src/rt/normal.c

/* Copyright (c) 1992 Regents of the University of California */

#ifndef lint
static char SCCSid[] = "$SunId$ LBL";
#endif

/*
 *  normal.c - shading function for normal materials.
 *
 *     8/19/85
 *     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  "otypes.h"

#include  "random.h"

/*
 *      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.
 *      We orient the surface towards the incoming ray, so a single
 *  surface can be used to represent an infinitely thin object.
 *
 *  Arguments for MAT_PLASTIC and MAT_METAL are:
 *      red     grn     blu     specular-frac.  facet-slope
 *
 *  Arguments for MAT_TRANS are:
 *      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        010             /* purely specular (zero roughness) */

typedef struct {
        OBJREC  *mp;            /* material 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 */
        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 */


dirnorm(cval, np, ldir, omega)          /* compute source contribution */
COLOR  cval;                    /* returned coefficient */
register NORMDAT  *np;          /* material data */
FVECT  ldir;                    /* light source direction */
double  omega;                  /* light source size */
{
        double  ldot;
        double  dtmp;
        COLOR  ctmp;

        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 */

        if (ldot > FTINY && np->rdiff > 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 * np->rdiff / 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 + source */
                dtmp = 2.0*np->alpha2 + omega/(2.0*PI);
                                                /* gaussian */
                dtmp = exp((DOT(np->vrefl,ldir)-1.)/dtmp)/(2.*PI)/dtmp;
                                                /* worth using? */
                if (dtmp > FTINY) {
                        copycolor(ctmp, np->scolor);
                        dtmp *= omega / np->pdot;
                        scalecolor(ctmp, dtmp);
                        addcolor(cval, ctmp);
                }
        }
        if (ldot < -FTINY && np->tdiff > FTINY) {
                /*
                 *  Compute diffuse transmission.
                 */
                copycolor(ctmp, np->mcolor);
                dtmp = -ldot * omega * np->tdiff / 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/(2.0*PI);
                                                /* gaussian */
                dtmp = exp((DOT(np->prdir,ldir)-1.)/dtmp)/(2.*PI)/dtmp;
                                                /* worth using? */
                if (dtmp > FTINY) {
                        copycolor(ctmp, np->mcolor);
                        dtmp *= np->tspec * omega / np->pdot;
                        scalecolor(ctmp, dtmp);
                        addcolor(cval, ctmp);
                }
        }
}


m_normal(m, r)                  /* color a ray that hit something normal */
register OBJREC  *m;
register RAY  *r;
{
        NORMDAT  nd;
        double  transtest, transdist;
        double  dtmp;
        COLOR  ctmp;
        register int  i;
                                                /* easy shadow test */
        if (r->crtype & SHADOW && m->otype != MAT_TRANS)
                return;

        if (m->oargs.nfargs != (m->otype == MAT_TRANS ? 7 : 5))
                objerror(m, USER, "bad number of arguments");
        nd.mp = m;
                                                /* get material color */
        setcolor(nd.mcolor, m->oargs.farg[0],
                           m->oargs.farg[1],
                           m->oargs.farg[2]);
                                                /* get roughness */
        nd.specfl = 0;
        nd.alpha2 = m->oargs.farg[4];
        if ((nd.alpha2 *= nd.alpha2) <= FTINY)
                nd.specfl |= SP_PURE;
                                                /* reorient if necessary */
        if (r->rod < 0.0)
                flipsurface(r);
                                                /* get modifiers */
        raytexture(r, m->omod);
        nd.pdot = raynormal(nd.pnorm, r);       /* perturb normal */
        if (nd.pdot < .001)
                nd.pdot = .001;                 /* non-zero for dirnorm() */
        multcolor(nd.mcolor, r->pcol);          /* modify material color */
        transtest = 0;
                                                /* get specular component */
        if ((nd.rspec = m->oargs.farg[3]) > FTINY) {
                nd.specfl |= SP_REFL;
                                                /* compute specular color */
                if (m->otype == MAT_METAL)
                        copycolor(nd.scolor, nd.mcolor);
                else
                        setcolor(nd.scolor, 1.0, 1.0, 1.0);
                scalecolor(nd.scolor, nd.rspec);
                                                /* improved model */
                dtmp = exp(-BSPEC(m)*nd.pdot);
                for (i = 0; i < 3; i++)
                        colval(nd.scolor,i) += (1.0-colval(nd.scolor,i))*dtmp;
                nd.rspec += (1.0-nd.rspec)*dtmp;
                                                /* compute reflected ray */
                for (i = 0; i < 3; i++)
                        nd.vrefl[i] = r->rdir[i] + 2.0*nd.pdot*nd.pnorm[i];

