *h, |
| 605 |
RAY *r |
| 606 |
) |
| 607 |
{ |
| 608 |
RAY ar; |
| 609 |
int hlist[3]; |
| 610 |
double spt[2]; |
| 611 |
double xd, yd, zd; |
| 612 |
double b2; |
| 613 |
double phi; |
| 614 |
int i; |
| 615 |
/* ambient coefficient for weight */ |
| 616 |
if (ambacc > FTINY) |
| 617 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
| 618 |
else |
| 619 |
copycolor(ar.rcoef, h->acoef); |
| 620 |
if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0) |
| 621 |
return(-1); |
| 622 |
if (ambacc > FTINY) { |
| 623 |
multcolor(ar.rcoef, h->acoef); |
| 624 |
scalecolor(ar.rcoef, 1./AVGREFL); |
| 625 |
} |
| 626 |
hlist[0] = r->rno; |
| 627 |
hlist[1] = dp->t; |
| 628 |
hlist[2] = dp->p; |
| 629 |
multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n)); |
| 630 |
zd = sqrt((dp->t + spt[0])/h->nt); |
| 631 |
phi = 2.0*PI * (dp->p + spt[1])/h->np; |
| 632 |
xd = tcos(phi) * zd; |
| 633 |
yd = tsin(phi) * zd; |
| 634 |
zd = sqrt(1.0 - zd*zd); |
| 635 |
for (i = 0; i < 3; i++) |
| 636 |
ar.rdir[i] = xd*h->ux[i] + |
| 637 |
yd*h->uy[i] + |
| 638 |
zd*h->uz[i]; |
| 639 |
checknorm(ar.rdir); |
| 640 |
dimlist[ndims++] = dp->t*h->np + dp->p + 90171; |
| 641 |
rayvalue(&ar); |
| 642 |
ndims--; |
| 643 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
| 644 |
addcolor(dp->v, ar.rcol); |
| 645 |
/* use rt to improve gradient calc */ |
| 646 |
if (ar.rt > FTINY && ar.rt < FHUGE) |
| 647 |
dp->r += 1.0/ar.rt; |
| 648 |
/* (re)initialize error */ |
| 649 |
if (dp->n++) { |
| 650 |
b2 = bright(dp->v)/dp->n - bright(ar.rcol); |
| 651 |
b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1)); |
| 652 |
dp->k = b2/(dp->n*dp->n); |
| 653 |
} else |
| 654 |
dp->k = 0.0; |
| 655 |
return(0); |
| 656 |
} |
| 657 |
|
| 658 |
|
| 659 |
static int |
| 660 |
ambcmp( /* decreasing order */ |
| 661 |
const void *p1, |
| 662 |
const void *p2 |
| 663 |
) |
| 664 |
{ |
| 665 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
| 666 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
| 667 |
|
| 668 |
if (d1->k < d2->k) |
| 669 |
return(1); |
| 670 |
if (d1->k > d2->k) |
| 671 |
return(-1); |
| 672 |
return(0); |
| 673 |
} |
| 674 |
|
| 675 |
|
| 676 |
static int |
| 677 |
ambnorm( /* standard order */ |
| 678 |
const void *p1, |
| 679 |
const void *p2 |
| 680 |
) |
| 681 |
{ |
| 682 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
| 683 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
| 684 |
int c; |
| 685 |
|
| 686 |
if ( (c = d1->t - d2->t) ) |
| 687 |
return(c); |
| 688 |
return(d1->p - d2->p); |
| 689 |
} |
| 690 |
|
| 691 |
|
| 692 |
double |
| 693 |
doambient( /* compute ambient component */ |
| 694 |
COLOR rcol, |
| 695 |
RAY *r, |
| 696 |
double wt, |
| 697 |
FVECT pg, |
| 698 |
FVECT dg |
| 699 |
) |
| 700 |
{ |
| 701 |
double b, d=0; |
| 702 |
