src/rt/srcsamp.c

#ifndef lint
static const char       RCSid[] = "$Id: srcsamp.c,v 2.11 2003/09/13 17:31:35 greg Exp $";
#endif
/*
 * Source sampling routines
 *
 *  External symbols declared in source.h
 */

#include "copyright.h"

#include  "ray.h"

#include  "source.h"

#include  "random.h"


static int  cyl_partit(), flt_partit();


double
nextssamp(r, si)                /* compute sample for source, rtn. distance */
register RAY  *r;               /* origin is read, direction is set */
register SRCINDEX  *si;         /* source index (modified to current) */
{
        int  cent[3], size[3], parr[2];
        FVECT  vpos;
        double  d;
        register int  i;
nextsample:
        while (++si->sp >= si->np) {    /* get next sample */
                if (++si->sn >= nsources)
                        return(0.0);    /* no more */
                if (source[si->sn].sflags & SSKIP)
                        si->np = 0;
                else if (srcsizerat <= FTINY)
                        nopart(si, r);
                else {
                        for (i = si->sn; source[i].sflags & SVIRTUAL;
                                        i = source[i].sa.sv.sn)
                                ;               /* partition source */
                        (*sfun[source[i].so->otype].of->partit)(si, r);
                }
                si->sp = -1;
        }
                                        /* get partition */
        cent[0] = cent[1] = cent[2] = 0;
        size[0] = size[1] = size[2] = MAXSPART;
        parr[0] = 0; parr[1] = si->sp;
        if (!skipparts(cent, size, parr, si->spt))
                error(CONSISTENCY, "bad source partition in nextssamp");
                                        /* compute sample */
        if (dstrsrc > FTINY) {                  /* jitter sample */
                dimlist[ndims] = si->sn + 8831;
                dimlist[ndims+1] = si->sp + 3109;
                d = urand(ilhash(dimlist,ndims+2)+samplendx);
                if (source[si->sn].sflags & SFLAT) {
                        multisamp(vpos, 2, d);
                        vpos[SW] = 0.5;
                } else
                        multisamp(vpos, 3, d);
                for (i = 0; i < 3; i++)
                        vpos[i] = dstrsrc * (1. - 2.*vpos[i]) *
                                        (double)size[i]/MAXSPART;
        } else
                vpos[0] = vpos[1] = vpos[2] = 0.0;

        for (i = 0; i < 3; i++)
                vpos[i] += (double)cent[i]/MAXSPART;
                                        /* avoid circular aiming failures */
        if (source[si->sn].sflags & SCIR) {
                FVECT   trim;
                double  d;
                if (source[si->sn].sflags & (SFLAT|SDISTANT)) {
                        d = 1.12837917;         /* correct setflatss() */
                        trim[SU] = d*sqrt(1.0 - 0.5*vpos[SV]*vpos[SV]);
                        trim[SV] = d*sqrt(1.0 - 0.5*vpos[SU]*vpos[SU]);
                        trim[SW] = 0.0;
                } else {
                        trim[SW] = trim[SU] = vpos[SU]*vpos[SU];
                        d = vpos[SV]*vpos[SV];
                        if (d > trim[SW]) trim[SW] = d;
                        trim[SU] += d;
                        d = vpos[SW]*vpos[SW];
                        if (d > trim[SW]) trim[SW] = d;
                        trim[SU] += d;
                        d = 1.0/0.7236;         /* correct sphsetsrc() */
                        trim[SW] = trim[SV] = trim[SU] =
                                        d*sqrt(trim[SW]/trim[SU]);
                }
                for (i = 0; i < 3; i++)
                        vpos[i] *= trim[i];
        }
                                        /* compute direction */
        for (i = 0; i < 3; i++)
                r->rdir[i] = source[si->sn].sloc[i] +
                                vpos[SU]*source[si->sn].ss[SU][i] +
                                vpos[SV]*source[si->sn].ss[SV][i] +
                                vpos[SW]*source[si->sn].ss[SW][i];

        if (!(source[si->sn].sflags & SDISTANT))
                for (i = 0; i < 3; i++)
                        r->rdir[i] -= r->rorg[i];
                                        /* compute distance */
        if ((d = normalize(r->rdir)) == 0.0)
                goto nextsample;                /* at source! */