                if (!(r->crtype & SHADOW) && nd.specfl & 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);
                        }
                }
        }
                                                /* compute transmission */
        if (m->otype == MAT_TRANS) {
                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;
                        if (r->crtype & SHADOW ||
                                        DOT(r->pert,r->pert) <= FTINY*FTINY) {
                                VCOPY(nd.prdir, r->rdir);
                                transtest = 2;
                        } else {
                                for (i = 0; i < 3; i++)         /* perturb */
                                        nd.prdir[i] = r->rdir[i] -
                                                        .75*r->pert[i];
                                normalize(nd.prdir);
                        }
                }
        } else
                nd.tdiff = nd.tspec = nd.trans = 0.0;
                                                /* transmitted ray */
        if ((nd.specfl&(SP_TRAN|SP_PURE)) == (SP_TRAN|SP_PURE)) {
                RAY  lr;
                if (rayorigin(&lr, r, TRANS, nd.tspec) == 0) {
                        VCOPY(lr.rdir, nd.prdir);
                        rayvalue(&lr);
                        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;
                                                /* diffuse reflection */
        nd.rdiff = 1.0 - nd.trans - nd.rspec;

        if (nd.specfl & SP_PURE && nd.rdiff <= FTINY && nd.tdiff <= FTINY)
                return;                         /* 100% pure specular */

        if (nd.specfl & (SP_REFL|SP_TRAN) && !(nd.specfl & SP_PURE))
                gaussamp(r, &nd);

        if (nd.rdiff > FTINY) {         /* ambient from this side */
                ambient(ctmp, r);
                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);
                ambient(ctmp, r);
                scalecolor(ctmp, nd.tdiff);
                multcolor(ctmp, nd.mcolor);     /* modified by color */
                addcolor(r->rcol, ctmp);
                flipsurface(r);
        }
                                        /* add direct component */
        direct(r, dirnorm, &nd);
                                        /* check distance */
        if (transtest > bright(r->rcol))
                r->rt = transdist;
}


