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/* Copyright (c) 1986 Regents of the University of California */ |
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|
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#ifndef lint |
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static char SCCSid[] = "$SunId$ LBL"; |
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#endif |
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|
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/* |
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* dielectric.c - shading function for transparent materials. |
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* |
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* 9/6/85 |
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*/ |
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|
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#include "ray.h" |
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|
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#include "otypes.h" |
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|
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#ifdef DISPERSE |
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#include "source.h" |
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#endif |
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|
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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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|
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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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|
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#define MINCOS 0.997 /* minimum dot product for dispersion */ |
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|
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|
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m_dielectric(m, r) /* color a ray which hit something transparent */ |
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OBJREC *m; |
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register RAY *r; |
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{ |
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double sqrt(), pow(); |
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double cos1, cos2, nratio; |
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COLOR mcolor; |
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double mabsorp; |
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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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register int i; |
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|
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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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|
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raytexture(r, m->omod); /* get modifiers */ |
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|
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cos1 = raynormal(dnorm, r); /* cosine of theta1 */ |
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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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|
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if (cos1 < 0.0) { /* inside */ |
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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(mcolor, pow(m->oargs.farg[0], r->rot), |
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pow(m->oargs.farg[1], r->rot), |
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pow(m->oargs.farg[2], r->rot)); |
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} else { /* outside */ |
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nratio = 1.0 / nratio; |
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if (m->otype == MAT_INTERFACE) |
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setcolor(mcolor, pow(m->oargs.farg[4], r->rot), |
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pow(m->oargs.farg[5], r->rot), |
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pow(m->oargs.farg[6], r->rot)); |
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else |
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setcolor(mcolor, 1.0, 1.0, 1.0); |
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} |
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mabsorp = bright(mcolor); |
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|
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d2 = 1.0 - nratio*nratio*(1.0 - cos1*cos1); /* compute cos theta2 */ |
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|
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if (d2 < FTINY) /* total reflection */ |
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|
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refl = 1.0; |
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|
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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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|
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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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|
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refl /= 2.0; |
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trans = 1.0 - refl; |
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|
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if (rayorigin(&p, r, REFRACTED, mabsorp*trans) == 0) { |
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|
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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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|
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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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|| m->oargs.farg[4] == 0.0 |
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|| !disperse(m, r, p.rdir, trans)) |
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#endif |
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{ |
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rayvalue(&p); |
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multcolor(mcolor, r->pcol); /* modify */ |
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scalecolor(p.rcol, trans); |
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addcolor(r->rcol, p.rcol); |
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} |
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} |
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} |
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|
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if (!(r->crtype & SHADOW) && |
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rayorigin(&p, r, REFLECTED, mabsorp*refl) == 0) { |
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|
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/* compute reflected ray */ |
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for (i = 0; i < 3; i++) |
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p.rdir[i] = r->rdir[i] + 2.0*cos1*dnorm[i]; |
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|
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rayvalue(&p); /* reflected ray value */ |
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|
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scalecolor(p.rcol, refl); /* color contribution */ |
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addcolor(r->rcol, p.rcol); |
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} |
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|
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multcolor(r->rcol, mcolor); /* multiply by transmittance */ |
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} |
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|
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|
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#ifdef DISPERSE |
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|
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static |
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disperse(m, r, vt, tr) /* 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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{ |
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double sqrt(); |
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RAY sray, *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 sn, success = 0; |
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double omega; |
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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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/* |
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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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|
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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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|
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/* first order dispersion approx. */ |
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dtmp1 = DOT(n1, v1); |
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dtmp2 = 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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|
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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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|
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/* check sources */ |
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for (sn = 0; sn < nsources; sn++) { |
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|
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if ((omega = srcray(&sray, r, sn)) == 0.0 || |
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DOT(sray.rdir, v2) < MINCOS) |
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continue; /* bad source */ |
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|
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/* adjust source ray */ |
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|
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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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|
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l1 = lambda(m, v2, dv, sray.rdir); /* mean lambda */ |
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|
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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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normalize(sray.rdir); |
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rayvalue(&sray); |
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if (bright(sray.rcol) <= FTINY) /* missed it */ |
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continue; |
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|
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/* |
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* Compute spectral sum over diameter of source. |
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* 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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|
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fcross(vtmp1, v2Xdv, sray.rdir); |
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dtmp1 = sqrt(omega / v2Xdvv2Xdv / PI); |
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|
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/* compute first ray */ |
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for (i = 0; i < 3; i++) |
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vtmp2[i] = sray.rdir[i] + dtmp1*vtmp1[i]; |
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|
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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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/* compute second ray */ |
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for (i = 0; i < 3; i++) |
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vtmp2[i] = sray.rdir[i] - dtmp1*vtmp1[i]; |
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|
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l2 = lambda(m, v2, dv, vtmp2); /* second lambda */ |
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if (l2 < 0) |
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continue; |
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/* compute color from spectrum */ |
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if (l1 < l2) |
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spec_rgb(ctmp, l1, l2); |
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else |
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spec_rgb(ctmp, l2, l1); |
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multcolor(ctmp, sray.rcol); |
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scalecolor(ctmp, tr); |
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addcolor(r->rcol, ctmp); |
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success++; |
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} |
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return(success); |
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} |
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|
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|
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static int |
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lambda(m, v2, dv, lr) /* compute lambda for material */ |
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register OBJREC *m; |
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FVECT v2, dv, lr; |
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{ |
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FVECT lrXdv, v2Xlr; |
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double dtmp, denom; |
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int i; |
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|
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fcross(lrXdv, lr, dv); |
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for (i = 0; i < 3; i++) |
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if (lrXdv[i] > FTINY || lrXdv[i] < -FTINY) |
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break; |
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if (i >= 3) |
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return(-1); |
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|
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fcross(v2Xlr, v2, lr); |
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|
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dtmp = m->oargs.farg[4] / MLAMBDA; |
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denom = dtmp + v2Xlr[i]/lrXdv[i] * (m->oargs.farg[3] + dtmp); |
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|
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if (denom < FTINY) |
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return(-1); |
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|
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return(m->oargs.farg[4] / denom); |
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} |
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|
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#endif /* DISPERSE */ |
