src/rt/virtuals.c

/* Copyright (c) 1991 Regents of the University of California */

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

/*
 * Routines for simulating virtual light sources
 *      Thus far, we only support planar mirrors.
 */

#include  "ray.h"

#include  "otypes.h"

#include  "source.h"


double  intercircle(), getdisk();

static OBJECT  *vobject;                /* virtual source objects */
static int  nvobjects = 0;              /* number of virtual source objects */


markvirtuals()                  /* find and mark virtual sources */
{
        register OBJREC  *o;
        register int  i;
                                        /* check number of direct relays */
        if (directrelay <= 0)
                return;
                                        /* find virtual source objects */
        for (i = 0; i < nobjects; i++) {
                o = objptr(i);
                if (!issurface(o->otype) || o->omod == OVOID)
                        continue;
                if (!isvlight(objptr(o->omod)->otype))
                        continue;
                if (sfun[o->otype].of == NULL ||
                                sfun[o->otype].of->getpleq == NULL)
                        objerror(o, USER, "illegal material");
                if (nvobjects == 0)
                        vobject = (OBJECT *)malloc(sizeof(OBJECT));
                else
                        vobject = (OBJECT *)realloc((char *)vobject,
                                (unsigned)(nvobjects+1)*sizeof(OBJECT));
                if (vobject == NULL)
                        error(SYSTEM, "out of memory in addvirtuals");
                vobject[nvobjects++] = i;
        }
        if (nvobjects == 0)
                return;
#ifdef DEBUG
        fprintf(stderr, "found %d virtual source objects\n", nvobjects);
#endif
                                        /* append virtual sources */
        for (i = nsources; i-- > 0; )
                if (!(source[i].sflags & SSKIP))
                        addvirtuals(i, directrelay);
                                        /* done with our object list */
        free((char *)vobject);
        nvobjects = 0;
}


addvirtuals(sn, nr)             /* add virtuals associated with source */
int  sn;
int  nr;
{
        register int  i;
                                /* check relay limit first */
        if (nr <= 0)
                return;
                                /* check each virtual object for projection */
        for (i = 0; i < nvobjects; i++)
                                        /* vproject() calls us recursively */
                vproject(objptr(vobject[i]), sn, nr-1);
}


vproject(o, sn, n)              /* create projected source(s) if they exist */
OBJREC  *o;
int  sn;
int  n;
{
        register int  i;
        register VSMATERIAL  *vsmat;
        MAT4  proj;
        int  ns;

        if (o == source[sn].so) /* objects cannot project themselves */
                return;
                                /* get virtual source material */
        vsmat = sfun[objptr(o->omod)->otype].mf;
                                /* project virtual sources */
        for (i = 0; i < vsmat->nproj; i++)
                if ((*vsmat->vproj)(proj, o, &source[sn], i))
                        if ((ns = makevsrc(o, sn, proj)) >= 0) {
#ifdef DEBUG
                                virtverb(ns, stderr);
#endif
                                addvirtuals(ns, n);
                        }
}


int
makevsrc(op, sn, pm)            /* make virtual source if reasonable */
OBJREC  *op;
register int  sn;
MAT4  pm;
{
        FVECT  nsloc, nsnorm, ocent;
        double  maxrad2;
        int  nsflags;
        double  d1;
        SPOT  theirspot, ourspot;
        register int  i;

