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#ifndef lint
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static const char RCSid[] = "$Id: dielectric.c,v 2.31 2023/11/15 18:02:52 greg Exp $";
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#endif
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/*
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* dielectric.c - shading function for transparent materials.
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*/
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#include "copyright.h"
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#include "ray.h"
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#include "otypes.h"
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#include "rtotypes.h"
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#include "pmapmat.h"
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#ifdef DISPERSE
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#include "source.h"
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static int disperse(OBJREC *m,RAY *r,FVECT vt,double tr,COLOR cet,COLOR abt);
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static int lambda(OBJREC *m, FVECT v2, FVECT dv, FVECT lr);
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#endif
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static double mylog(double x);
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/*
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* Explicit calculations for Fresnel's equation are performed,
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* but only one square root computation is necessary.
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* The index of refraction is given as a Hartmann equation
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* with lambda0 equal to zero. If the slope of Hartmann's
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* equation is non-zero, the material disperses light upon
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* refraction. This condition is examined on rays traced to
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* light sources. If a ray is exiting a dielectric material, we
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* check the sources to see if any would cause bright color to be
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* directed to the viewer due to dispersion. This gives colorful
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* sparkle to crystals, etc. (Only if DISPERSE is defined!)
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*
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* Arguments for MAT_DIELECTRIC are:
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* red grn blu rndx Hartmann
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*
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* Arguments for MAT_INTERFACE are:
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* red1 grn1 blu1 rndx1 red2 grn2 blu2 rndx2
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*
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* The primaries are material transmission per unit length.
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* MAT_INTERFACE uses dielectric1 for inside and dielectric2 for
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* outside.
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*/
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#define MLAMBDA 500 /* mean lambda */
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#define MAXLAMBDA 779 /* maximum lambda */
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#define MINLAMBDA 380 /* minimum lambda */
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#define MINCOS 0.997 /* minimum dot product for dispersion */
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static double
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mylog( /* special log for extinction coefficients */
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double x
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)
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{
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if (x < 1e-40)
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return(-100.);
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if (x >= 1.)
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return(0.);
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return(log(x));
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}
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int
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m_dielectric( /* color a ray which hit a dielectric interface */
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OBJREC *m,
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RAY *r
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)
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{
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double cos1, cos2, nratio;
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COLOR pcol, ctrans, talb;
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int hastexture;
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int flatsurface;
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double refl, trans;
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FVECT dnorm;
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double d1, d2;
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RAY p;
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int i;
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/* PMAP: skip refracted shadow or ambient ray if accounted for in
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photon map */
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if (shadowRayInPmap(r) || ambRayInPmap(r))
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return(1);
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if (m->oargs.nfargs != (m->otype==MAT_DIELECTRIC ? 5 : 8))
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objerror(m, USER, "bad arguments");
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raytexture(r, m->omod); /* get modifiers */
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if ( (hastexture = DOT(r->pert,r->pert) > FTINY*FTINY) )
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cos1 = raynormal(dnorm, r); /* perturb normal */
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else {
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VCOPY(dnorm, r->ron);
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cos1 = r->rod;
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}
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flatsurface = r->ro != NULL && isflat(r->ro->otype) &&
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!hastexture | (r->crtype & AMBIENT);
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/* index of refraction */
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if (m->otype == MAT_DIELECTRIC)
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nratio = m->oargs.farg[3] + m->oargs.farg[4]/MLAMBDA;
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else
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nratio = m->oargs.farg[3] / m->oargs.farg[7];
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scolor_rgb(pcol, r->pcol);
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if (cos1 < 0.0) { /* inside */
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hastexture = -hastexture;
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cos1 = -cos1;
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dnorm[0] = -dnorm[0];
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dnorm[1] = -dnorm[1];
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dnorm[2] = -dnorm[2];
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setcolor(r->cext, -mylog(m->oargs.farg[0]*colval(pcol,RED)),
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-mylog(m->oargs.farg[1]*colval(pcol,GRN)),
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-mylog(m->oargs.farg[2]*colval(pcol,BLU)));
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setcolor(r->albedo, 0., 0., 0.);
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r->gecc = 0.;
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if (m->otype == MAT_INTERFACE) {
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setcolor(ctrans,
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-mylog(m->oargs.farg[4]*colval(pcol,RED)),
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-mylog(m->oargs.farg[5]*colval(pcol,GRN)),
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-mylog(m->oargs.farg[6]*colval(pcol,BLU)));
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setcolor(talb, 0., 0., 0.);
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} else {
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copycolor(ctrans, cextinction);
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copycolor(talb, salbedo);
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}
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} else { /* outside */
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nratio = 1.0 / nratio;
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setcolor(ctrans, -mylog(m->oargs.farg[0]*colval(pcol,RED)),
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-mylog(m->oargs.farg[1]*colval(pcol,GRN)),
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-mylog(m->oargs.farg[2]*colval(pcol,BLU)));
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setcolor(talb, 0., 0., 0.);
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if (m->otype == MAT_INTERFACE) {
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setcolor(r->cext,
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-mylog(m->oargs.farg[4]*colval(pcol,RED)),
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-mylog(m->oargs.farg[5]*colval(pcol,GRN)),
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-mylog(m->oargs.farg[6]*colval(pcol,BLU)));