AMBHEMI hemi; |
| 703 |
AMBSAMP *div; |
| 704 |
AMBSAMP dnew; |
| 705 |
double acol[3]; |
| 706 |
AMBSAMP *dp; |
| 707 |
double arad; |
| 708 |
int divcnt; |
| 709 |
int i, j; |
| 710 |
/* initialize hemisphere */ |
| 711 |
inithemi(&hemi, rcol, r, wt); |
| 712 |
divcnt = hemi.nt * hemi.np; |
| 713 |
/* initialize */ |
| 714 |
if (pg != NULL) |
| 715 |
pg[0] = pg[1] = pg[2] = 0.0; |
| 716 |
if (dg != NULL) |
| 717 |
dg[0] = dg[1] = dg[2] = 0.0; |
| 718 |
setcolor(rcol, 0.0, 0.0, 0.0); |
| 719 |
if (divcnt == 0) |
| 720 |
return(0.0); |
| 721 |
/* allocate super-samples */ |
| 722 |
if (hemi.ns > 0 || pg != NULL || dg != NULL) { |
| 723 |
div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP)); |
| 724 |
if (div == NULL) |
| 725 |
error(SYSTEM, "out of memory in doambient"); |
| 726 |
} else |
| 727 |
div = NULL; |
| 728 |
/* sample the divisions */ |
| 729 |
arad = 0.0; |
| 730 |
acol[0] = acol[1] = acol[2] = 0.0; |
| 731 |
if ((dp = div) == NULL) |
| 732 |
dp = &dnew; |
| 733 |
divcnt = 0; |
| 734 |
for (i = 0; i < hemi.nt; i++) |
| 735 |
for (j = 0; j < hemi.np; j++) { |
| 736 |
dp->t = i; dp->p = j; |
| 737 |
setcolor(dp->v, 0.0, 0.0, 0.0); |
| 738 |
dp->r = 0.0; |
| 739 |
dp->n = 0; |
| 740 |
if (divsample(dp, &hemi, r) < 0) { |
| 741 |
if (div != NULL) |
| 742 |
dp++; |
| 743 |
continue; |
| 744 |
} |
| 745 |
arad += dp->r; |
| 746 |
divcnt++; |
| 747 |
if (div != NULL) |
| 748 |
dp++; |
| 749 |
else |
| 750 |
addcolor(acol, dp->v); |
| 751 |
} |
| 752 |
if (!divcnt) { |
| 753 |
if (div != NULL) |
| 754 |
free((void *)div); |
| 755 |
return(0.0); /* no samples taken */ |
| 756 |
} |
| 757 |
if (divcnt < hemi.nt*hemi.np) { |
| 758 |
pg = dg = NULL; /* incomplete sampling */ |
| 759 |
hemi.ns = 0; |
| 760 |
} else if (arad > FTINY && divcnt/arad < minarad) { |
| 761 |
hemi.ns = 0; /* close enough */ |
| 762 |
} else if (hemi.ns > 0) { /* else perform super-sampling? */ |
| 763 |
comperrs(div, &hemi); /* compute errors */ |
| 764 |
qsort(div, divcnt, sizeof(AMBSAMP), ambcmp); /* sort divs */ |
| 765 |
/* super-sample */ |
| 766 |
for (i = hemi.ns; i > 0; i--) { |
| 767 |
dnew = *div; |
| 768 |
if (divsample(&dnew, &hemi, r) < 0) { |
| 769 |
dp++; |
| 770 |
continue; |
| 771 |
} |
| 772 |
dp = div; /* reinsert */ |
| 773 |
j = divcnt < i ? divcnt : i; |
| 774 |
while (--j > 0 && dnew.k < dp[1].k) { |
| 775 |
*dp = *(dp+1); |
| 776 |
dp++; |
| 777 |
} |
| 778 |
*dp = dnew; |
| 779 |
} |
| 780 |
if (pg != NULL || dg != NULL) /* restore order */ |
| 781 |
qsort(div, divcnt, sizeof(AMBSAMP), ambnorm); |
| 782 |
} |
| 783 |
/* compute returned values */ |
| 784 |
if (div != NULL) { |
| 785 |
arad = 0.0; /* note: divcnt may be < nt*np */ |
| 786 |
for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) { |
| 787 |
arad += dp->r; |
| 788 |