                                        /* compute sample size */
        if (source[si->sn].sflags & SFLAT) {
                si->dom = sflatform(si->sn, r->rdir);
                si->dom *= size[SU]*size[SV]/(MAXSPART*(double)MAXSPART);
        } else if (source[si->sn].sflags & SCYL) {
                si->dom = scylform(si->sn, r->rdir);
                si->dom *= size[SU]/(double)MAXSPART;
        } else {
                si->dom = size[SU]*size[SV]*(double)size[SW] /
                                (MAXSPART*MAXSPART*(double)MAXSPART) ;
        }
        if (source[si->sn].sflags & SDISTANT) {
                si->dom *= source[si->sn].ss2;
                return(FHUGE);
        }
        if (si->dom <= 1e-4)
                goto nextsample;                /* behind source? */
        si->dom *= source[si->sn].ss2/(d*d);
        return(d);              /* sample OK, return distance */
}


int
skipparts(ct, sz, pp, pt)               /* skip to requested partition */
int  ct[3], sz[3];              /* center and size of partition (returned) */
register int  pp[2];            /* current index, number to skip (modified) */
unsigned char  *pt;             /* partition array */
{
        register int  p;
                                        /* check this partition */
        p = spart(pt, pp[0]);
        pp[0]++;
        if (p == S0) {                  /* leaf partition */
                if (pp[1]) {
                        pp[1]--;
                        return(0);      /* not there yet */
                } else
                        return(1);      /* we've arrived */
        }
                                /* else check lower */
        sz[p] >>= 1;
        ct[p] -= sz[p];
        if (skipparts(ct, sz, pp, pt))
                return(1);      /* return hit */
                                /* else check upper */
        ct[p] += sz[p] << 1;
        if (skipparts(ct, sz, pp, pt))
                return(1);      /* return hit */
                                /* else return to starting position */
        ct[p] -= sz[p];
        sz[p] <<= 1;
        return(0);              /* return miss */
}


void
nopart(si, r)                   /* single source partition */
register SRCINDEX  *si;
RAY  *r;
{
        clrpart(si->spt);
        setpart(si->spt, 0, S0);
        si->np = 1;
}


void
cylpart(si, r)                  /* partition a cylinder */
SRCINDEX  *si;
register RAY  *r;
{
        double  dist2, safedist2, dist2cent, rad2;
        FVECT  v;
        register SRCREC  *sp;
        int  pi;
                                        /* first check point location */
        clrpart(si->spt);
        sp = source + si->sn;
        rad2 = 1.365 * DOT(sp->ss[SV],sp->ss[SV]);
        v[0] = r->rorg[0] - sp->sloc[0];
        v[1] = r->rorg[1] - sp->sloc[1];
        v[2] = r->rorg[2] - sp->sloc[2];
        dist2 = DOT(v,sp->ss[SU]);
        safedist2 = DOT(sp->ss[SU],sp->ss[SU]);
        dist2 *= dist2 / safedist2;
        dist2cent = DOT(v,v);
        dist2 = dist2cent - dist2;
        if (dist2 <= rad2) {            /* point inside extended cylinder */
                si->np = 0;
                return;
        }
        safedist2 *= 4.*r->rweight*r->rweight/(srcsizerat*srcsizerat);
        if (dist2 <= 4.*rad2 ||         /* point too close to subdivide */
                        dist2cent >= safedist2) {       /* or too far */
                setpart(si->spt, 0, S0);
                si->np = 1;
                return;
        }
        pi = 0;
        si->np = cyl_partit(r->rorg, si->spt, &pi, MAXSPART,
                        sp->sloc, sp->ss[SU], safedist2);
}


