| 1 |
/* Copyright (c) 1986 Regents of the University of California */ |
| 2 |
|
| 3 |
#ifndef lint |
| 4 |
static char SCCSid[] = "$SunId$ LBL"; |
| 5 |
#endif |
| 6 |
|
| 7 |
/* |
| 8 |
* dielectric.c - shading function for transparent materials. |
| 9 |
* |
| 10 |
* 9/6/85 |
| 11 |
*/ |
| 12 |
|
| 13 |
#include "ray.h" |
| 14 |
|
| 15 |
#include "otypes.h" |
| 16 |
|
| 17 |
#ifdef DISPERSE |
| 18 |
#include "source.h" |
| 19 |
static disperse(); |
| 20 |
static int lambda(); |
| 21 |
#endif |
| 22 |
|
| 23 |
/* |
| 24 |
* Explicit calculations for Fresnel's equation are performed, |
| 25 |
* but only one square root computation is necessary. |
| 26 |
* The index of refraction is given as a Hartmann equation |
| 27 |
* with lambda0 equal to zero. If the slope of Hartmann's |
| 28 |
* equation is non-zero, the material disperses light upon |
| 29 |
* refraction. This condition is examined on rays traced to |
| 30 |
* light sources. If a ray is exiting a dielectric material, we |
| 31 |
* check the sources to see if any would cause bright color to be |
| 32 |
* directed to the viewer due to dispersion. This gives colorful |
| 33 |
* sparkle to crystals, etc. (Only if DISPERSE is defined!) |
| 34 |
* |
| 35 |
* Arguments for MAT_DIELECTRIC are: |
| 36 |
* red grn blu rndx Hartmann |
| 37 |
* |
| 38 |
* Arguments for MAT_INTERFACE are: |
| 39 |
* red1 grn1 blu1 rndx1 red2 grn2 blu2 rndx2 |
| 40 |
* |
| 41 |
* The primaries are material transmission per unit length. |
| 42 |
* MAT_INTERFACE uses dielectric1 for inside and dielectric2 for |
| 43 |
* outside. |
| 44 |
*/ |
| 45 |
|
| 46 |
|
| 47 |
#define MLAMBDA 500 /* mean lambda */ |
| 48 |
#define MAXLAMBDA 779 /* maximum lambda */ |
| 49 |
#define MINLAMBDA 380 /* minimum lambda */ |
| 50 |
|
| 51 |
#define MINCOS 0.997 /* minimum dot product for dispersion */ |
| 52 |
|
| 53 |
extern COLOR cextinction; /* global coefficient of extinction */ |
| 54 |
extern COLOR salbedo; /* global scattering albedo */ |
| 55 |
|
| 56 |
|
| 57 |
static double |
| 58 |
mylog(x) /* special log for extinction coefficients */ |
| 59 |
double x; |
| 60 |
{ |
| 61 |
if (x < 1e-40) |
| 62 |
return(-100.); |
| 63 |
if (x >= 1.) |
| 64 |
return(0.); |
| 65 |
return(log(x)); |
| 66 |
} |
| 67 |
|
| 68 |
|
| 69 |
m_dielectric(m, r) /* color a ray which hit a dielectric interface */ |
| 70 |
OBJREC *m; |
| 71 |
register RAY *r; |
| 72 |
{ |
| 73 |
double cos1, cos2, nratio; |
| 74 |
COLOR ctrans; |
| 75 |
COLOR talb; |
| 76 |
double mabsorp; |
| 77 |
double refl, trans; |
| 78 |
FVECT dnorm; |
| 79 |
double d1, d2; |
| 80 |
RAY p; |
| 81 |
register int i; |
| 82 |
|
| 83 |
if (m->oargs.nfargs != (m->otype==MAT_DIELECTRIC ? 5 : 8)) |
| 84 |
objerror(m, USER, "bad arguments"); |
| 85 |
|
| 86 |
raytexture(r, m->omod); /* get modifiers */ |
| 87 |
|
| 88 |
cos1 = raynormal(dnorm, r); /* cosine of theta1 */ |
| 89 |
/* index of refraction */ |
| 90 |
if (m->otype == MAT_DIELECTRIC) |
| 91 |
nratio = m->oargs.farg[3] + m->oargs.farg[4]/MLAMBDA; |
| 92 |
else |
| 93 |
nratio = m->oargs.farg[3] / m->oargs.farg[7]; |
| 94 |
|
| 95 |
if (cos1 < 0.0) { /* inside */ |
