--- ray/src/rt/normal.c	1989/02/02 10:41:30	1.1
+++ ray/src/rt/normal.c	2005/01/05 19:34:11	2.49
@@ -1,9 +1,6 @@
-/* Copyright (c) 1986 Regents of the University of California */
-
 #ifndef lint
-static char SCCSid[] = "$SunId$ LBL";
+static const char RCSid[] = "$Id: normal.c,v 2.49 2005/01/05 19:34:11 greg Exp $";
 #endif
-
 /*
  *  normal.c - shading function for normal materials.
  *
@@ -11,19 +8,28 @@ static char SCCSid[] = "$SunId$ LBL";
  *     12/19/85 - added stuff for metals.
  *     6/26/87 - improved specular model.
  *     9/28/87 - added model for translucent materials.
+ *     Later changes described in delta comments.
  */
 
-#include  "ray.h"
+#include "copyright.h"
 
+#include  "ray.h"
+#include  "ambient.h"
 #include  "source.h"
-
 #include  "otypes.h"
+#include  "rtotypes.h"
+#include  "random.h"
 
+#ifndef  MAXITER
+#define  MAXITER	10		/* maximum # specular ray attempts */
+#endif
+					/* estimate of Fresnel function */
+#define  FRESNE(ci)	(exp(-5.85*(ci)) - 0.00287989916)
+
+
 /*
- *	This routine uses portions of the reflection
- *  model described by Cook and Torrance.
- *	The computation of specular components has been simplified by
- *  numerous approximations and ommisions to improve speed.
+ *	This routine implements the isotropic Gaussian
+ *  model described by Ward in Siggraph `92 article.
  *	We orient the surface towards the incoming ray, so a single
  *  surface can be used to represent an infinitely thin object.
  *
@@ -34,182 +40,414 @@ static char SCCSid[] = "$SunId$ LBL";
  *	red 	grn	blu	rspec	rough	trans	tspec
  */
 
-#define  BSPEC(m)	(6.0)		/* specularity parameter b */
+				/* specularity flags */
+#define  SP_REFL	01		/* has reflected specular component */
+#define  SP_TRAN	02		/* has transmitted specular */
+#define  SP_PURE	04		/* purely specular (zero roughness) */
+#define  SP_FLAT	010		/* flat reflecting surface */
+#define  SP_RBLT	020		/* reflection below sample threshold */
+#define  SP_TBLT	040		/* transmission below threshold */
 
-
-m_normal(m, r)			/* color a ray which hit something normal */
-register OBJREC  *m;
-register RAY  *r;
-{
-	double  exp();
+typedef struct {
+	OBJREC  *mp;		/* material pointer */
+	RAY  *rp;		/* ray pointer */
+	short  specfl;		/* specularity flags, defined above */
 	COLOR  mcolor;		/* color of this material */
 	COLOR  scolor;		/* color of specular component */
 	FVECT  vrefl;		/* vector in direction of reflected ray */
-	double  alpha2;		/* roughness squared times 2 */
-	RAY  lr;		/* ray to illumination source */
+	FVECT  prdir;		/* vector in transmitted direction */
+	double  alpha2;		/* roughness squared */
 	double  rdiff, rspec;	/* reflected specular, diffuse */
 	double  trans;		/* transmissivity */
 	double  tdiff, tspec;	/* transmitted specular, diffuse */
 	FVECT  pnorm;		/* perturbed surface normal */
 	double  pdot;		/* perturbed dot product */
+}  NORMDAT;		/* normal material data */
+
+static srcdirf_t dirnorm;
+static void gaussamp(RAY  *r, NORMDAT  *np);
+
+
+static void
+dirnorm(		/* compute source contribution */
+	COLOR  cval,			/* returned coefficient */
+	void  *nnp,		/* material data */
+	FVECT  ldir,			/* light source direction */
+	double  omega			/* light source size */
+)
+{
+	register NORMDAT *np = nnp;
 	double  ldot;
-	double  omega;
-	double  dtmp;
+	double  lrdiff, ltdiff;
+	double  dtmp, d2;
+	FVECT  vtmp;
 	COLOR  ctmp;
-	register int  i;
 