static int
cyl_partit(ro, pt, pi, mp, cent, axis, d2)      /* slice a cylinder */
FVECT  ro;
unsigned char  *pt;
register int  *pi;
int  mp;
FVECT  cent, axis;
double  d2;
{
        FVECT  newct, newax;
        int  npl, npu;

        if (mp < 2 || dist2(ro, cent) >= d2) {  /* hit limit? */
                setpart(pt, *pi, S0);
                (*pi)++;
                return(1);
        }
                                        /* subdivide */
        setpart(pt, *pi, SU);
        (*pi)++;
        newax[0] = .5*axis[0];
        newax[1] = .5*axis[1];
        newax[2] = .5*axis[2];
        d2 *= 0.25;
                                        /* lower half */
        newct[0] = cent[0] - newax[0];
        newct[1] = cent[1] - newax[1];
        newct[2] = cent[2] - newax[2];
        npl = cyl_partit(ro, pt, pi, mp/2, newct, newax, d2);
                                        /* upper half */
        newct[0] = cent[0] + newax[0];
        newct[1] = cent[1] + newax[1];
        newct[2] = cent[2] + newax[2];
        npu = cyl_partit(ro, pt, pi, mp/2, newct, newax, d2);
                                        /* return total */
        return(npl + npu);
}


void
flatpart(si, r)                         /* partition a flat source */
register SRCINDEX  *si;
register RAY  *r;
{
        register RREAL  *vp;
        FVECT  v;
        double  du2, dv2;
        int  pi;

        clrpart(si->spt);
        vp = source[si->sn].sloc;
        v[0] = r->rorg[0] - vp[0];
        v[1] = r->rorg[1] - vp[1];
        v[2] = r->rorg[2] - vp[2];
        vp = source[si->sn].snorm;
        if (DOT(v,vp) <= 0.) {          /* behind source */
                si->np = 0;
                return;
        }
        dv2 = 2.*r->rweight/srcsizerat;
        dv2 *= dv2;
        vp = source[si->sn].ss[SU];
        du2 = dv2 * DOT(vp,vp);
        vp = source[si->sn].ss[SV];
        dv2 *= DOT(vp,vp);
        pi = 0;
        si->np = flt_partit(r->rorg, si->spt, &pi, MAXSPART,
                source[si->sn].sloc,
                source[si->sn].ss[SU], source[si->sn].ss[SV], du2, dv2);
}


static int
flt_partit(ro, pt, pi, mp, cent, u, v, du2, dv2)        /* partition flatty */
FVECT  ro;
unsigned char  *pt;
register int  *pi;
int  mp;
FVECT  cent, u, v;
double  du2, dv2;
{
        double  d2;
        FVECT  newct, newax;
        int  npl, npu;

        if (mp < 2 || ((d2 = dist2(ro, cent)) >= du2
                        && d2 >= dv2)) {        /* hit limit? */
                setpart(pt, *pi, S0);
                (*pi)++;
                return(1);
        }
        if (du2 > dv2) {                        /* subdivide in U */
                setpart(pt, *pi, SU);
                (*pi)++;
                newax[0] = .5*u[0];
                newax[1] = .5*u[1];
                newax[2] = .5*u[2];
                u = newax;
                du2 *= 0.25;
        } else {                                /* subdivide in V */
                setpart(pt, *pi, SV);
                (*pi)++;
                newax[0] = .5*v[0];
                newax[1] = .5*v[1];
                newax[2] = .5*v[2];
                v = newax;
                dv2 *= 0.25;
        }
                                        /* lower half */
        newct[0] = cent[0] - newax[0];
        newct[1] = cent[1] - newax[1];
        newct[2] = cent[2] - newax[2];
        npl = flt_partit(ro, pt, pi, mp/2, newct, u, v, du2, dv2);
                                        /* upper half */
        newct[0] = cent[0] + newax[0];
        newct[1] = cent[1] + newax[1];
        newct[2] = cent[2] + newax[2];
        npu = flt_partit(ro, pt, pi, mp/2, newct, u, v, du2, dv2);
                                /* return total */
        return(npl + npu);
}