        nsflags = source[sn].sflags | (SVIRTUAL|SSPOT|SFOLLOW);
                                        /* get object center and max. radius */
        maxrad2 = getdisk(ocent, op, sn);
        if (maxrad2 <= FTINY)                   /* too small? */
                return(-1);
                                        /* get location and spot */
        if (source[sn].sflags & SDISTANT) {             /* distant source */
                if (source[sn].sflags & SPROX)
                        return(-1);             /* should never get here! */
                multv3(nsloc, source[sn].sloc, pm);
                VCOPY(ourspot.aim, ocent);
                ourspot.siz = PI*maxrad2;
                ourspot.flen = 0.;
                if (source[sn].sflags & SSPOT) {
                        copystruct(&theirspot, source[sn].sl.s);
                        multp3(theirspot.aim, source[sn].sl.s->aim, pm);
                        if (!commonbeam(&ourspot, &theirspot, nsloc))
                                return(-1);             /* no overlap */
                }
        } else {                                /* local source */
                multp3(nsloc, source[sn].sloc, pm);
                for (i = 0; i < 3; i++)
                        ourspot.aim[i] = ocent[i] - nsloc[i];
                if ((d1 = normalize(ourspot.aim)) == 0.)
                        return(-1);             /* at source!! */
                if (source[sn].sflags & SPROX && d1 > source[sn].sl.prox)
                        return(-1);             /* too far away */
                ourspot.siz = 2.*PI*(1. - d1/sqrt(d1*d1+maxrad2));
                ourspot.flen = 0.;
                if (source[sn].sflags & SSPOT) {
                        copystruct(&theirspot, source[sn].sl.s);
                        multv3(theirspot.aim, source[sn].sl.s->aim, pm);
                        if (!commonspot(&ourspot, &theirspot, nsloc))
                                return(-1);     /* no overlap */
                        ourspot.flen = theirspot.flen;
                }
                if (source[sn].sflags & SFLAT) {        /* behind source? */
                        multv3(nsnorm, source[sn].snorm, pm);
                        if (checkspot(&ourspot, nsnorm) < 0)
                                return(-1);
                }
        }
                                        /* everything is OK, make source */
        if ((i = newsource()) < 0)
                goto memerr;
        source[i].sflags = nsflags;
        VCOPY(source[i].sloc, nsloc);
        if (nsflags & SFLAT)
                VCOPY(source[i].snorm, nsnorm);
        source[i].ss = source[sn].ss; source[i].ss2 = source[sn].ss2;
        if ((source[i].sl.s = (SPOT *)malloc(sizeof(SPOT))) == NULL)
                goto memerr;
        copystruct(source[i].sl.s, &ourspot);
        if (nsflags & SPROX)
                source[i].sl.prox = source[sn].sl.prox;
        source[i].sa.svnext = sn;
        source[i].so = op;
        return(i);
memerr:
        error(SYSTEM, "out of memory in makevsrc");
}


double
getdisk(oc, op, sn)             /* get visible object disk */
FVECT  oc;
OBJREC  *op;
register int  sn;
{
        double  rad2, roffs, offs, d, rd, rdoto;
        FVECT  rnrm, nrm;
                                /* first, use object getdisk function */
        rad2 = (*sfun[op->otype].of->getdisk)(oc, op);
        if (!(source[sn].sflags & SVIRTUAL))
                return(rad2);           /* all done for normal source */
                                /* check for correct side of relay surface */
        roffs = (*sfun[source[sn].so->otype].of->getpleq)(rnrm, source[sn].so);
        rd = DOT(rnrm, source[sn].sloc);        /* source projection */
        if (!(source[sn].sflags & SDISTANT))
                rd -= roffs;
        d = DOT(rnrm, oc) - roffs;      /* disk distance to relay plane */
        if ((d > 0.) ^ (rd > 0.))
                return(rad2);           /* OK if opposite sides */
        if (d*d >= rad2)
                return(.0);             /* no relay is possible */
                                /* we need a closer look */
        offs = (*sfun[op->otype].of->getpleq)(nrm, op);
        rdoto = DOT(rnrm, nrm);
        if (d*d >= rad2*(1.-rdoto*rdoto))
                return(0.);             /* disk entirely on projection side */
                                /* should shrink disk but I'm lazy */
        return(rad2);
}


commonspot(sp1, sp2, org)       /* set sp1 to intersection of sp1 and sp2 */
register SPOT  *sp1, *sp2;
FVECT  org;
{
        FVECT  cent;
        double  rad2, cos1, cos2;