static
gaussamp(r, np)                 /* sample gaussian specular */
RAY  *r;
register NORMDAT  *np;
{
        RAY  sr;
        FVECT  u, v, h;
        double  rv[2];
        double  d, sinp, cosp;
        int  confuse;
        register int  i;
                                        /* 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 &&
                        rayorigin(&sr, r, SPECULAR, np->rspec) == 0) {
                confuse = 0;
                dimlist[ndims++] = (int)np->mp;
        refagain:
                dimlist[ndims] = confuse += 3601;
                d = urand(ilhash(dimlist,ndims+1)+samplendx);
                multisamp(rv, 2, d);
                d = 2.0*PI * rv[0];
                cosp = cos(d);
                sinp = sin(d);
                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)      /* oops! */
                        goto refagain;
                rayvalue(&sr);
                multcolor(sr.rcol, np->scolor);
                addcolor(r->rcol, sr.rcol);
                ndims--;
        }
                                        /* compute transmission */
}
Revision:	2.2
Committed:	Sat Jan 4 19:53:53 1992 UTC (32 years, 4 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.1:	+96 -33 lines
Log Message:	added specular sampling
#	User	Rev	Content
1	greg	2.2	/* Copyright (c) 1992 Regents of the University of California */
2	greg	1.1
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* normal.c - shading function for normal materials.
9			*
10			* 8/19/85
11			* 12/19/85 - added stuff for metals.
12			* 6/26/87 - improved specular model.
13			* 9/28/87 - added model for translucent materials.
14	greg	2.2	* Later changes described in delta comments.
15	greg	1.1	*/
16
17			#include "ray.h"
18
19			#include "otypes.h"
20
21	greg	2.2	#include "random.h"
22
23	greg	1.1	/*
24			* This routine uses portions of the reflection
25			* model described by Cook and Torrance.
26			* The computation of specular components has been simplified by
27			* numerous approximations and ommisions to improve speed.
28			* We orient the surface towards the incoming ray, so a single
29			* surface can be used to represent an infinitely thin object.
30			*
31			* Arguments for MAT_PLASTIC and MAT_METAL are:
32			* red grn blu specular-frac. facet-slope
33			*
34			* Arguments for MAT_TRANS are:
35			* red grn blu rspec rough trans tspec
36			*/
37
38			#define BSPEC(m) (6.0) /* specularity parameter b */
39
40	greg	2.2	/* specularity flags */
41			#define SP_REFL 01 /* has reflected specular component */
42			#define SP_TRAN 02 /* has transmitted specular */
43			#define SP_PURE 010 /* purely specular (zero roughness) */
44	greg	1.1
45	greg	1.3	typedef struct {
46			OBJREC mp; / material pointer */
47	greg	2.2	short specfl; /* specularity flags, defined above */
48	greg	1.1	COLOR mcolor; /* color of this material */
49			COLOR scolor; /* color of specular component */
50			FVECT vrefl; /* vector in direction of reflected ray */
51	greg	1.14	FVECT prdir; /* vector in transmitted direction */
52	greg	2.2	double alpha2; /* roughness squared */
53	greg	1.1	double rdiff, rspec; /* reflected specular, diffuse */
54			double trans; /* transmissivity */
55			double tdiff, tspec; /* transmitted specular, diffuse */
56			FVECT pnorm; /* perturbed surface normal */
57			double pdot; /* perturbed dot product */
58	greg	1.3	} NORMDAT; /* normal material data */
59
60
61			dirnorm(cval, np, ldir, omega) /* compute source contribution */
62			COLOR cval; /* returned coefficient */
63			register NORMDAT np; / material data */
64			FVECT ldir; /* light source direction */
65			double omega; /* light source size */
66			{
67	greg	1.1	double ldot;
68	greg	1.3	double dtmp;
69			COLOR ctmp;
70
71			setcolor(cval, 0.0, 0.0, 0.0);
72
73			ldot = DOT(np->pnorm, ldir);
74
75			if (ldot < 0.0 ? np->trans <= FTINY : np->trans >= 1.0-FTINY)
76			return; /* wrong side */
77