double
scylform(sn, dir)               /* compute cosine for cylinder's projection */
int  sn;
register FVECT  dir;            /* assume normalized */
{
        register RREAL  *dv;
        double  d;

        dv = source[sn].ss[SU];
        d = DOT(dir, dv);
        d *= d / DOT(dv,dv);
        return(sqrt(1. - d));
}
Revision:	2.12
Committed:	Sat Dec 6 01:08:53 2008 UTC (15 years, 4 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.11:	+26 -2 lines
Log Message:	Reduced occurrence of aiming failures for circular sources (Thanks to David G-M)
#	User	Rev	Content
1	greg	1.1	#ifndef lint
2	greg	2.12	static const char RCSid[] = "$Id: srcsamp.c,v 2.11 2003/09/13 17:31:35 greg Exp $";
3	greg	1.1	#endif
4			/*
5			* Source sampling routines
6	greg	2.7	*
7			* External symbols declared in source.h
8			*/
9
10	greg	2.8	#include "copyright.h"
11	greg	1.1
12	greg	1.4	#include "ray.h"
13	greg	1.1
14			#include "source.h"
15
16			#include "random.h"
17
18
19	greg	2.5	static int cyl_partit(), flt_partit();
20
21
22	greg	1.1	double
23	greg	1.4	nextssamp(r, si) /* compute sample for source, rtn. distance */
24			register RAY r; / origin is read, direction is set */
25	greg	1.1	register SRCINDEX si; / source index (modified to current) */
26			{
27			int cent[3], size[3], parr[2];
28			FVECT vpos;
29			double d;
30			register int i;
31	greg	2.2	nextsample:
32	greg	1.1	while (++si->sp >= si->np) { /* get next sample */
33			if (++si->sn >= nsources)
34			return(0.0); /* no more */
35	greg	1.7	if (source[si->sn].sflags & SSKIP)
36			si->np = 0;
37			else if (srcsizerat <= FTINY)
38	greg	1.4	nopart(si, r);
39	greg	1.1	else {
40			for (i = si->sn; source[i].sflags & SVIRTUAL;
41			i = source[i].sa.sv.sn)
42			; /* partition source */
43	greg	1.4	(*sfun[source[i].so->otype].of->partit)(si, r);
44	greg	1.1	}
45			si->sp = -1;
46			}
47			/* get partition */
48			cent[0] = cent[1] = cent[2] = 0;
49			size[0] = size[1] = size[2] = MAXSPART;
50			parr[0] = 0; parr[1] = si->sp;
51			if (!skipparts(cent, size, parr, si->spt))
52			error(CONSISTENCY, "bad source partition in nextssamp");
53			/* compute sample */
54			if (dstrsrc > FTINY) { /* jitter sample */
55			dimlist[ndims] = si->sn + 8831;
56			dimlist[ndims+1] = si->sp + 3109;
57			d = urand(ilhash(dimlist,ndims+2)+samplendx);
58			if (source[si->sn].sflags & SFLAT) {
59			multisamp(vpos, 2, d);
60	greg	2.12	vpos[SW] = 0.5;
61	greg	1.1	} else
62			multisamp(vpos, 3, d);
63			for (i = 0; i < 3; i++)
64			vpos[i] = dstrsrc * (1. - 2.vpos[i])
65			(double)size[i]/MAXSPART;
66			} else
67			vpos[0] = vpos[1] = vpos[2] = 0.0;
68
69			for (i = 0; i < 3; i++)
70			vpos[i] += (double)cent[i]/MAXSPART;
71	greg	2.12	/* avoid circular aiming failures */