        cos1 = 1. - sp1->siz/(2.*PI);
        cos2 = 1. - sp2->siz/(2.*PI);
        if (sp2->siz >= 2.*PI-FTINY)            /* BIG, just check overlap */
                return(DOT(sp1->aim,sp2->aim) >= cos1*cos2 -
                                        sqrt((1.-cos1*cos1)*(1.-cos2*cos2)));
                                /* compute and check disks */
        rad2 = intercircle(cent, sp1->aim, sp2->aim,
                        1./(cos1*cos1) - 1.,  1./(cos2*cos2) - 1.);
        if (rad2 <= FTINY || normalize(cent) == 0.)
                return(0);
        VCOPY(sp1->aim, cent);
        sp1->siz = 2.*PI*(1. - 1./sqrt(1.+rad2));
        return(1);
}


commonbeam(sp1, sp2, dir)       /* set sp1 to intersection of sp1 and sp2 */
register SPOT  *sp1, *sp2;
FVECT  dir;
{
        FVECT  cent, c1, c2;
        double  rad2, d;
        register int  i;
                                        /* move centers to common plane */
        d = DOT(sp1->aim, dir);
        for (i = 0; i < 3; i++)
                c1[i] = sp1->aim[i] - d*dir[i];
        d = DOT(sp2->aim, dir);
        for (i = 0; i < 3; i++)
                c2[i] = sp2->aim[i] - d*dir[i];
                                        /* compute overlap */
        rad2 = intercircle(cent, c1, c2, sp1->siz/PI, sp2->siz/PI);
        if (rad2 <= FTINY)
                return(0);
        VCOPY(sp1->aim, cent);
        sp1->siz = PI*rad2;
        return(1);
}


checkspot(sp, nrm)              /* check spotlight for behind source */
register SPOT  *sp;
FVECT  nrm;
{
        double  d, d1;

        d = DOT(sp->aim, nrm);
        if (d > FTINY)                  /* center in front? */
                return(0);
                                        /* else check horizon */
        d1 = 1. - sp->siz/(2.*PI);
        return(1.-FTINY-d*d > d1*d1);
}


double
intercircle(cc, c1, c2, r1s, r2s)       /* intersect two circles */
FVECT  cc;                      /* midpoint (return value) */
FVECT  c1, c2;                  /* circle centers */
double  r1s, r2s;               /* radii squared */
{
        double  a2, d2, l;
        FVECT  disp;
        register int  i;

        for (i = 0; i < 3; i++)
                disp[i] = c2[i] - c1[i];
        d2 = DOT(disp,disp);
                                        /* circle within overlap? */
        if (r1s < r2s) {
                if (r2s >= r1s + d2) {
                        VCOPY(cc, c1);
                        return(r1s);
                }
        } else {
                if (r1s >= r2s + d2) {
                        VCOPY(cc, c2);
                        return(r2s);
                }
        }
        a2 = .25*(2.*(r1s+r2s) - d2 - (r2s-r1s)*(r2s-r1s)/d2);
                                        /* no overlap? */
        if (a2 <= 0.)
                return(0.);
                                        /* overlap, compute center */
        l = sqrt((r1s - a2)/d2);
        for (i = 0; i < 3; i++)
                cc[i] = c1[i] + l*disp[i];
        return(a2);
}