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setcolor(r->albedo, 0., 0., 0.);
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r->gecc = 0.;
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}
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}
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d2 = 1.0 - nratio*nratio*(1.0 - cos1*cos1); /* compute cos theta2 */
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if (d2 < FTINY) /* total reflection */
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refl = 1.0;
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else { /* refraction occurs */
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/* compute Fresnel's equations */
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cos2 = sqrt(d2);
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d1 = cos1;
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d2 = nratio*cos2;
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d1 = (d1 - d2) / (d1 + d2);
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refl = d1 * d1;
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d1 = 1.0 / cos1;
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d2 = nratio / cos2;
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d1 = (d1 - d2) / (d1 + d2);
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refl += d1 * d1;
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refl *= 0.5;
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trans = 1.0 - refl;
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trans *= nratio*nratio; /* solid angle ratio */
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setscolor(p.rcoef, trans, trans, trans);
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if (rayorigin(&p, REFRACTED, r, p.rcoef) == 0) {
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/* compute refracted ray */
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d1 = nratio*cos1 - cos2;
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for (i = 0; i < 3; i++)
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p.rdir[i] = nratio*r->rdir[i] + d1*dnorm[i];
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/* accidental reflection? */
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if (hastexture &&
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DOT(p.rdir,r->ron)*hastexture >= -FTINY) {
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d1 *= (double)hastexture;
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for (i = 0; i < 3; i++) /* ignore texture */
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p.rdir[i] = nratio*r->rdir[i] +
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d1*r->ron[i];
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normalize(p.rdir); /* not exact */
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} else
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checknorm(p.rdir);
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#ifdef DISPERSE
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if (m->otype != MAT_DIELECTRIC
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|| r->rod > 0.0
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|| r->crtype & SHADOW
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|| !directvis
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|| m->oargs.farg[4] == 0.0
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|| !disperse(m, r, p.rdir,
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trans, ctrans, talb))
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#endif
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{
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copycolor(p.cext, ctrans);
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copycolor(p.albedo, talb);
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rayvalue(&p);
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smultscolor(p.rcol, p.rcoef);
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saddscolor(r->rcol, p.rcol);
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/* virtual distance */
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if (flatsurface ||
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(1.-FTINY <= nratio) &
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(nratio <= 1.+FTINY))
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r->rxt = r->rot + raydistance(&p);
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}
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}
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}
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setscolor(p.rcoef, refl, refl, refl);
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if (!(r->crtype & SHADOW) &&
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rayorigin(&p, REFLECTED, r, p.rcoef) == 0) {
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/* compute reflected ray */
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VSUM(p.rdir, r->rdir, dnorm, 2.*cos1);
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/* accidental penetration? */
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if (hastexture && DOT(p.rdir,r->ron)*hastexture <= FTINY)
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VSUM(p.rdir, r->rdir, r->ron, 2.*r->rod);
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checknorm(p.rdir);
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rayvalue(&p); /* reflected ray value */
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smultscolor(p.rcol, p.rcoef); /* color contribution */
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copyscolor(r->mcol, p.rcol);
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saddscolor(r->rcol, p.rcol);
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/* virtual distance */
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r->rmt = r->rot;
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if (flatsurface)
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r->rmt += raydistance(&p);
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}
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/* rayvalue() computes absorption */
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return(1);
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}
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#ifdef DISPERSE
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static int
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disperse( /* check light sources for dispersion */
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OBJREC *m,
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RAY *r,
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FVECT vt,
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double tr,
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COLOR cet,
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COLOR abt
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)
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{
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RAY sray;
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const RAY *entray;
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FVECT v1, v2, n1, n2;
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FVECT dv, v2Xdv;
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double v2Xdvv2Xdv;
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int success = 0;
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SRCINDEX si;
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FVECT vtmp1, vtmp2;
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double dtmp1, dtmp2;
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int l1, l2;
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COLOR ctmp;
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int i;
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/*
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* This routine computes dispersion to the first order using
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* the following assumptions:
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*
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* 1) The dependency of the index of refraction on wavelength
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* is approximated by Hartmann's equation with lambda0
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* equal to zero.
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* 2) The entry and exit locations are constant with respect
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* to dispersion.
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*
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* The second assumption permits us to model dispersion without
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* having to sample refracted directions. We assume that the
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* geometry inside the material is constant, and concern ourselves
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* only with the relationship between the entering and exiting ray.
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* We compute the first derivatives of the entering and exiting
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* refraction with respect to the index of refraction. This
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* is then used in a first order Taylor series to determine the
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* index of refraction necessary to send the exiting ray to each
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* light source.
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* If an exiting ray hits a light source within the refraction
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* boundaries, we sum all the frequencies over the disc of the
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* light source to determine the resulting color. A smaller light
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* source will therefore exhibit a sharper spectrum.