if (dp->n > 1) { |
| 789 |
b = 1.0/dp->n; |
| 790 |
scalecolor(dp->v, b); |
| 791 |
dp->r *= b; |
| 792 |
dp->n = 1; |
| 793 |
} |
| 794 |
addcolor(acol, dp->v); |
| 795 |
} |
| 796 |
b = bright(acol); |
| 797 |
if (b > FTINY) { |
| 798 |
b = 1.0/b; /* compute & normalize gradient(s) */ |
| 799 |
if (pg != NULL) { |
| 800 |
posgradient(pg, div, &hemi); |
| 801 |
for (i = 0; i < 3; i++) |
| 802 |
pg[i] *= b; |
| 803 |
} |
| 804 |
if (dg != NULL) { |
| 805 |
dirgradient(dg, div, &hemi); |
| 806 |
for (i = 0; i < 3; i++) |
| 807 |
dg[i] *= b; |
| 808 |
} |
| 809 |
} |
| 810 |
free((void *)div); |
| 811 |
} |
| 812 |
copycolor(rcol, acol); |
| 813 |
if (arad <= FTINY) |
| 814 |
arad = maxarad; |
| 815 |
else |
| 816 |
arad = (divcnt+hemi.ns)/arad; |
| 817 |
if (pg != NULL) { /* reduce radius if gradient large */ |
| 818 |
d = DOT(pg,pg); |
| 819 |
if (d*arad*arad > 1.0) |
| 820 |
arad = 1.0/sqrt(d); |
| 821 |
} |
| 822 |
if (arad < minarad) { |
| 823 |
arad = minarad; |
| 824 |
if (pg != NULL && d*arad*arad > 1.0) { /* cap gradient */ |
| 825 |
d = 1.0/arad/sqrt(d); |
| 826 |
for (i = 0; i < 3; i++) |
| 827 |
pg[i] *= d; |
| 828 |
} |
| 829 |
} |
| 830 |
if ((arad /= sqrt(wt)) > maxarad) |
| 831 |
arad = maxarad; |
| 832 |
return(arad); |
| 833 |
} |
| 834 |
|
| 835 |
|
| 836 |
void |
| 837 |
comperrs( /* compute initial error estimates */ |
| 838 |
AMBSAMP *da, /* assumes standard ordering */ |
| 839 |
AMBHEMI *hp |
| 840 |
) |
| 841 |
{ |
| 842 |
double b, b2; |
| 843 |
int i, j; |
| 844 |
AMBSAMP *dp; |
| 845 |
/* sum differences from neighbors */ |
| 846 |
dp = da; |
| 847 |
for (i = 0; i < hp->nt; i++) |
| 848 |
for (j = 0; j < hp->np; j++) { |
| 849 |
#ifdef DEBUG |
| 850 |
if (dp->t != i || dp->p != j) |
| 851 |
error(CONSISTENCY, |
| 852 |
"division order in comperrs"); |
| 853 |
#endif |
| 854 |
b = bright(dp[0].v); |
| 855 |
if (i > 0) { /* from above */ |
| 856 |
b2 = bright(dp[-hp->np].v) - b; |
| 857 |
b2 *= b2 * 0.25; |
| 858 |
dp[0].k += b2; |
| 859 |
dp[-hp->np].k += b2; |
| 860 |
} |
| 861 |
if (j > 0) { /* from behind */ |
| 862 |
b2 = bright(dp[-1].v) - b; |
| 863 |
b2 *= b2 * 0.25; |
| 864 |
dp[0].k += b2; |
| 865 |
dp[-1].k += b2; |
| 866 |
} else { /* around */ |
| 867 |
b2 = bright(dp[hp->np-1].v) - b; |
| 868 |
b2 *= b2 * 0.25; |
| 869 |
dp[0].k += b2; |
| 870 |
dp[hp->np-1].k += b2; |
| 871 |
} |
| 872 |
dp++; |
| 873 |
} |
| 874 |
/* divide by number of neighbors */ |
| 875 |
dp = da; |
| 876 |
for (j = 0; j < hp->np; j++) /* top row */ |
| 877 |
(dp++)->k *= 1.0/3.0; |
| 878 |
if (hp->nt < 2) |
| 879 |
return; |
| 880 |
for (i = 1; i < hp->nt-1; i++) /* central region */ |
| 881 |
for (j = 0; j < hp->np; j++) |
| 882 |
(dp++)->k *= 0.25; |
| 883 |
for (j = 0; j < hp->np; j++) /* bottom row */ |
| 884 |
(dp++)->k *= 1.0/3.0; |