#ifdef DEBUG
virtverb(sn, fp)        /* print verbose description of virtual source */
register int  sn;
FILE  *fp;
{
        register int  i;

        fprintf(fp, "%s virtual source %d in %s %s\n",
                        source[sn].sflags & SDISTANT ? "distant" : "local",
                        sn, ofun[source[sn].so->otype].funame,
                        source[sn].so->oname);
        fprintf(fp, "\tat (%f,%f,%f)\n",
                source[sn].sloc[0], source[sn].sloc[1], source[sn].sloc[2]);
        fprintf(fp, "\tlinked to source %d (%s)\n",
                source[sn].sa.svnext, source[source[sn].sa.svnext].so->oname);
        if (source[sn].sflags & SFOLLOW)
                fprintf(fp, "\talways followed\n");
        else
                fprintf(fp, "\tnever followed\n");
        if (!(source[sn].sflags & SSPOT))
                return;
        fprintf(fp, "\twith spot aim (%f,%f,%f) and size %f\n",
                        source[sn].sl.s->aim[0], source[sn].sl.s->aim[1],
                        source[sn].sl.s->aim[2], source[sn].sl.s->siz);
}
#endif
Revision:	1.6
Committed:	Fri Jun 21 13:25:42 1991 UTC (32 years, 10 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 1.5:	+79 -73 lines
Log Message:	added test for relay object on same side as virtual source
#	User	Rev	Content
1	greg	1.1	/* Copyright (c) 1991 Regents of the University of California */
2
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* Routines for simulating virtual light sources
9			* Thus far, we only support planar mirrors.
10			*/
11
12			#include "ray.h"
13
14	greg	1.3	#include "otypes.h"
15
16	greg	1.1	#include "source.h"
17
18
19	greg	1.6	double intercircle(), getdisk();
20	greg	1.1
21			static OBJECT vobject; / virtual source objects */
22			static int nvobjects = 0; /* number of virtual source objects */
23
24
25			markvirtuals() /* find and mark virtual sources */
26			{
27			register OBJREC *o;
28			register int i;
29			/* check number of direct relays */
30			if (directrelay <= 0)
31			return;
32			/* find virtual source objects */
33			for (i = 0; i < nobjects; i++) {
34			o = objptr(i);
35	greg	1.3	if (!issurface(o->otype) \|\| o->omod == OVOID)
36	greg	1.1	continue;
37			if (!isvlight(objptr(o->omod)->otype))
38			continue;
39	greg	1.3	if (sfun[o->otype].of == NULL \|\|
40			sfun[o->otype].of->getpleq == NULL)
41			objerror(o, USER, "illegal material");
42	greg	1.1	if (nvobjects == 0)
43			vobject = (OBJECT *)malloc(sizeof(OBJECT));
44			else
45			vobject = (OBJECT )realloc((char )vobject,
46			(unsigned)(nvobjects+1)*sizeof(OBJECT));
47			if (vobject == NULL)
48			error(SYSTEM, "out of memory in addvirtuals");
49			vobject[nvobjects++] = i;
50			}
51			if (nvobjects == 0)
52			return;
53	greg	1.4	#ifdef DEBUG
54			fprintf(stderr, "found %d virtual source objects\n", nvobjects);
55			#endif
56	greg	1.1	/* append virtual sources */
57			for (i = nsources; i-- > 0; )
58			if (!(source[i].sflags & SSKIP))
59	greg	1.4	addvirtuals(i, directrelay);