72			if (source[si->sn].sflags & SCIR) {
73			FVECT trim;
74			double d;
75			if (source[si->sn].sflags & (SFLAT\|SDISTANT)) {
76			d = 1.12837917; /* correct setflatss() */
77			trim[SU] = dsqrt(1.0 - 0.5vpos[SV]*vpos[SV]);
78			trim[SV] = dsqrt(1.0 - 0.5vpos[SU]*vpos[SU]);
79			trim[SW] = 0.0;
80			} else {
81			trim[SW] = trim[SU] = vpos[SU]*vpos[SU];
82			d = vpos[SV]*vpos[SV];
83			if (d > trim[SW]) trim[SW] = d;
84			trim[SU] += d;
85			d = vpos[SW]*vpos[SW];
86			if (d > trim[SW]) trim[SW] = d;
87			trim[SU] += d;
88			d = 1.0/0.7236; /* correct sphsetsrc() */
89			trim[SW] = trim[SV] = trim[SU] =
90			d*sqrt(trim[SW]/trim[SU]);
91			}
92			for (i = 0; i < 3; i++)
93			vpos[i] *= trim[i];
94			}
95	greg	1.1	/* compute direction */
96			for (i = 0; i < 3; i++)
97	greg	1.4	r->rdir[i] = source[si->sn].sloc[i] +
98	greg	1.1	vpos[SU]*source[si->sn].ss[SU][i] +
99			vpos[SV]*source[si->sn].ss[SV][i] +
100			vpos[SW]*source[si->sn].ss[SW][i];
101
102			if (!(source[si->sn].sflags & SDISTANT))
103			for (i = 0; i < 3; i++)
104	greg	1.4	r->rdir[i] -= r->rorg[i];
105	greg	1.1	/* compute distance */
106	greg	1.4	if ((d = normalize(r->rdir)) == 0.0)
107	greg	2.2	goto nextsample; /* at source! */
108	greg	1.1
109			/* compute sample size */
110			if (source[si->sn].sflags & SFLAT) {
111	greg	2.6	si->dom = sflatform(si->sn, r->rdir);
112	greg	2.4	si->dom = size[SU]size[SV]/(MAXSPART*(double)MAXSPART);
113	greg	1.1	} else if (source[si->sn].sflags & SCYL) {
114	greg	2.6	si->dom = scylform(si->sn, r->rdir);
115	greg	2.4	si->dom *= size[SU]/(double)MAXSPART;
116	greg	1.1	} else {
117	greg	2.6	si->dom = size[SU]size[SV](double)size[SW] /
118	greg	2.4	(MAXSPARTMAXSPART(double)MAXSPART) ;
119	greg	1.1	}
120	greg	2.6	if (source[si->sn].sflags & SDISTANT) {
121			si->dom *= source[si->sn].ss2;
122	greg	1.1	return(FHUGE);
123	greg	2.6	}
124	greg	2.3	if (si->dom <= 1e-4)
125	greg	2.2	goto nextsample; /* behind source? */
126	greg	2.6	si->dom = source[si->sn].ss2/(dd);
127	greg	1.1	return(d); /* sample OK, return distance */
128			}
129
130
131	greg	2.7	int
132	greg	1.1	skipparts(ct, sz, pp, pt) /* skip to requested partition */
133			int ct[3], sz[3]; /* center and size of partition (returned) */
134			register int pp[2]; /* current index, number to skip (modified) */
135			unsigned char pt; / partition array */
136			{
137			register int p;
138			/* check this partition */
139			p = spart(pt, pp[0]);
140			pp[0]++;
141	schorsch	2.10	if (p == S0) { /* leaf partition */
142	greg	1.1	if (pp[1]) {
143			pp[1]--;
144			return(0); /* not there yet */
145			} else
146			return(1); /* we've arrived */
147	schorsch	2.10	}
148	greg	1.1	/* else check lower */
149			sz[p] >>= 1;
150			ct[p] -= sz[p];
151			if (skipparts(ct, sz, pp, pt))