-	if (m->oargs.nfargs != (m->otype == MAT_TRANS ? 7 : 5))
-		objerror(m, USER, "bad # arguments");
+	setcolor(cval, 0.0, 0.0, 0.0);
+
+	ldot = DOT(np->pnorm, ldir);
+
+	if (ldot < 0.0 ? np->trans <= FTINY : np->trans >= 1.0-FTINY)
+		return;		/* wrong side */
+
+				/* Fresnel estimate */
+	lrdiff = np->rdiff;
+	ltdiff = np->tdiff;
+	if (np->specfl & SP_PURE && np->rspec > FTINY &&
+			(lrdiff > FTINY) | (ltdiff > FTINY)) {
+		dtmp = 1. - FRESNE(fabs(ldot));
+		lrdiff *= dtmp;
+		ltdiff *= dtmp;
+	}
+
+	if (ldot > FTINY && lrdiff > FTINY) {
+		/*
+		 *  Compute and add diffuse reflected component to returned
+		 *  color.  The diffuse reflected component will always be
+		 *  modified by the color of the material.
+		 */
+		copycolor(ctmp, np->mcolor);
+		dtmp = ldot * omega * lrdiff * (1.0/PI);
+		scalecolor(ctmp, dtmp);
+		addcolor(cval, ctmp);
+	}
+	if (ldot > FTINY && (np->specfl&(SP_REFL|SP_PURE)) == SP_REFL) {
+		/*
+		 *  Compute specular reflection coefficient using
+		 *  gaussian distribution model.
+		 */
+						/* roughness */
+		dtmp = np->alpha2;
+						/* + source if flat */
+		if (np->specfl & SP_FLAT)
+			dtmp += omega * (0.25/PI);
+						/* half vector */
+		vtmp[0] = ldir[0] - np->rp->rdir[0];
+		vtmp[1] = ldir[1] - np->rp->rdir[1];
+		vtmp[2] = ldir[2] - np->rp->rdir[2];
+		d2 = DOT(vtmp, np->pnorm);
+		d2 *= d2;
+		d2 = (DOT(vtmp,vtmp) - d2) / d2;
+						/* gaussian */
+		dtmp = exp(-d2/dtmp)/(4.*PI * np->pdot * dtmp);
+						/* worth using? */
+		if (dtmp > FTINY) {
+			copycolor(ctmp, np->scolor);
+			dtmp *= omega;
+			scalecolor(ctmp, dtmp);
+			addcolor(cval, ctmp);
+		}
+	}
+	if (ldot < -FTINY && ltdiff > FTINY) {
+		/*
+		 *  Compute diffuse transmission.
+		 */
+		copycolor(ctmp, np->mcolor);
+		dtmp = -ldot * omega * ltdiff * (1.0/PI);
+		scalecolor(ctmp, dtmp);
+		addcolor(cval, ctmp);
+	}
+	if (ldot < -FTINY && (np->specfl&(SP_TRAN|SP_PURE)) == SP_TRAN) {
+		/*
+		 *  Compute specular transmission.  Specular transmission
+		 *  is always modified by material color.
+		 */
+						/* roughness + source */
+		dtmp = np->alpha2 + omega*(1.0/PI);
+						/* gaussian */
+		dtmp = exp((2.*DOT(np->prdir,ldir)-2.)/dtmp) /
+					(PI*np->pdot*dtmp);
+						/* worth using? */
+		if (dtmp > FTINY) {
+			copycolor(ctmp, np->mcolor);
+			dtmp *= np->tspec * omega;
+			scalecolor(ctmp, dtmp);
+			addcolor(cval, ctmp);
+		}
+	}
+}
+
+
+extern int
+m_normal(			/* color a ray that hit something normal */
+	register OBJREC  *m,
+	register RAY  *r
+)
+{
+	NORMDAT  nd;
+	double  fest;
+	double  transtest, transdist;
+	double	mirtest, mirdist;
+	int	hastexture;
+	double	d;
+	COLOR  ctmp;
+	register int  i;
 						/* easy shadow test */
 	if (r->crtype & SHADOW && m->otype != MAT_TRANS)
-		return;
+		return(1);
+
+	if (m->oargs.nfargs != (m->otype == MAT_TRANS ? 7 : 5))
+		objerror(m, USER, "bad number of arguments");
+						/* check for back side */
+	if (r->rod < 0.0) {
+		if (!backvis && m->otype != MAT_TRANS) {
+			raytrans(r);
+			return(1);
+		}
+		raytexture(r, m->omod);
+		flipsurface(r);			/* reorient if backvis */
+	} else
+		raytexture(r, m->omod);
+	nd.mp = m;
+	nd.rp = r;
 						/* get material color */
-	setcolor(mcolor, m->oargs.farg[0],
+	setcolor(nd.mcolor, m->oargs.farg[0],
 			   m->oargs.farg[1],
 			   m->oargs.farg[2]);
 						/* get roughness */
-	alpha2 = m->oargs.farg[4];
-	alpha2 *= 2.0 * alpha2;
-						/* reorient if necessary */
-	if (r->rod < 0.0)
-		flipsurface(r);
-						/* get modifiers */
-	raytexture(r, m->omod);
-	pdot = raynormal(pnorm, r);		/* perturb normal */
-	multcolor(mcolor, r->pcol);		/* modify material color */
-						/* get specular component */
-	rspec = m->oargs.farg[3];
+	nd.specfl = 0;
+	nd.alpha2 = m->oargs.farg[4];
+	if ((nd.alpha2 *= nd.alpha2) <= FTINY)
+		nd.specfl |= SP_PURE;
 