| 885 |
} |
| 886 |
|
| 887 |
|
| 888 |
void |
| 889 |
posgradient( /* compute position gradient */ |
| 890 |
FVECT gv, |
| 891 |
AMBSAMP *da, /* assumes standard ordering */ |
| 892 |
AMBHEMI *hp |
| 893 |
) |
| 894 |
{ |
| 895 |
int i, j; |
| 896 |
double nextsine, lastsine, b, d; |
| 897 |
double mag0, mag1; |
| 898 |
double phi, cosp, sinp, xd, yd; |
| 899 |
AMBSAMP *dp; |
| 900 |
|
| 901 |
xd = yd = 0.0; |
| 902 |
for (j = 0; j < hp->np; j++) { |
| 903 |
dp = da + j; |
| 904 |
mag0 = mag1 = 0.0; |
| 905 |
lastsine = 0.0; |
| 906 |
for (i = 0; i < hp->nt; i++) { |
| 907 |
#ifdef DEBUG |
| 908 |
if (dp->t != i || dp->p != j) |
| 909 |
error(CONSISTENCY, |
| 910 |
"division order in posgradient"); |
| 911 |
#endif |
| 912 |
b = bright(dp->v); |
| 913 |
if (i > 0) { |
| 914 |
d = dp[-hp->np].r; |
| 915 |
if (dp[0].r > d) d = dp[0].r; |
| 916 |
/* sin(t)*cos(t)^2 */ |
| 917 |
d *= lastsine * (1.0 - (double)i/hp->nt); |
| 918 |
mag0 += d*(b - bright(dp[-hp->np].v)); |
| 919 |
} |
| 920 |
nextsine = sqrt((double)(i+1)/hp->nt); |
| 921 |
if (j > 0) { |
| 922 |
d = dp[-1].r; |
| 923 |
if (dp[0].r > d) d = dp[0].r; |
| 924 |
mag1 += d * (nextsine - lastsine) * |
| 925 |
(b - bright(dp[-1].v)); |
| 926 |
} else { |
| 927 |
d = dp[hp->np-1].r; |
| 928 |
if (dp[0].r > d) d = dp[0].r; |
| 929 |
mag1 += d * (nextsine - lastsine) * |
| 930 |
(b - bright(dp[hp->np-1].v)); |
| 931 |
} |
| 932 |
dp += hp->np; |
| 933 |
lastsine = nextsine; |
| 934 |
} |
| 935 |
mag0 *= 2.0*PI / hp->np; |
| 936 |
phi = 2.0*PI * (double)j/hp->np; |
| 937 |
cosp = tcos(phi); sinp = tsin(phi); |
| 938 |
xd += mag0*cosp - mag1*sinp; |
| 939 |
yd += mag0*sinp + mag1*cosp; |
| 940 |
} |
| 941 |
for (i = 0; i < 3; i++) |
| 942 |
gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI; |
| 943 |
} |
| 944 |
|
| 945 |
|
| 946 |
void |
| 947 |
dirgradient( /* compute direction gradient */ |
| 948 |
FVECT gv, |
| 949 |
AMBSAMP *da, /* assumes standard ordering */ |
| 950 |
AMBHEMI *hp |
| 951 |
) |
| 952 |
{ |
| 953 |
int i, j; |
| 954 |
double mag; |
| 955 |
double phi, xd, yd; |
| 956 |
AMBSAMP *dp; |
| 957 |
|
| 958 |
xd = yd = 0.0; |
| 959 |
for (j = 0; j < hp->np; j++) { |
| 960 |
dp = da + j; |
| 961 |
mag = 0.0; |
| 962 |
for (i = 0; i < hp->nt; i++) { |
| 963 |
#ifdef DEBUG |
| 964 |
if (dp->t != i || dp->p != j) |
| 965 |
error(CONSISTENCY, |
| 966 |
"division order in dirgradient"); |
| 967 |
#endif |
| 968 |
/* tan(t) */ |
| 969 |
mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0); |
| 970 |
dp += hp->np; |
| 971 |
} |
| 972 |
phi = 2.0*PI * (j+.5)/hp->np + PI/2.0; |
| 973 |
xd += mag * tcos(phi); |
| 974 |
yd += mag * tsin(phi); |
| 975 |
} |
| 976 |
for (i = 0; i < 3; i++) |
| 977 |
gv[i] = xd*hp->ux[i] + yd*hp->uy[i]; |
| 978 |
} |
| 979 |
|
| 980 |
#endif /* ! NEWAMB */ |
