--- ray/src/hd/rholo2.c	1998/12/01 15:47:05	3.19
+++ ray/src/hd/rholo2.c	2003/07/21 22:30:18	3.26
@@ -1,9 +1,6 @@
-/* Copyright (c) 1998 Silicon Graphics, Inc. */
-
 #ifndef lint
-static char SCCSid[] = "$SunId$ SGI";
+static const char	RCSid[] = "$Id: rholo2.c,v 3.26 2003/07/21 22:30:18 schorsch Exp $";
 #endif
-
 /*
  * Rtrace support routines for holodeck rendering
  */
@@ -19,67 +16,130 @@ struct gclim {
 	HOLO	*hp;			/* holodeck pointer */
 	GCOORD	gc;			/* grid cell */
 	FVECT	egp;			/* eye grid point */
-	double	erg[2];			/* eye range in wall grid coords */
+	double	erg2;			/* mean square eye grid range */
 	double	gmin[2], gmax[2];	/* grid coordinate limits */
 };				/* a grid coordinate range */
 
 
 static
-initeyelim(gcl, hd, gc)		/* initialize grid coordinate limits */
+initeyelim(gcl, hp, gc)		/* initialize grid coordinate limits */
 register struct gclim	*gcl;
-int	hd;
+register HOLO	*hp;
 GCOORD	*gc;
 {
-	register FLOAT	*v;
+	register RREAL	*v;
 	register int	i;
 
-	gcl->hp = hdlist[hd];
-	copystruct(&gcl->gc, gc);
-	hdgrid(gcl->egp, gcl->hp, myeye.vpt);
-	for (i = 0; i < 2; i++) {
-		v = gcl->hp->wg[((gcl->gc.w>>1)+i+1)%3];
-		gcl->erg[i] = myeye.rng * VLEN(v);
-		gcl->gmin[i] = FHUGE; gcl->gmax[i] = -FHUGE;
+	if (hp != NULL) {
+		hdgrid(gcl->egp, gcl->hp = hp, myeye.vpt);
+		gcl->erg2 = 0;
+		for (i = 0, v = hp->wg[0]; i < 3; i++, v += 3)
+			gcl->erg2 += DOT(v,v);
+		gcl->erg2 *= (1./3.) * myeye.rng*myeye.rng;
 	}
+	if (gc != NULL)
+		gcl->gc = *gc;
+	gcl->gmin[0] = gcl->gmin[1] = FHUGE;
+	gcl->gmax[0] = gcl->gmax[1] = -FHUGE;
 }
 