60	greg	1.1	/* done with our object list */
61			free((char *)vobject);
62			nvobjects = 0;
63			}
64
65
66	greg	1.4	addvirtuals(sn, nr) /* add virtuals associated with source */
67			int sn;
68	greg	1.1	int nr;
69			{
70			register int i;
71			/* check relay limit first */
72			if (nr <= 0)
73			return;
74			/* check each virtual object for projection */
75			for (i = 0; i < nvobjects; i++)
76	greg	1.3	/* vproject() calls us recursively */
77	greg	1.4	vproject(objptr(vobject[i]), sn, nr-1);
78	greg	1.1	}
79
80
81	greg	1.4	vproject(o, sn, n) /* create projected source(s) if they exist */
82	greg	1.3	OBJREC *o;
83	greg	1.4	int sn;
84	greg	1.3	int n;
85			{
86			register int i;
87			register VSMATERIAL *vsmat;
88			MAT4 proj;
89	greg	1.4	int ns;
90
91			if (o == source[sn].so) /* objects cannot project themselves */
92			return;
93	greg	1.3	/* get virtual source material */
94			vsmat = sfun[objptr(o->omod)->otype].mf;
95			/* project virtual sources */
96			for (i = 0; i < vsmat->nproj; i++)
97	greg	1.4	if ((*vsmat->vproj)(proj, o, &source[sn], i))
98			if ((ns = makevsrc(o, sn, proj)) >= 0) {
99			#ifdef DEBUG
100	greg	1.6	virtverb(ns, stderr);
101	greg	1.4	#endif
102	greg	1.3	addvirtuals(ns, n);
103	greg	1.4	}
104	greg	1.3	}
105
106
107	greg	1.4	int
108			makevsrc(op, sn, pm) /* make virtual source if reasonable */
109	greg	1.1	OBJREC *op;
110	greg	1.4	register int sn;
111	greg	1.1	MAT4 pm;
112			{
113	greg	1.6	FVECT nsloc, nsnorm, ocent;
114			double maxrad2;
115	greg	1.3	int nsflags;
116			double d1;
117	greg	1.1	SPOT theirspot, ourspot;
118			register int i;
119	greg	1.3
120	greg	1.6	nsflags = source[sn].sflags \| (SVIRTUAL\|SSPOT\|SFOLLOW);
121	greg	1.1	/* get object center and max. radius */
122	greg	1.6	maxrad2 = getdisk(ocent, op, sn);
123			if (maxrad2 <= FTINY) /* too small? */
124			return(-1);
125	greg	1.1	/* get location and spot */
126	greg	1.4	if (source[sn].sflags & SDISTANT) { /* distant source */
127			if (source[sn].sflags & SPROX)
128	greg	1.5	return(-1); /* should never get here! */
129	greg	1.4	multv3(nsloc, source[sn].sloc, pm);
130	greg	1.6	VCOPY(ourspot.aim, ocent);
131			ourspot.siz = PI*maxrad2;
132			ourspot.flen = 0.;
133	greg	1.4	if (source[sn].sflags & SSPOT) {
134			copystruct(&theirspot, source[sn].sl.s);
135			multp3(theirspot.aim, source[sn].sl.s->aim, pm);
136	greg	1.6	if (!commonbeam(&ourspot, &theirspot, nsloc))
137	greg	1.5	return(-1); /* no overlap */
138	greg	1.1	}
139			} else { /* local source */
140	greg	1.4	multp3(nsloc, source[sn].sloc, pm);
141	greg	1.6	for (i = 0; i < 3; i++)
142			ourspot.aim[i] = ocent[i] - nsloc[i];
143			if ((d1 = normalize(ourspot.aim)) == 0.)
144			return(-1); /* at source!! */
145			if (source[sn].sflags & SPROX && d1 > source[sn].sl.prox)
146			return(-1); /* too far away */
147			ourspot.siz = 2.PI(1. - d1/sqrt(d1*d1+maxrad2));
148			ourspot.flen = 0.;
149	greg	1.4	if (source[sn].sflags & SSPOT) {
150			copystruct(&theirspot, source[sn].sl.s);
151			multv3(theirspot.aim, source[sn].sl.s->aim, pm);