152			return(1); /* return hit */
153			/* else check upper */
154			ct[p] += sz[p] << 1;
155			if (skipparts(ct, sz, pp, pt))
156			return(1); /* return hit */
157			/* else return to starting position */
158			ct[p] -= sz[p];
159			sz[p] <<= 1;
160			return(0); /* return miss */
161			}
162
163
164	greg	2.7	void
165	greg	1.4	nopart(si, r) /* single source partition */
166	greg	1.1	register SRCINDEX *si;
167	greg	1.4	RAY *r;
168	greg	1.1	{
169			clrpart(si->spt);
170			setpart(si->spt, 0, S0);
171			si->np = 1;
172			}
173
174
175	greg	2.7	void
176	greg	1.4	cylpart(si, r) /* partition a cylinder */
177	greg	1.1	SRCINDEX *si;
178	greg	1.4	register RAY *r;
179	greg	1.1	{
180			double dist2, safedist2, dist2cent, rad2;
181			FVECT v;
182			register SRCREC *sp;
183			int pi;
184			/* first check point location */
185			clrpart(si->spt);
186	greg	1.4	sp = source + si->sn;
187	greg	1.3	rad2 = 1.365 * DOT(sp->ss[SV],sp->ss[SV]);
188	greg	1.4	v[0] = r->rorg[0] - sp->sloc[0];
189			v[1] = r->rorg[1] - sp->sloc[1];
190			v[2] = r->rorg[2] - sp->sloc[2];
191	greg	1.1	dist2 = DOT(v,sp->ss[SU]);
192			safedist2 = DOT(sp->ss[SU],sp->ss[SU]);
193			dist2 *= dist2 / safedist2;
194			dist2cent = DOT(v,v);
195			dist2 = dist2cent - dist2;
196			if (dist2 <= rad2) { /* point inside extended cylinder */
197			si->np = 0;
198			return;
199			}
200	greg	1.4	safedist2 = 4.r->rweightr->rweight/(srcsizeratsrcsizerat);
201	greg	1.5	if (dist2 <= 4.rad2 \|\| / point too close to subdivide */
202			dist2cent >= safedist2) { /* or too far */
203	greg	1.1	setpart(si->spt, 0, S0);
204			si->np = 1;
205			return;
206			}
207			pi = 0;
208	greg	1.4	si->np = cyl_partit(r->rorg, si->spt, &pi, MAXSPART,
209	greg	1.1	sp->sloc, sp->ss[SU], safedist2);
210			}
211
212
213			static int
214			cyl_partit(ro, pt, pi, mp, cent, axis, d2) /* slice a cylinder */
215			FVECT ro;
216			unsigned char *pt;
217			register int *pi;
218			int mp;
219			FVECT cent, axis;
220			double d2;
221			{
222			FVECT newct, newax;
223			int npl, npu;
224
225			if (mp < 2 \|\| dist2(ro, cent) >= d2) { /* hit limit? */
226			setpart(pt, *pi, S0);
227			(*pi)++;
228			return(1);
229			}
230			/* subdivide */
231			setpart(pt, *pi, SU);
232			(*pi)++;
233			newax[0] = .5*axis[0];
234			newax[1] = .5*axis[1];
235			newax[2] = .5*axis[2];
236			d2 *= 0.25;
237			/* lower half */
238			newct[0] = cent[0] - newax[0];
239			newct[1] = cent[1] - newax[1];
240			newct[2] = cent[2] - newax[2];
241	greg	1.2	npl = cyl_partit(ro, pt, pi, mp/2, newct, newax, d2);
242	greg	1.1	/* upper half */
243			newct[0] = cent[0] + newax[0];
244			newct[1] = cent[1] + newax[1];
245			newct[2] = cent[2] + newax[2];
246	greg	1.2	npu = cyl_partit(ro, pt, pi, mp/2, newct, newax, d2);