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*/
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if (!(r->crtype & REFRACTED)) { /* ray started in material */
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VCOPY(v1, r->rdir);
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n1[0] = -r->rdir[0]; n1[1] = -r->rdir[1]; n1[2] = -r->rdir[2];
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} else {
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/* find entry point */
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for (entray = r; entray->rtype != REFRACTED;
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entray = entray->parent)
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;
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entray = entray->parent;
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if (entray->crtype & REFRACTED) /* too difficult */
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return(0);
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VCOPY(v1, entray->rdir);
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VCOPY(n1, entray->ron);
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}
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VCOPY(v2, vt); /* exiting ray */
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VCOPY(n2, r->ron);
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/* first order dispersion approx. */
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dtmp1 = 1./DOT(n1, v1);
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dtmp2 = 1./DOT(n2, v2);
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for (i = 0; i < 3; i++)
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dv[i] = v1[i] + v2[i] - n1[i]*dtmp1 - n2[i]*dtmp2;
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if (DOT(dv, dv) <= FTINY) /* null effect */
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return(0);
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/* compute plane normal */
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fcross(v2Xdv, v2, dv);
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v2Xdvv2Xdv = DOT(v2Xdv, v2Xdv);
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/* check sources */
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initsrcindex(&si);
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while (srcray(&sray, r, &si)) {
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if (DOT(sray.rdir, v2) < MINCOS)
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continue; /* bad source */
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/* adjust source ray */
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dtmp1 = DOT(v2Xdv, sray.rdir) / v2Xdvv2Xdv;
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sray.rdir[0] -= dtmp1 * v2Xdv[0];
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sray.rdir[1] -= dtmp1 * v2Xdv[1];
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sray.rdir[2] -= dtmp1 * v2Xdv[2];
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l1 = lambda(m, v2, dv, sray.rdir); /* mean lambda */
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if (l1 > MAXLAMBDA || l1 < MINLAMBDA) /* not visible */
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continue;
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/* trace source ray */
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copycolor(sray.cext, cet);
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copycolor(sray.albedo, abt);
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normalize(sray.rdir);
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rayvalue(&sray);
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if (pbright(sray.rcol) <= FTINY) /* missed it */
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continue;
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/*
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* Compute spectral sum over diameter of source.
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| 344 |
* First find directions for rays going to opposite
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* sides of source, then compute wavelengths for each.
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*/
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| 347 |
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fcross(vtmp1, v2Xdv, sray.rdir);
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dtmp1 = sqrt(si.dom / v2Xdvv2Xdv / PI);
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| 350 |
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| 351 |
/* compute first ray */
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VSUM(vtmp2, sray.rdir, vtmp1, dtmp1);
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l1 = lambda(m, v2, dv, vtmp2); /* first lambda */
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if (l1 < 0)
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continue;
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| 357 |
/* compute second ray */
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| 358 |
VSUM(vtmp2, sray.rdir, vtmp1, -dtmp1);
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| 359 |
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| 360 |
l2 = lambda(m, v2, dv, vtmp2); /* second lambda */
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| 361 |
if (l2 < 0)
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| 362 |
continue;
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| 363 |
/* compute color from spectrum */
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| 364 |
if (l1 < l2) /* XXX should use direct spectral xfer */
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spec_rgb(ctmp, l1, l2);
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| 366 |
else
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spec_rgb(ctmp, l2, l1);
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| 368 |
multscolor(ctmp, sray.rcol);
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| 369 |
scalecolor(ctmp, tr);
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| 370 |
saddcolor(r->rcol, ctmp);
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| 371 |
success++;
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| 372 |
}
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| 373 |
return(success);
|
| 374 |
}
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| 375 |
|
| 376 |
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| 377 |
static int
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| 378 |
lambda( /* compute lambda for material */
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| 379 |
OBJREC *m,
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| 380 |
FVECT v2,
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| 381 |
FVECT dv,
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| 382 |
FVECT lr
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| 383 |
)
|
| 384 |
{
|
| 385 |
FVECT lrXdv, v2Xlr;
|
| 386 |
double dtmp, denom;
|
| 387 |
int i;
|
| 388 |
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| 389 |
fcross(lrXdv, lr, dv);
|
| 390 |
for (i = 0; i < 3; i++)
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| 391 |
if ((lrXdv[i] > FTINY) | (lrXdv[i] < -FTINY))
|
| 392 |
break;
|
| 393 |
if (i >= 3)
|
| 394 |
return(-1);
|
| 395 |
|
| 396 |
fcross(v2Xlr, v2, lr);
|
| 397 |
|
| 398 |
dtmp = m->oargs.farg[4] / MLAMBDA;
|
| 399 |
denom = dtmp + v2Xlr[i]/lrXdv[i] * (m->oargs.farg[3] + dtmp);
|
| 400 |
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| 401 |
if (denom < FTINY)
|
| 402 |
return(-1);
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| 403 |
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| 404 |
return(m->oargs.farg[4] / denom);
|
| 405 |
}
|
| 406 |
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| 407 |
#endif /* DISPERSE */
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