-	if (rspec > FTINY) {			/* has specular component */
-						/* compute specular color */
-		if (m->otype == MAT_METAL)
-			copycolor(scolor, mcolor);
-		else
-			setcolor(scolor, 1.0, 1.0, 1.0);
-		scalecolor(scolor, rspec);
-						/* improved model */
-		dtmp = exp(-BSPEC(m)*pdot);
-		for (i = 0; i < 3; i++)
-			colval(scolor,i) += (1.0-colval(scolor,i))*dtmp;
-		rspec += (1.0-rspec)*dtmp;
-						/* compute reflected ray */
-		for (i = 0; i < 3; i++)
-			vrefl[i] = r->rdir[i] + 2.0*pdot*pnorm[i];
-
-		if (alpha2 <= FTINY && !(r->crtype & SHADOW))
-			if (rayorigin(&lr, r, REFLECTED, rspec) == 0) {
-				VCOPY(lr.rdir, vrefl);
-				rayvalue(&lr);
-				multcolor(lr.rcol, scolor);
-				addcolor(r->rcol, lr.rcol);
-			}
+	if ( (hastexture = (DOT(r->pert,r->pert) > FTINY*FTINY)) ) {
+		nd.pdot = raynormal(nd.pnorm, r);	/* perturb normal */
+	} else {
+		VCOPY(nd.pnorm, r->ron);
+		nd.pdot = r->rod;
 	}
-
+	if (r->ro != NULL && isflat(r->ro->otype))
+		nd.specfl |= SP_FLAT;
+	if (nd.pdot < .001)
+		nd.pdot = .001;			/* non-zero for dirnorm() */
+	multcolor(nd.mcolor, r->pcol);		/* modify material color */
+	mirtest = transtest = 0;
+	mirdist = transdist = r->rot;
+	nd.rspec = m->oargs.farg[3];
+						/* compute Fresnel approx. */
+	if (nd.specfl & SP_PURE && nd.rspec > FTINY) {
+		fest = FRESNE(r->rod);
+		nd.rspec += fest*(1. - nd.rspec);
+	} else
+		fest = 0.;
+						/* compute transmission */
 	if (m->otype == MAT_TRANS) {
-		trans = m->oargs.farg[5]*(1.0 - rspec);
-		tspec = trans * m->oargs.farg[6];
-		tdiff = trans - tspec;
+		nd.trans = m->oargs.farg[5]*(1.0 - nd.rspec);
+		nd.tspec = nd.trans * m->oargs.farg[6];
+		nd.tdiff = nd.trans - nd.tspec;
+		if (nd.tspec > FTINY) {
+			nd.specfl |= SP_TRAN;
+							/* check threshold */
+			if (!(nd.specfl & SP_PURE) &&
+					specthresh >= nd.tspec-FTINY)
+				nd.specfl |= SP_TBLT;
+			if (!hastexture || r->crtype & SHADOW) {
+				VCOPY(nd.prdir, r->rdir);
+				transtest = 2;
+			} else {
+				for (i = 0; i < 3; i++)		/* perturb */
+					nd.prdir[i] = r->rdir[i] - r->pert[i];
+				if (DOT(nd.prdir, r->ron) < -FTINY)
+					normalize(nd.prdir);	/* OK */
+				else
+					VCOPY(nd.prdir, r->rdir);
+			}
+		}