247	greg	1.1	/* return total */
248			return(npl + npu);
249			}
250
251
252	greg	2.7	void
253	greg	1.4	flatpart(si, r) /* partition a flat source */
254	greg	1.1	register SRCINDEX *si;
255	greg	1.5	register RAY *r;
256	greg	1.1	{
257	schorsch	2.9	register RREAL *vp;
258	greg	1.5	FVECT v;
259	greg	1.1	double du2, dv2;
260			int pi;
261
262	greg	1.5	clrpart(si->spt);
263			vp = source[si->sn].sloc;
264			v[0] = r->rorg[0] - vp[0];
265			v[1] = r->rorg[1] - vp[1];
266			v[2] = r->rorg[2] - vp[2];
267			vp = source[si->sn].snorm;
268	greg	2.11	if (DOT(v,vp) <= 0.) { /* behind source */
269	greg	1.5	si->np = 0;
270			return;
271			}
272	greg	1.4	dv2 = 2.*r->rweight/srcsizerat;
273			dv2 *= dv2;
274	greg	1.1	vp = source[si->sn].ss[SU];
275	greg	1.4	du2 = dv2 * DOT(vp,vp);
276	greg	1.1	vp = source[si->sn].ss[SV];
277	greg	1.4	dv2 *= DOT(vp,vp);
278	greg	1.1	pi = 0;
279	greg	1.4	si->np = flt_partit(r->rorg, si->spt, &pi, MAXSPART,
280			source[si->sn].sloc,
281	greg	1.1	source[si->sn].ss[SU], source[si->sn].ss[SV], du2, dv2);
282			}
283
284
285			static int
286			flt_partit(ro, pt, pi, mp, cent, u, v, du2, dv2) /* partition flatty */
287			FVECT ro;
288			unsigned char *pt;
289			register int *pi;
290			int mp;
291			FVECT cent, u, v;
292			double du2, dv2;
293			{
294			double d2;
295			FVECT newct, newax;
296			int npl, npu;
297
298			if (mp < 2 \|\| ((d2 = dist2(ro, cent)) >= du2
299			&& d2 >= dv2)) { /* hit limit? */
300			setpart(pt, *pi, S0);
301			(*pi)++;
302			return(1);
303			}
304			if (du2 > dv2) { /* subdivide in U */
305			setpart(pt, *pi, SU);
306			(*pi)++;
307			newax[0] = .5*u[0];
308			newax[1] = .5*u[1];
309			newax[2] = .5*u[2];
310			u = newax;
311			du2 *= 0.25;
312			} else { /* subdivide in V */
313			setpart(pt, *pi, SV);
314			(*pi)++;
315			newax[0] = .5*v[0];
316			newax[1] = .5*v[1];
317			newax[2] = .5*v[2];
318			v = newax;
319			dv2 *= 0.25;
320			}
321			/* lower half */
322			newct[0] = cent[0] - newax[0];
323			newct[1] = cent[1] - newax[1];
324			newct[2] = cent[2] - newax[2];
325	greg	1.2	npl = flt_partit(ro, pt, pi, mp/2, newct, u, v, du2, dv2);
326	greg	1.1	/* upper half */
327			newct[0] = cent[0] + newax[0];
328			newct[1] = cent[1] + newax[1];
329			newct[2] = cent[2] + newax[2];
330	greg	1.2	npu = flt_partit(ro, pt, pi, mp/2, newct, u, v, du2, dv2);
331	greg	1.1	/* return total */
332			return(npl + npu);
333			}
334
335
336			double
337			scylform(sn, dir) /* compute cosine for cylinder's projection */
338			int sn;
339			register FVECT dir; /* assume normalized */
340			{
341	schorsch	2.9	register RREAL *dv;
342	greg	1.1	double d;
343
344			dv = source[sn].ss[SU];
345			d = DOT(dir, dv);
346			d *= d / DOT(dv,dv);
347			return(sqrt(1. - d));
348			}