| 96 |
cos1 = -cos1; |
| 97 |
dnorm[0] = -dnorm[0]; |
| 98 |
dnorm[1] = -dnorm[1]; |
| 99 |
dnorm[2] = -dnorm[2]; |
| 100 |
setcolor(r->cext, -mylog(m->oargs.farg[0]*colval(r->pcol,RED)), |
| 101 |
-mylog(m->oargs.farg[1]*colval(r->pcol,GRN)), |
| 102 |
-mylog(m->oargs.farg[2]*colval(r->pcol,BLU))); |
| 103 |
setcolor(r->albedo, 0., 0., 0.); |
| 104 |
r->gecc = 0.; |
| 105 |
if (m->otype == MAT_INTERFACE) { |
| 106 |
setcolor(ctrans, |
| 107 |
-mylog(m->oargs.farg[4]*colval(r->pcol,RED)), |
| 108 |
-mylog(m->oargs.farg[5]*colval(r->pcol,GRN)), |
| 109 |
-mylog(m->oargs.farg[6]*colval(r->pcol,BLU))); |
| 110 |
setcolor(talb, 0., 0., 0.); |
| 111 |
} else { |
| 112 |
copycolor(ctrans, cextinction); |
| 113 |
copycolor(talb, salbedo); |
| 114 |
} |
| 115 |
} else { /* outside */ |
| 116 |
nratio = 1.0 / nratio; |
| 117 |
|
| 118 |
setcolor(ctrans, -mylog(m->oargs.farg[0]*colval(r->pcol,RED)), |
| 119 |
-mylog(m->oargs.farg[1]*colval(r->pcol,GRN)), |
| 120 |
-mylog(m->oargs.farg[2]*colval(r->pcol,BLU))); |
| 121 |
setcolor(talb, 0., 0., 0.); |
| 122 |
if (m->otype == MAT_INTERFACE) { |
| 123 |
setcolor(r->cext, |
| 124 |
-mylog(m->oargs.farg[4]*colval(r->pcol,RED)), |
| 125 |
-mylog(m->oargs.farg[5]*colval(r->pcol,GRN)), |
| 126 |
-mylog(m->oargs.farg[6]*colval(r->pcol,BLU))); |
| 127 |
setcolor(r->albedo, 0., 0., 0.); |
| 128 |
r->gecc = 0.; |
| 129 |
} |
| 130 |
} |
| 131 |
/* estimate absorption */ |
| 132 |
mabsorp = colval(r->cext,RED) < colval(r->cext,GRN) ? |
| 133 |
colval(r->cext,RED) : colval(r->cext,GRN); |
| 134 |
if (colval(r->cext,BLU) < mabsorp) mabsorp = colval(r->cext,BLU); |
| 135 |
if (mabsorp > 0.) |
| 136 |
mabsorp = exp(-mabsorp*r->rot); /* conservative */ |
| 137 |
else |
| 138 |
mabsorp = 1.0; |
| 139 |
|
| 140 |
d2 = 1.0 - nratio*nratio*(1.0 - cos1*cos1); /* compute cos theta2 */ |
| 141 |
|
| 142 |
if (d2 < FTINY) /* total reflection */ |
| 143 |
|
| 144 |
refl = 1.0; |
| 145 |
|
| 146 |
else { /* refraction occurs */ |
| 147 |
/* compute Fresnel's equations */ |
| 148 |
cos2 = sqrt(d2); |
| 149 |
d1 = cos1; |
| 150 |
d2 = nratio*cos2; |
| 151 |
d1 = (d1 - d2) / (d1 + d2); |
| 152 |
refl = d1 * d1; |
| 153 |
|
| 154 |
d1 = 1.0 / cos1; |
| 155 |
d2 = nratio / cos2; |
| 156 |
d1 = (d1 - d2) / (d1 + d2); |
| 157 |
refl += d1 * d1; |
| 158 |
|
| 159 |
refl *= 0.5; |
| 160 |
trans = 1.0 - refl; |
| 161 |
|
| 162 |
if (rayorigin(&p, r, REFRACTED, mabsorp*trans) == 0) { |
| 163 |
|
| 164 |
/* compute refracted ray */ |
| 165 |
d1 = nratio*cos1 - cos2; |
| 166 |
for (i = 0; i < 3; i++) |
| 167 |
p.rdir[i] = nratio*r->rdir[i] + d1*dnorm[i]; |
| 168 |
|
| 169 |
#ifdef DISPERSE |
| 170 |
if (m->otype != MAT_DIELECTRIC |
| 171 |
|| r->rod > 0.0 |
| 172 |
|| r->crtype & SHADOW |
| 173 |
|| !directvis |
| 174 |
|| m->oargs.farg[4] == 0.0 |
| 175 |
|| !disperse(m, r, p.rdir, |
| 176 |
trans, ctrans, talb)) |
| 177 |
#endif |
| 178 |
{ |
| 179 |
copycolor(p.cext, ctrans); |
| 180 |
copycolor(p.albedo, talb); |
| 181 |
rayvalue(&p); |
| 182 |
scalecolor(p.rcol, trans); |
| 183 |
addcolor(r->rcol, p.rcol); |
| 184 |
if (nratio >= 1.0-FTINY && nratio <= 1.0+FTINY) |