152	greg	1.6	if (!commonspot(&ourspot, &theirspot, nsloc))
153			return(-1); /* no overlap */
154			ourspot.flen = theirspot.flen;
155	greg	1.1	}
156	greg	1.4	if (source[sn].sflags & SFLAT) { /* behind source? */
157			multv3(nsnorm, source[sn].snorm, pm);
158	greg	1.6	if (checkspot(&ourspot, nsnorm) < 0)
159	greg	1.5	return(-1);
160	greg	1.1	}
161			}
162			/* everything is OK, make source */
163	greg	1.6	if ((i = newsource()) < 0)
164	greg	1.1	goto memerr;
165	greg	1.6	source[i].sflags = nsflags;
166			VCOPY(source[i].sloc, nsloc);
167	greg	1.3	if (nsflags & SFLAT)
168	greg	1.6	VCOPY(source[i].snorm, nsnorm);
169			source[i].ss = source[sn].ss; source[i].ss2 = source[sn].ss2;
170			if ((source[i].sl.s = (SPOT *)malloc(sizeof(SPOT))) == NULL)
171			goto memerr;
172			copystruct(source[i].sl.s, &ourspot);
173	greg	1.3	if (nsflags & SPROX)
174	greg	1.6	source[i].sl.prox = source[sn].sl.prox;
175			source[i].sa.svnext = sn;
176			source[i].so = op;
177			return(i);
178	greg	1.1	memerr:
179			error(SYSTEM, "out of memory in makevsrc");
180			}
181
182
183	greg	1.6	double
184			getdisk(oc, op, sn) /* get visible object disk */
185			FVECT oc;
186			OBJREC *op;
187			register int sn;
188			{
189			double rad2, roffs, offs, d, rd, rdoto;
190			FVECT rnrm, nrm;
191			/* first, use object getdisk function */
192			rad2 = (*sfun[op->otype].of->getdisk)(oc, op);
193			if (!(source[sn].sflags & SVIRTUAL))
194			return(rad2); /* all done for normal source */
195			/* check for correct side of relay surface */
196			roffs = (*sfun[source[sn].so->otype].of->getpleq)(rnrm, source[sn].so);
197			rd = DOT(rnrm, source[sn].sloc); /* source projection */
198			if (!(source[sn].sflags & SDISTANT))
199			rd -= roffs;
200			d = DOT(rnrm, oc) - roffs; /* disk distance to relay plane */
201			if ((d > 0.) ^ (rd > 0.))
202			return(rad2); /* OK if opposite sides */
203			if (d*d >= rad2)
204			return(.0); /* no relay is possible */
205			/* we need a closer look */
206			offs = (*sfun[op->otype].of->getpleq)(nrm, op);
207			rdoto = DOT(rnrm, nrm);
208			if (dd >= rad2(1.-rdoto*rdoto))
209			return(0.); /* disk entirely on projection side */
210			/* should shrink disk but I'm lazy */
211			return(rad2);
212			}
213
214
215	greg	1.1	commonspot(sp1, sp2, org) /* set sp1 to intersection of sp1 and sp2 */
216			register SPOT sp1, sp2;
217			FVECT org;
218			{
219			FVECT cent;
220	greg	1.2	double rad2, cos1, cos2;
221	greg	1.1
222	greg	1.2	cos1 = 1. - sp1->siz/(2.*PI);
223			cos2 = 1. - sp2->siz/(2.*PI);
224	greg	1.1	if (sp2->siz >= 2.PI-FTINY) / BIG, just check overlap */
225	greg	1.2	return(DOT(sp1->aim,sp2->aim) >= cos1*cos2 -
226			sqrt((1.-cos1cos1)(1.-cos2*cos2)));
227	greg	1.1	/* compute and check disks */
228	greg	1.2	rad2 = intercircle(cent, sp1->aim, sp2->aim,
229			1./(cos1cos1) - 1., 1./(cos2cos2) - 1.);
230	greg	1.1	if (rad2 <= FTINY \|\| normalize(cent) == 0.)
231			return(0);
232			VCOPY(sp1->aim, cent);
233			sp1->siz = 2.PI(1. - 1./sqrt(1.+rad2));