 	} else
-		tdiff = tspec = trans = 0.0;
+		nd.tdiff = nd.tspec = nd.trans = 0.0;
 						/* transmitted ray */
-	if (tspec > FTINY && alpha2 <= FTINY)
-		if (rayorigin(&lr, r, TRANS, tspec) == 0) {
-			VCOPY(lr.rdir, r->rdir);
+	if ((nd.specfl&(SP_TRAN|SP_PURE|SP_TBLT)) == (SP_TRAN|SP_PURE)) {
+		RAY  lr;
+		if (rayorigin(&lr, r, TRANS, nd.tspec) == 0) {
+			VCOPY(lr.rdir, nd.prdir);
 			rayvalue(&lr);
-			scalecolor(lr.rcol, tspec);
+			scalecolor(lr.rcol, nd.tspec);
+			multcolor(lr.rcol, nd.mcolor);	/* modified by color */
 			addcolor(r->rcol, lr.rcol);
+			transtest *= bright(lr.rcol);
+			transdist = r->rot + lr.rt;
 		}
-	if (r->crtype & SHADOW)			/* the rest is shadow */
-		return;
+	} else
+		transtest = 0;
+
+	if (r->crtype & SHADOW) {		/* the rest is shadow */
+		r->rt = transdist;
+		return(1);
+	}
+						/* get specular reflection */
+	if (nd.rspec > FTINY) {
+		nd.specfl |= SP_REFL;
+						/* compute specular color */
+		if (m->otype != MAT_METAL) {
+			setcolor(nd.scolor, nd.rspec, nd.rspec, nd.rspec);
+		} else if (fest > FTINY) {
+			d = nd.rspec*(1. - fest);
+			for (i = 0; i < 3; i++)
+				nd.scolor[i] = fest + nd.mcolor[i]*d;
+		} else {
+			copycolor(nd.scolor, nd.mcolor);
+			scalecolor(nd.scolor, nd.rspec);
+		}
+						/* check threshold */
+		if (!(nd.specfl & SP_PURE) && specthresh >= nd.rspec-FTINY)
+			nd.specfl |= SP_RBLT;
+						/* compute reflected ray */
+		for (i = 0; i < 3; i++)
+			nd.vrefl[i] = r->rdir[i] + 2.*nd.pdot*nd.pnorm[i];
+						/* penetration? */
+		if (hastexture && DOT(nd.vrefl, r->ron) <= FTINY)
+			for (i = 0; i < 3; i++)		/* safety measure */
+				nd.vrefl[i] = r->rdir[i] + 2.*r->rod*r->ron[i];
+	}
+						/* reflected ray */
+	if ((nd.specfl&(SP_REFL|SP_PURE|SP_RBLT)) == (SP_REFL|SP_PURE)) {
+		RAY  lr;
+		if (rayorigin(&lr, r, REFLECTED, nd.rspec) == 0) {
+			VCOPY(lr.rdir, nd.vrefl);
+			rayvalue(&lr);
+			multcolor(lr.rcol, nd.scolor);
+			addcolor(r->rcol, lr.rcol);
+			if (!hastexture && nd.specfl & SP_FLAT) {
+				mirtest = 2.*bright(lr.rcol);
+				mirdist = r->rot + lr.rt;
+			}
+		}
+	}
 						/* diffuse reflection */
-	rdiff = 1.0 - trans - rspec;
+	nd.rdiff = 1.0 - nd.trans - nd.rspec;
 