| 185 |
r->rt = r->rot + p.rt; |
| 186 |
} |
| 187 |
} |
| 188 |
} |
| 189 |
|
| 190 |
if (!(r->crtype & SHADOW) && |
| 191 |
rayorigin(&p, r, REFLECTED, mabsorp*refl) == 0) { |
| 192 |
|
| 193 |
/* compute reflected ray */ |
| 194 |
for (i = 0; i < 3; i++) |
| 195 |
p.rdir[i] = r->rdir[i] + 2.0*cos1*dnorm[i]; |
| 196 |
|
| 197 |
rayvalue(&p); /* reflected ray value */ |
| 198 |
|
| 199 |
scalecolor(p.rcol, refl); /* color contribution */ |
| 200 |
addcolor(r->rcol, p.rcol); |
| 201 |
} |
| 202 |
/* rayvalue() computes absorption */ |
| 203 |
return(1); |
| 204 |
} |
| 205 |
|
| 206 |
|
| 207 |
#ifdef DISPERSE |
| 208 |
|
| 209 |
static |
| 210 |
disperse(m, r, vt, tr, cet, abt) /* check light sources for dispersion */ |
| 211 |
OBJREC *m; |
| 212 |
RAY *r; |
| 213 |
FVECT vt; |
| 214 |
double tr; |
| 215 |
COLOR cet, abt; |
| 216 |
{ |
| 217 |
RAY sray, *entray; |
| 218 |
FVECT v1, v2, n1, n2; |
| 219 |
FVECT dv, v2Xdv; |
| 220 |
double v2Xdvv2Xdv; |
| 221 |
int success = 0; |
| 222 |
SRCINDEX si; |
| 223 |
FVECT vtmp1, vtmp2; |
| 224 |
double dtmp1, dtmp2; |
| 225 |
int l1, l2; |
| 226 |
COLOR ctmp; |
| 227 |
int i; |
| 228 |
|
| 229 |
/* |
| 230 |
* This routine computes dispersion to the first order using |
| 231 |
* the following assumptions: |
| 232 |
* |
| 233 |
* 1) The dependency of the index of refraction on wavelength |
| 234 |
* is approximated by Hartmann's equation with lambda0 |
| 235 |
* equal to zero. |
| 236 |
* 2) The entry and exit locations are constant with respect |
| 237 |
* to dispersion. |
| 238 |
* |
| 239 |
* The second assumption permits us to model dispersion without |
| 240 |
* having to sample refracted directions. We assume that the |
| 241 |
* geometry inside the material is constant, and concern ourselves |
| 242 |
* only with the relationship between the entering and exiting ray. |
| 243 |
* We compute the first derivatives of the entering and exiting |
| 244 |
* refraction with respect to the index of refraction. This |
| 245 |
* is then used in a first order Taylor series to determine the |
| 246 |
* index of refraction necessary to send the exiting ray to each |
| 247 |
* light source. |
| 248 |
* If an exiting ray hits a light source within the refraction |
| 249 |
* boundaries, we sum all the frequencies over the disc of the |
| 250 |
* light source to determine the resulting color. A smaller light |
| 251 |
* source will therefore exhibit a sharper spectrum. |
| 252 |
*/ |
| 253 |
|
| 254 |
if (!(r->crtype & REFRACTED)) { /* ray started in material */ |
| 255 |
VCOPY(v1, r->rdir); |
| 256 |
n1[0] = -r->rdir[0]; n1[1] = -r->rdir[1]; n1[2] = -r->rdir[2]; |
| 257 |
} else { |
| 258 |
/* find entry point */ |
| 259 |
for (entray = r; entray->rtype != REFRACTED; |
| 260 |
entray = entray->parent) |
| 261 |
; |
| 262 |
entray = entray->parent; |
| 263 |
if (entray->crtype & REFRACTED) /* too difficult */ |
| 264 |
return(0); |
| 265 |
VCOPY(v1, entray->rdir); |
| 266 |
VCOPY(n1, entray->ron); |
| 267 |
} |
| 268 |
VCOPY(v2, vt); /* exiting ray */ |
| 269 |
VCOPY(n2, r->ron); |
| 270 |
|
| 271 |
/* first order dispersion approx. */ |