78			if (ldot > FTINY && np->rdiff > FTINY) {
79			/*
80	greg	1.4	* Compute and add diffuse reflected component to returned
81			* color. The diffuse reflected component will always be
82			* modified by the color of the material.
83	greg	1.3	*/
84			copycolor(ctmp, np->mcolor);
85			dtmp = ldot * omega * np->rdiff / PI;
86			scalecolor(ctmp, dtmp);
87			addcolor(cval, ctmp);
88			}
89	greg	2.2	if (ldot > FTINY && (np->specfl&(SP_REFL\|SP_PURE)) == SP_REFL) {
90	greg	1.3	/*
91			* Compute specular reflection coefficient using
92			* gaussian distribution model.
93			*/
94			/* roughness + source */
95	greg	2.2	dtmp = 2.0np->alpha2 + omega/(2.0PI);
96	greg	1.3	/* gaussian */
97			dtmp = exp((DOT(np->vrefl,ldir)-1.)/dtmp)/(2.*PI)/dtmp;
98			/* worth using? */
99			if (dtmp > FTINY) {
100			copycolor(ctmp, np->scolor);
101	greg	1.13	dtmp *= omega / np->pdot;
102	greg	1.3	scalecolor(ctmp, dtmp);
103			addcolor(cval, ctmp);
104			}
105			}
106			if (ldot < -FTINY && np->tdiff > FTINY) {
107			/*
108			* Compute diffuse transmission.
109			*/
110			copycolor(ctmp, np->mcolor);
111			dtmp = -ldot * omega * np->tdiff / PI;
112			scalecolor(ctmp, dtmp);
113			addcolor(cval, ctmp);
114			}
115	greg	2.2	if (ldot < -FTINY && (np->specfl&(SP_TRAN\|SP_PURE)) == SP_TRAN) {
116	greg	1.3	/*
117	greg	1.4	* Compute specular transmission. Specular transmission
118	greg	1.13	* is always modified by material color.
119	greg	1.3	*/
120			/* roughness + source */
121			dtmp = np->alpha2 + omega/(2.0*PI);
122			/* gaussian */
123	greg	1.14	dtmp = exp((DOT(np->prdir,ldir)-1.)/dtmp)/(2.*PI)/dtmp;
124	greg	1.3	/* worth using? */
125			if (dtmp > FTINY) {
126	greg	1.13	copycolor(ctmp, np->mcolor);
127			dtmp = np->tspec omega / np->pdot;
128			scalecolor(ctmp, dtmp);
129	greg	1.3	addcolor(cval, ctmp);
130			}
131			}
132			}
133
134
135	greg	2.2	m_normal(m, r) /* color a ray that hit something normal */
136	greg	1.3	register OBJREC *m;
137			register RAY *r;
138			{
139			NORMDAT nd;
140	greg	1.9	double transtest, transdist;
141	greg	1.1	double dtmp;
142			COLOR ctmp;
143			register int i;
144			/* easy shadow test */
145			if (r->crtype & SHADOW && m->otype != MAT_TRANS)
146			return;
147	greg	2.2
148			if (m->oargs.nfargs != (m->otype == MAT_TRANS ? 7 : 5))
149			objerror(m, USER, "bad number of arguments");
150	greg	1.3	nd.mp = m;
151	greg	1.1	/* get material color */
152	greg	1.3	setcolor(nd.mcolor, m->oargs.farg[0],
153	greg	1.1	m->oargs.farg[1],
154			m->oargs.farg[2]);
155			/* get roughness */
156	greg	2.2	nd.specfl = 0;
157	greg	1.3	nd.alpha2 = m->oargs.farg[4];
158	greg	2.2	if ((nd.alpha2 *= nd.alpha2) <= FTINY)
159			nd.specfl \|= SP_PURE;
160	greg	1.1	/* reorient if necessary */
161			if (r->rod < 0.0)
162			flipsurface(r);
163			/* get modifiers */
164			raytexture(r, m->omod);
165	greg	1.3	nd.pdot = raynormal(nd.pnorm, r); /* perturb normal */
166	greg	1.13	if (nd.pdot < .001)
167			nd.pdot = .001; /* non-zero for dirnorm() */
168	greg	1.3	multcolor(nd.mcolor, r->pcol); /* modify material color */
169	greg	1.9	transtest = 0;
170	greg	1.1	/* get specular component */
171	greg	2.2	if ((nd.rspec = m->oargs.farg[3]) > FTINY) {
172			nd.specfl \|= SP_REFL;
173	greg	1.1	/* compute specular color */
174			if (m->otype == MAT_METAL)
175	greg	1.3	copycolor(nd.scolor, nd.mcolor);
176	greg	1.1	else
177	greg	1.3	setcolor(nd.scolor, 1.0, 1.0, 1.0);
178			scalecolor(nd.scolor, nd.rspec);
179	greg	1.1	/* improved model */
180	greg	1.3	dtmp = exp(-BSPEC(m)*nd.pdot);
181	greg	1.1	for (i = 0; i < 3; i++)
182	greg	1.3	colval(nd.scolor,i) += (1.0-colval(nd.scolor,i))*dtmp;
183			nd.rspec += (1.0-nd.rspec)*dtmp;
184	greg	1.1	/* compute reflected ray */
185			for (i = 0; i < 3; i++)
186	greg	1.3	nd.vrefl[i] = r->rdir[i] + 2.0nd.pdotnd.pnorm[i];
187	greg	1.1
188	greg	2.2	if (!(r->crtype & SHADOW) && nd.specfl & SP_PURE) {
189	greg	1.3	RAY lr;
190			if (rayorigin(&lr, r, REFLECTED, nd.rspec) == 0) {
191			VCOPY(lr.rdir, nd.vrefl);