 
 static
-groweyelim(gcl, gp)		/* grow grid limits about eye point */
+groweyelim(gcl, gc, r0, r1, tight)	/* grow grid limits about eye point */
 register struct gclim	*gcl;
-FVECT	gp;
+GCOORD	*gc;
+double	r0, r1;
+int	tight;
 {
-	FVECT	ab;
-	double	l2, d, mult, wg;
-	register int	i, g;
-
+	FVECT	gp, ab;
+	double	ab2, od, cfact;
+	double	sqcoef[3], ctcoef[3], licoef[3], cnst;
+	int	gw, gi[2];
+	double	wallpos, a, b, c, d, e, f;
+	double	root[2], yex;
+	int	n, i, j, nex;
+						/* point/view cone */
+	i = gc->w>>1;
+	gp[i] = gc->w&1 ? gcl->hp->grid[i] : 0;
+	gp[hdwg0[gc->w]] = gc->i[0] + r0;
+	gp[hdwg1[gc->w]] = gc->i[1] + r1;
 	VSUB(ab, gcl->egp, gp);
-	l2 = DOT(ab,ab);
-	if (l2 <= gcl->erg[0]*gcl->erg[1]) {
+	ab2 = DOT(ab, ab);
+	gw = gcl->gc.w>>1;
+	if ((i==gw ? ab[gw]*ab[gw] : ab2)  <= gcl->erg2 + FTINY) {
 		gcl->gmin[0] = gcl->gmin[1] = -FHUGE;
 		gcl->gmax[0] = gcl->gmax[1] = FHUGE;
-		return;
+		return;			/* too close (to wall) */
 	}
-	mult = gp[g = gcl->gc.w>>1];
-	if (gcl->gc.w&1)
-		mult -= gcl->hp->grid[g];
-	if (ab[g]*ab[g] > gcl->erg[0]*gcl->erg[1])
-		mult /= -ab[g];
-	else if (fabs(ab[hdwg0[gcl->gc.w]]) > fabs(ab[hdwg1[gcl->gc.w]]))
-		mult = (gcl->gc.i[0] + .5 - gp[hdwg0[gcl->gc.w]]) /
-				ab[hdwg0[gcl->gc.w]];
-	else
-		mult = (gcl->gc.i[1] + .5 - gp[hdwg1[gcl->gc.w]]) /
-				ab[hdwg1[gcl->gc.w]];
+	ab2 = 1./ab2;				/* 1/norm2(ab) */
+	od = DOT(gp, ab);			/* origin dot direction */
+	cfact = 1./(1. - ab2*gcl->erg2);	/* tan^2 + 1 of cone angle */
+	for (i = 0; i < 3; i++) {		/* compute cone equation */
+		sqcoef[i] = ab[i]*ab[i]*cfact*ab2 - 1.;
+		ctcoef[i] = 2.*ab[i]*ab[(i+1)%3]*cfact*ab2;
+		licoef[i] = 2.*(gp[i] - ab[i]*cfact*od*ab2);
+	}
+	cnst = cfact*od*od*ab2 - DOT(gp,gp);
+	/*
+	 * CONE:	sqcoef[0]*x*x + sqcoef[1]*y*y + sqcoef[2]*z*z
+	 *		+ ctcoef[0]*x*y + ctcoef[1]*y*z + ctcoef[2]*z*x
+	 *		+ licoef[0]*x + licoef[1]*y + licoef[2]*z + cnst == 0
+	 */
+				/* equation for conic section in plane */
+	gi[0] = hdwg0[gcl->gc.w];
+	gi[1] = hdwg1[gcl->gc.w];
+	wallpos = gcl->gc.w&1 ? gcl->hp->grid[gw] : 0;
+	a = sqcoef[gi[0]];					/* x2 */
+	b = ctcoef[gi[0]];					/* xy */
+	c = sqcoef[gi[1]];					/* y2 */
+	d = ctcoef[gw]*wallpos + licoef[gi[0]];			/* x */
+	e = ctcoef[gi[1]]*wallpos + licoef[gi[1]];		/* y */
+	f = wallpos*(wallpos*sqcoef[gw] + licoef[gw]) + cnst;
 	for (i = 0; i < 2; i++) {
-		g = ((gcl->gc.w>>1)+i+1)%3;
-		wg = gp[g] + mult*ab[g];
-		d = mult*gcl->erg[i];
-		if (d < 0.) d = -d;
-		if (wg - d < gcl->gmin[i])
-			gcl->gmin[i] = wg - d;
-		if (wg + d > gcl->gmax[i])
-			gcl->gmax[i] = wg + d;
+		if (i) {		/* swap x and y coefficients */
+			register double	t;
+			t = a; a = c; c = t;
+			t = d; d = e; e = t;
+		}
+		nex = 0;		/* check global extrema */
+		n = quadratic(root, a*(4.*a*c-b*b), 2.*a*(2.*c*d-b*e),
+				d*(c*d-b*e) + f*b*b);
+		while (n-- > 0) {
+			if (gc->w>>1 == gi[i] &&
+					(gc->w&1) ^ root[n] < gp[gc->w>>1]) {
+				if (gc->w&1)
+					gcl->gmin[i] = -FHUGE;
+				else
+					gcl->gmax[i] = FHUGE;
+				nex++;
+				continue;		/* hyperbolic */
+			}
+			if (tight) {
+				yex = (-2.*a*root[n] - d)/b;
+				if (yex < gcl->gc.i[1-i] ||
+						yex > gcl->gc.i[1-i]+1)
+					continue;	/* outside cell */
+			}
+			if (root[n] < gcl->gmin[i])
+				gcl->gmin[i] = root[n];
+			if (root[n] > gcl->gmax[i])
+				gcl->gmax[i] = root[n];
+			nex++;
+		}
+					/* check local extrema */
+		for (j = nex < 2 ? 2 : 0; j--; ) {
+			yex = gcl->gc.i[1-i] + j;
+			n = quadratic(root, a, b*yex+d, yex*(yex*c+e)+f);
+			while (n-- > 0) {
+				if (gc->w>>1 == gi[i] &&
+					(gc->w&1) ^ root[n] < gp[gc->w>>1])
+					continue;
+				if (root[n] < gcl->gmin[i])
+					gcl->gmin[i] = root[n];
+				if (root[n] > gcl->gmax[i])
+					gcl->gmax[i] = root[n];
+			}
+		}
 	}
 }
 