-	if (rdiff <= FTINY && tdiff <= FTINY && alpha2 <= FTINY)
-		return;				/* purely specular */
+	if (nd.specfl & SP_PURE && nd.rdiff <= FTINY && nd.tdiff <= FTINY)
+		return(1);			/* 100% pure specular */
 
-	ambient(ctmp, r);		/* compute ambient component */
-	scalecolor(ctmp, 1.0-trans);	/* from this side */
-	multcolor(ctmp, mcolor);	/* modified by material color */
-	addcolor(r->rcol, ctmp);	/* add to returned color */
+	if (!(nd.specfl & SP_PURE))
+		gaussamp(r, &nd);		/* checks *BLT flags */
 
-	if (trans > FTINY) {		/* ambient from other side */
+	if (nd.rdiff > FTINY) {		/* ambient from this side */
+		ambient(ctmp, r, hastexture?nd.pnorm:r->ron);
+		if (nd.specfl & SP_RBLT)
+			scalecolor(ctmp, 1.0-nd.trans);
+		else
+			scalecolor(ctmp, nd.rdiff);
+		multcolor(ctmp, nd.mcolor);	/* modified by material color */
+		addcolor(r->rcol, ctmp);	/* add to returned color */
+	}
+	if (nd.tdiff > FTINY) {		/* ambient from other side */
 		flipsurface(r);
-		scalecolor(ctmp, trans);
-		multcolor(ctmp, mcolor);
+		if (hastexture) {
+			FVECT  bnorm;
+			bnorm[0] = -nd.pnorm[0];
+			bnorm[1] = -nd.pnorm[1];
+			bnorm[2] = -nd.pnorm[2];
+			ambient(ctmp, r, bnorm);
+		} else
+			ambient(ctmp, r, r->ron);
+		if (nd.specfl & SP_TBLT)
+			scalecolor(ctmp, nd.trans);
+		else
+			scalecolor(ctmp, nd.tdiff);
+		multcolor(ctmp, nd.mcolor);	/* modified by color */
 		addcolor(r->rcol, ctmp);
 		flipsurface(r);
 	}
-	
-	for (i = 0; i < nsources; i++) {	/* add specular and diffuse */
+					/* add direct component */
+	direct(r, dirnorm, &nd);
+					/* check distance */
+	d = bright(r->rcol);
+	if (transtest > d)
+		r->rt = transdist;
+	else if (mirtest > d)
+		r->rt = mirdist;
 
-		if ((omega = srcray(&lr, r, i)) == 0.0)
-			continue;		/* bad source */
+	return(1);
+}
 
-		ldot = DOT(pnorm, lr.rdir);
-	
-		if (ldot < 0.0 ? trans <= FTINY : trans >= 1.0-FTINY)
-			continue;		/* wrong side */
-	
-		rayvalue(&lr);			/* compute light ray value */
-	
-		if (intens(lr.rcol) <= FTINY)
-			continue;		/* didn't hit light source */
 