192	greg	1.1	rayvalue(&lr);
193	greg	1.3	multcolor(lr.rcol, nd.scolor);
194	greg	1.1	addcolor(r->rcol, lr.rcol);
195			}
196	greg	1.3	}
197	greg	1.1	}
198	greg	1.3	/* compute transmission */
199	greg	1.1	if (m->otype == MAT_TRANS) {
200	greg	1.3	nd.trans = m->oargs.farg[5]*(1.0 - nd.rspec);
201			nd.tspec = nd.trans * m->oargs.farg[6];
202			nd.tdiff = nd.trans - nd.tspec;
203	greg	2.2	if (nd.tspec > FTINY) {
204			nd.specfl \|= SP_TRAN;
205			if (r->crtype & SHADOW \|\|
206			DOT(r->pert,r->pert) <= FTINY*FTINY) {
207			VCOPY(nd.prdir, r->rdir);
208			transtest = 2;
209			} else {
210			for (i = 0; i < 3; i++) /* perturb */
211			nd.prdir[i] = r->rdir[i] -
212			.75*r->pert[i];
213			normalize(nd.prdir);
214			}
215	greg	1.14	}
216	greg	1.1	} else
217	greg	1.3	nd.tdiff = nd.tspec = nd.trans = 0.0;
218	greg	1.1	/* transmitted ray */
219	greg	2.2	if ((nd.specfl&(SP_TRAN\|SP_PURE)) == (SP_TRAN\|SP_PURE)) {
220	greg	1.3	RAY lr;
221			if (rayorigin(&lr, r, TRANS, nd.tspec) == 0) {
222	greg	1.14	VCOPY(lr.rdir, nd.prdir);
223	greg	1.1	rayvalue(&lr);
224	greg	1.3	scalecolor(lr.rcol, nd.tspec);
225	greg	1.8	multcolor(lr.rcol, nd.mcolor); /* modified by color */
226	greg	1.1	addcolor(r->rcol, lr.rcol);
227	greg	1.9	transtest *= bright(lr.rcol);
228			transdist = r->rot + lr.rt;
229	greg	1.1	}
230	greg	1.3	}
231	greg	2.2
232	greg	1.1	if (r->crtype & SHADOW) /* the rest is shadow */
233			return;
234			/* diffuse reflection */
235	greg	1.3	nd.rdiff = 1.0 - nd.trans - nd.rspec;
236	greg	1.1
237	greg	2.2	if (nd.specfl & SP_PURE && nd.rdiff <= FTINY && nd.tdiff <= FTINY)
238			return; /* 100% pure specular */
239	greg	1.1
240	greg	2.2	if (nd.specfl & (SP_REFL\|SP_TRAN) && !(nd.specfl & SP_PURE))
241			gaussamp(r, &nd);
242
243	greg	1.3	if (nd.rdiff > FTINY) { /* ambient from this side */
244	greg	1.2	ambient(ctmp, r);
245	greg	2.2	scalecolor(ctmp, nd.rdiff);
246	greg	1.3	multcolor(ctmp, nd.mcolor); /* modified by material color */
247	greg	1.2	addcolor(r->rcol, ctmp); /* add to returned color */
248			}
249	greg	1.3	if (nd.tdiff > FTINY) { /* ambient from other side */
250	greg	1.1	flipsurface(r);
251	greg	1.2	ambient(ctmp, r);
252	greg	2.2	scalecolor(ctmp, nd.tdiff);
253	greg	1.13	multcolor(ctmp, nd.mcolor); /* modified by color */
254	greg	1.1	addcolor(r->rcol, ctmp);
255			flipsurface(r);
256			}
257	greg	1.3	/* add direct component */
258			direct(r, dirnorm, &nd);
259	greg	1.9	/* check distance */
260			if (transtest > bright(r->rcol))
261			r->rt = transdist;
262	greg	2.2	}
263
264
265			static
266			gaussamp(r, np) /* sample gaussian specular */
267			RAY *r;
268			register NORMDAT *np;
269			{
270			RAY sr;
271			FVECT u, v, h;
272			double rv[2];
273			double d, sinp, cosp;
274			int confuse;
275			register int i;
276			/* set up sample coordinates */
277			v[0] = v[1] = v[2] = 0.0;
278			for (i = 0; i < 3; i++)
279			if (np->pnorm[i] < 0.6 && np->pnorm[i] > -0.6)
280			break;
281			v[i] = 1.0;
282			fcross(u, v, np->pnorm);
283			normalize(u);
284			fcross(v, np->pnorm, u);
285			/* compute reflection */
286			if (np->specfl & SP_REFL &&
287			rayorigin(&sr, r, SPECULAR, np->rspec) == 0) {
288			confuse = 0;
289			dimlist[ndims++] = (int)np->mp;
290			refagain:
291			dimlist[ndims] = confuse += 3601;
292			d = urand(ilhash(dimlist,ndims+1)+samplendx);
293			multisamp(rv, 2, d);
294			d = 2.0PI rv[0];
295			cosp = cos(d);
296			sinp = sin(d);
297			if (rv[1] <= FTINY)
298			d = 1.0;
299			else
300			d = sqrt( np->alpha2 * -log(rv[1]) );
301			for (i = 0; i < 3; i++)
302			h[i] = np->pnorm[i] + d(cospu[i] + sinp*v[i]);
303			d = -2.0 * DOT(h, r->rdir) / (1.0 + d*d);
304			for (i = 0; i < 3; i++)
305			sr.rdir[i] = r->rdir[i] + d*h[i];
306			if (DOT(sr.rdir, r->ron) <= FTINY) /* oops! */
307			goto refagain;
308			rayvalue(&sr);
309			multcolor(sr.rcol, np->scolor);
310			addcolor(r->rcol, sr.rcol);
311			ndims--;
312			}
313			/* compute transmission */
314	greg	1.1	}