@@ -97,13 +157,14 @@ register struct gclim	*gcl;
 			gcl->gmin[i] = gcl->gc.i[i];
 		if (gcl->gmax[i] > gcl->gc.i[i]+1)
 			gcl->gmax[i] = gcl->gc.i[i]+1;
-		if ((incell &= gcl->gmax[i] > gcl->gmin[i])) {
+		if (gcl->gmax[i] > gcl->gmin[i]) {
 			rrng[i][0] = 256.*(gcl->gmin[i] - gcl->gc.i[i]) +
 					(1.-FTINY);
 			rrng[i][1] = 256.*(gcl->gmax[i] - gcl->gc.i[i]) +
 					(1.-FTINY) - rrng[i][0];
-			incell &= rrng[i][1] > 0;
-		}
+		} else
+			rrng[i][0] = rrng[i][1] = 0;
+		incell &= rrng[i][1] > 0;
 	}
 	return(incell);
 }
@@ -113,9 +174,8 @@ packrays(rod, p)		/* pack ray origins and directions *
 register float	*rod;
 register PACKET	*p;
 {
-#define gp	ro
-#ifdef DEBUG
-	double dist2sum = 0.;
+#if 0
+	double	dist2sum = 0.;
 	FVECT	vt;
 #endif
 	int	nretries = p->nr + 2;
@@ -130,37 +190,32 @@ register PACKET	*p;
 	if (!hdbcoord(gc, hdlist[p->hd], p->bi))
 		error(CONSISTENCY, "bad beam index in packrays");
 	if ((useyelim = myeye.rng > FTINY)) {
-		initeyelim(&eyelim, p->hd, gc);
-		gp[gc[1].w>>1] = gc[1].w&1 ?
-				hdlist[p->hd]->grid[gc[1].w>>1] : 0;
-		gp[hdwg0[gc[1].w]] = gc[1].i[0];
-		gp[hdwg1[gc[1].w]] = gc[1].i[1];
-		groweyelim(&eyelim, gp);
-		gp[hdwg0[gc[1].w]]++;
-		gp[hdwg1[gc[1].w]]++;
-		groweyelim(&eyelim, gp);
-		useyelim &= clipeyelim(rrng0, &eyelim);
+		initeyelim(&eyelim, hdlist[p->hd], gc);
+		groweyelim(&eyelim, gc+1, 0., 0., 0);
+		groweyelim(&eyelim, gc+1, 1., 1., 0);
+		useyelim = clipeyelim(rrng0, &eyelim);
+#ifdef DEBUG
+		if (!useyelim)
+			error(WARNING, "no eye overlap in packrays");
+#endif
 	}
 	for (i = 0; i < p->nr; i++) {
 	retry:
 		if (useyelim) {
+			initeyelim(&eyelim, NULL, gc+1);
 			p->ra[i].r[0][0] = (int)(frandom()*rrng0[0][1])
 						+ rrng0[0][0];
 			p->ra[i].r[0][1] = (int)(frandom()*rrng0[1][1])
 						+ rrng0[1][0];
-			initeyelim(&eyelim, p->hd, gc+1);
-			gp[gc[0].w>>1] = gc[0].w&1 ?
-					hdlist[p->hd]->grid[gc[0].w>>1] : 0;
-			gp[hdwg0[gc[0].w]] = gc[0].i[0] +
-					(1./256.)*(p->ra[i].r[0][0]+.5);
-			gp[hdwg1[gc[0].w]] = gc[0].i[1] +
-					(1./256.)*(p->ra[i].r[0][1]+.5);
-			groweyelim(&eyelim, gp);
+			groweyelim(&eyelim, gc,
+					(1./256.)*(p->ra[i].r[0][0]+.5),
+					(1./256.)*(p->ra[i].r[0][1]+.5), 1);
 			if (!clipeyelim(rrng1, &eyelim)) {
-				useyelim &= nretries-- > 0;
+				useyelim = nretries-- > 0;
 #ifdef DEBUG
 				if (!useyelim)
-					error(WARNING, "exceeded retry limit in packrays");
+					error(WARNING,
+					"exceeded retry limit in packrays");
 #endif
 				goto retry;
 			}
@@ -175,7 +230,7 @@ register PACKET	*p;
 			p->ra[i].r[1][1] = frandom() * 256.;
 		}
 		d = hdray(ro, rd, hdlist[p->hd], gc, p->ra[i].r);
-#ifdef DEBUG
+#if 0
 		VSUM(vt, ro, rd, d);
 		dist2sum += dist2line(myeye.vpt, ro, vt);
 #endif
@@ -190,10 +245,10 @@ register PACKET	*p;
 		VCOPY(rod, rd);
 		rod += 3;
 	}
-#ifdef DEBUG
-	fprintf(stderr, "RMS distance = %f\n", sqrt(dist2sum/p->nr));
+#if 0
+	fprintf(stderr, "%f RMS (%d retries)\t", sqrt(dist2sum/p->nr),
+			p->nr + 2 - nretries);
 #endif
-#undef gp
 }
 
 
@@ -222,7 +277,7 @@ done_rtrace()			/* clean up and close rtrace calculati
 	int	status;
 					/* already closed? */
 	if (!nprocs)
-		return;
+		return(0);
 					/* flush beam queue */
 	done_packets(flush_queue());
 					/* sync holodeck */
@@ -293,7 +348,7 @@ getradfile()			/* run rad and get needed variables */
 			pippt = NULL;
 		}
 	if (pippt != NULL)
-		strcpy(pippt, "> /dev/null");	/* nothing to match */
+		strcpy(pippt, "> " NULL_DEVICE);	/* nothing to match */
 	else
 		sprintf(cp, ")[ \t]*=' > %s", tf2);
 #ifdef DEBUG