| 272 |
dtmp1 = DOT(n1, v1); |
| 273 |
dtmp2 = DOT(n2, v2); |
| 274 |
for (i = 0; i < 3; i++) |
| 275 |
dv[i] = v1[i] + v2[i] - n1[i]/dtmp1 - n2[i]/dtmp2; |
| 276 |
|
| 277 |
if (DOT(dv, dv) <= FTINY) /* null effect */ |
| 278 |
return(0); |
| 279 |
/* compute plane normal */ |
| 280 |
fcross(v2Xdv, v2, dv); |
| 281 |
v2Xdvv2Xdv = DOT(v2Xdv, v2Xdv); |
| 282 |
|
| 283 |
/* check sources */ |
| 284 |
initsrcindex(&si); |
| 285 |
while (srcray(&sray, r, &si)) { |
| 286 |
|
| 287 |
if (DOT(sray.rdir, v2) < MINCOS) |
| 288 |
continue; /* bad source */ |
| 289 |
/* adjust source ray */ |
| 290 |
|
| 291 |
dtmp1 = DOT(v2Xdv, sray.rdir) / v2Xdvv2Xdv; |
| 292 |
sray.rdir[0] -= dtmp1 * v2Xdv[0]; |
| 293 |
sray.rdir[1] -= dtmp1 * v2Xdv[1]; |
| 294 |
sray.rdir[2] -= dtmp1 * v2Xdv[2]; |
| 295 |
|
| 296 |
l1 = lambda(m, v2, dv, sray.rdir); /* mean lambda */ |
| 297 |
|
| 298 |
if (l1 > MAXLAMBDA || l1 < MINLAMBDA) /* not visible */ |
| 299 |
continue; |
| 300 |
/* trace source ray */ |
| 301 |
copycolor(sray.cext, cet); |
| 302 |
copycolor(sray.albedo, abt); |
| 303 |
normalize(sray.rdir); |
| 304 |
rayvalue(&sray); |
| 305 |
if (bright(sray.rcol) <= FTINY) /* missed it */ |
| 306 |
continue; |
| 307 |
|
| 308 |
/* |
| 309 |
* Compute spectral sum over diameter of source. |
| 310 |
* First find directions for rays going to opposite |
| 311 |
* sides of source, then compute wavelengths for each. |
| 312 |
*/ |
| 313 |
|
| 314 |
fcross(vtmp1, v2Xdv, sray.rdir); |
| 315 |
dtmp1 = sqrt(si.dom / v2Xdvv2Xdv / PI); |
| 316 |
|
| 317 |
/* compute first ray */ |
| 318 |
for (i = 0; i < 3; i++) |
| 319 |
vtmp2[i] = sray.rdir[i] + dtmp1*vtmp1[i]; |
| 320 |
|
| 321 |
l1 = lambda(m, v2, dv, vtmp2); /* first lambda */ |
| 322 |
if (l1 < 0) |
| 323 |
continue; |
| 324 |
/* compute second ray */ |
| 325 |
for (i = 0; i < 3; i++) |
| 326 |
vtmp2[i] = sray.rdir[i] - dtmp1*vtmp1[i]; |
| 327 |
|
| 328 |
l2 = lambda(m, v2, dv, vtmp2); /* second lambda */ |
| 329 |
if (l2 < 0) |
| 330 |
continue; |
| 331 |
/* compute color from spectrum */ |
| 332 |
if (l1 < l2) |
| 333 |
spec_rgb(ctmp, l1, l2); |
| 334 |
else |
| 335 |
spec_rgb(ctmp, l2, l1); |
| 336 |
multcolor(ctmp, sray.rcol); |
| 337 |
scalecolor(ctmp, tr); |
| 338 |
addcolor(r->rcol, ctmp); |
| 339 |
success++; |
| 340 |
} |
| 341 |
return(success); |
| 342 |
} |
| 343 |
|
| 344 |
|
| 345 |
static int |
| 346 |
lambda(m, v2, dv, lr) /* compute lambda for material */ |
| 347 |
register OBJREC *m; |
| 348 |
FVECT v2, dv, lr; |
| 349 |
{ |
| 350 |
FVECT lrXdv, v2Xlr; |
| 351 |
double dtmp, denom; |
| 352 |
int i; |
| 353 |
|
| 354 |
fcross(lrXdv, lr, dv); |
| 355 |
for (i = 0; i < 3; i++) |
| 356 |
if (lrXdv[i] > FTINY || lrXdv[i] < -FTINY) |
| 357 |
break; |
| 358 |
if (i >= 3) |
| 359 |
return(-1); |
| 360 |
|
| 361 |
fcross(v2Xlr, v2, lr); |
| 362 |
|
| 363 |
dtmp = m->oargs.farg[4] / MLAMBDA; |
| 364 |
denom = dtmp + v2Xlr[i]/lrXdv[i] * (m->oargs.farg[3] + dtmp); |
| 365 |
|
| 366 |
if (denom < FTINY) |
| 367 |
return(-1); |
| 368 |
|
| 369 |
return(m->oargs.farg[4] / denom); |
| 370 |
} |
| 371 |
|
| 372 |
#endif /* DISPERSE */ |