234			return(1);
235			}
236
237
238			commonbeam(sp1, sp2, dir) /* set sp1 to intersection of sp1 and sp2 */
239			register SPOT sp1, sp2;
240			FVECT dir;
241			{
242			FVECT cent, c1, c2;
243			double rad2, d;
244			register int i;
245			/* move centers to common plane */
246			d = DOT(sp1->aim, dir);
247			for (i = 0; i < 3; i++)
248	greg	1.2	c1[i] = sp1->aim[i] - d*dir[i];
249	greg	1.1	d = DOT(sp2->aim, dir);
250			for (i = 0; i < 3; i++)
251			c2[i] = sp2->aim[i] - d*dir[i];
252			/* compute overlap */
253			rad2 = intercircle(cent, c1, c2, sp1->siz/PI, sp2->siz/PI);
254			if (rad2 <= FTINY)
255			return(0);
256			VCOPY(sp1->aim, cent);
257			sp1->siz = PI*rad2;
258			return(1);
259			}
260
261
262			checkspot(sp, nrm) /* check spotlight for behind source */
263			register SPOT *sp;
264			FVECT nrm;
265			{
266			double d, d1;
267
268			d = DOT(sp->aim, nrm);
269			if (d > FTINY) /* center in front? */
270			return(0);
271			/* else check horizon */
272			d1 = 1. - sp->siz/(2.*PI);
273			return(1.-FTINY-dd > d1d1);
274			}
275
276
277			double
278			intercircle(cc, c1, c2, r1s, r2s) /* intersect two circles */
279			FVECT cc; /* midpoint (return value) */
280			FVECT c1, c2; /* circle centers */
281			double r1s, r2s; /* radii squared */
282			{
283			double a2, d2, l;
284			FVECT disp;
285			register int i;
286
287			for (i = 0; i < 3; i++)
288			disp[i] = c2[i] - c1[i];
289			d2 = DOT(disp,disp);
290			/* circle within overlap? */
291			if (r1s < r2s) {
292			if (r2s >= r1s + d2) {
293			VCOPY(cc, c1);
294			return(r1s);
295			}
296			} else {
297			if (r1s >= r2s + d2) {
298			VCOPY(cc, c2);
299			return(r2s);
300			}
301			}
302			a2 = .25(2.(r1s+r2s) - d2 - (r2s-r1s)*(r2s-r1s)/d2);
303			/* no overlap? */
304			if (a2 <= 0.)
305			return(0.);
306	greg	1.2	/* overlap, compute center */
307	greg	1.1	l = sqrt((r1s - a2)/d2);
308			for (i = 0; i < 3; i++)
309			cc[i] = c1[i] + l*disp[i];
310			return(a2);
311			}
312	greg	1.4
313
314			#ifdef DEBUG
315	greg	1.6	virtverb(sn, fp) /* print verbose description of virtual source */
316			register int sn;
317	greg	1.4	FILE *fp;
318			{
319			register int i;
320
321			fprintf(fp, "%s virtual source %d in %s %s\n",
322	greg	1.6	source[sn].sflags & SDISTANT ? "distant" : "local",
323			sn, ofun[source[sn].so->otype].funame,
324			source[sn].so->oname);
325	greg	1.4	fprintf(fp, "\tat (%f,%f,%f)\n",
326	greg	1.6	source[sn].sloc[0], source[sn].sloc[1], source[sn].sloc[2]);
327	greg	1.4	fprintf(fp, "\tlinked to source %d (%s)\n",
328	greg	1.6	source[sn].sa.svnext, source[source[sn].sa.svnext].so->oname);
329			if (source[sn].sflags & SFOLLOW)
330	greg	1.4	fprintf(fp, "\talways followed\n");
331			else
332			fprintf(fp, "\tnever followed\n");
333	greg	1.6	if (!(source[sn].sflags & SSPOT))
334	greg	1.4	return;
335			fprintf(fp, "\twith spot aim (%f,%f,%f) and size %f\n",
336	greg	1.6	source[sn].sl.s->aim[0], source[sn].sl.s->aim[1],
337			source[sn].sl.s->aim[2], source[sn].sl.s->siz);
338	greg	1.4	}
339			#endif