-		if (ldot > FTINY && rdiff > FTINY) {
-			/*
-			 *  Compute and add diffuse component to returned color.
-			 *  The diffuse component will always be modified by the
-			 *  color of the material.
-			 */
-			copycolor(ctmp, lr.rcol);
-			dtmp = ldot * omega * rdiff / PI;
-			scalecolor(ctmp, dtmp);
-			multcolor(ctmp, mcolor);
-			addcolor(r->rcol, ctmp);
-		}
-		if (ldot > FTINY && rspec > FTINY && alpha2 > FTINY) {
-			/*
-			 *  Compute specular reflection coefficient using
-			 *  gaussian distribution model.
-			 */
-							/* roughness + source */
-			dtmp = alpha2 + omega/(2.0*PI);
-							/* gaussian */
-			dtmp = exp((DOT(vrefl,lr.rdir)-1.)/dtmp)/(2.*PI)/dtmp;
-							/* worth using? */
-			if (dtmp > FTINY) {
-				copycolor(ctmp, lr.rcol);
-				dtmp *= omega;
-				scalecolor(ctmp, dtmp);
-				multcolor(ctmp, scolor);
-				addcolor(r->rcol, ctmp);
+static void
+gaussamp(			/* sample gaussian specular */
+	RAY  *r,
+	register NORMDAT  *np
+)
+{
+	RAY  sr;
+	FVECT  u, v, h;
+	double  rv[2];
+	double  d, sinp, cosp;
+	int  niter;
+	register int  i;
+					/* quick test */
+	if ((np->specfl & (SP_REFL|SP_RBLT)) != SP_REFL &&
+			(np->specfl & (SP_TRAN|SP_TBLT)) != SP_TRAN)
+		return;
+					/* set up sample coordinates */
+	v[0] = v[1] = v[2] = 0.0;
+	for (i = 0; i < 3; i++)
+		if (np->pnorm[i] < 0.6 && np->pnorm[i] > -0.6)
+			break;
+	v[i] = 1.0;
+	fcross(u, v, np->pnorm);
+	normalize(u);
+	fcross(v, np->pnorm, u);
+					/* compute reflection */
+	if ((np->specfl & (SP_REFL|SP_RBLT)) == SP_REFL &&
+			rayorigin(&sr, r, SPECULAR, np->rspec) == 0) {
+		dimlist[ndims++] = (int)np->mp;
+		for (niter = 0; niter < MAXITER; niter++) {
+			if (niter)
+				d = frandom();
+			else
+				d = urand(ilhash(dimlist,ndims)+samplendx);
+			multisamp(rv, 2, d);
+			d = 2.0*PI * rv[0];
+			cosp = tcos(d);
+			sinp = tsin(d);
+			rv[1] = 1.0 - specjitter*rv[1];
+			if (rv[1] <= FTINY)
+				d = 1.0;
+			else
+				d = sqrt( np->alpha2 * -log(rv[1]) );
+			for (i = 0; i < 3; i++)
+				h[i] = np->pnorm[i] + d*(cosp*u[i] + sinp*v[i]);
+			d = -2.0 * DOT(h, r->rdir) / (1.0 + d*d);
+			for (i = 0; i < 3; i++)
+				sr.rdir[i] = r->rdir[i] + d*h[i];
+			if (DOT(sr.rdir, r->ron) > FTINY) {
+				rayvalue(&sr);
+				multcolor(sr.rcol, np->scolor);
+				addcolor(r->rcol, sr.rcol);
+				break;
 			}
 		}
-		if (ldot < -FTINY && tdiff > FTINY) {
-			/*
-			 *  Compute diffuse transmission.
-			 */
-			copycolor(ctmp, lr.rcol);
-			dtmp = -ldot * omega * tdiff / PI;
-			scalecolor(ctmp, dtmp);
-			multcolor(ctmp, mcolor);
-			addcolor(r->rcol, ctmp);
-		}
-		if (ldot < -FTINY && tspec > FTINY && alpha2 > FTINY) {
-			/*
-			 *  Compute specular transmission.
-			 */
-							/* roughness + source */
-			dtmp = alpha2 + omega/(2.0*PI);
-							/* gaussian */
-			dtmp = exp((DOT(r->rdir,lr.rdir)-1.)/dtmp)/(2.*PI)/dtmp;
-							/* worth using? */
-			if (dtmp > FTINY) {
-				copycolor(ctmp, lr.rcol);
-				dtmp *= tspec * omega;
-				scalecolor(ctmp, dtmp);
-				addcolor(r->rcol, ctmp);
+		ndims--;
+	}
+					/* compute transmission */
+	if ((np->specfl & (SP_TRAN|SP_TBLT)) == SP_TRAN &&
+			rayorigin(&sr, r, SPECULAR, np->tspec) == 0) {
+		dimlist[ndims++] = (int)np->mp;
+		for (niter = 0; niter < MAXITER; niter++) {
+			if (niter)
+				d = frandom();
+			else
+				d = urand(ilhash(dimlist,ndims)+1823+samplendx);
+			multisamp(rv, 2, d);
+			d = 2.0*PI * rv[0];
+			cosp = tcos(d);
+			sinp = tsin(d);
+			rv[1] = 1.0 - specjitter*rv[1];
+			if (rv[1] <= FTINY)
+				d = 1.0;
+			else
+				d = sqrt( np->alpha2 * -log(rv[1]) );
+			for (i = 0; i < 3; i++)
+				sr.rdir[i] = np->prdir[i] + d*(cosp*u[i] + sinp*v[i]);
+			if (DOT(sr.rdir, r->ron) < -FTINY) {
+				normalize(sr.rdir);	/* OK, normalize */
+				rayvalue(&sr);
+				scalecolor(sr.rcol, np->tspec);
+				multcolor(sr.rcol, np->mcolor);	/* modified */
+				addcolor(r->rcol, sr.rcol);
+				break;
 			}
 		}
+		ndims--;
 	}
 }