src/gen/mkillum2.c

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

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

/*
 * Routines to do the actual calculation for mkillum
 */

#include  "mkillum.h"

#include  "face.h"

#include  "cone.h"

#include  "random.h"


o_default(ob, il, rt, nm)       /* default illum action */
OBJREC  *ob;
struct illum_args  *il;
struct rtproc  *rt;
char  *nm;
{
        sprintf(errmsg, "(%s): cannot make illum for %s \"%s\"",
                        nm, ofun[ob->otype].funame, ob->oname);
        error(WARNING, errmsg);
        if (!(il->flags & IL_LIGHT))
                printobj(il->altmat, ob);
}


o_face(ob, il, rt, nm)          /* make an illum face */
OBJREC  *ob;
struct illum_args  *il;
struct rtproc  *rt;
char  *nm;
{
#define MAXMISS         (5*n*il->nsamps)
        int  dim[3];
        int  n, nalt, nazi, h;
        float  *distarr;
        double  sp[2], r1, r2;
        FVECT  dn, org, dir;
        FVECT  u, v;
        double  ur[2], vr[2];
        int  nmisses;
        register FACE  *fa;
        register int  i, j;
                                /* get/check arguments */
        fa = getface(ob);
        if (fa->area == 0.0) {
                freeface(ob);
                o_default(ob, il, rt, nm);
                return;
        }
                                /* set up sampling */
        if (il->sampdens <= 0)
                nalt = nazi = 1;
        else {
                n = PI * il->sampdens;
                nalt = sqrt(n/PI) + .5;
                nazi = PI*nalt + .5;
        }
        n = nalt*nazi;
        distarr = (float *)calloc(n, 3*sizeof(float));
        if (distarr == NULL)
                error(SYSTEM, "out of memory in o_face");
        mkaxes(u, v, fa->norm);
        ur[0] = vr[0] = FHUGE;
        ur[1] = vr[1] = -FHUGE;
        for (i = 0; i < fa->nv; i++) {
                r1 = DOT(VERTEX(fa,i),u);
                if (r1 < ur[0]) ur[0] = r1;
                if (r1 > ur[1]) ur[1] = r1;
                r2 = DOT(VERTEX(fa,i),v);
                if (r2 < vr[0]) vr[0] = r2;
                if (r2 > vr[1]) vr[1] = r2;
        }
        dim[0] = random();
                                /* sample polygon */
        nmisses = 0;
        for (dim[1] = 0; dim[1] < nalt; dim[1]++)
            for (dim[2] = 0; dim[2] < nazi; dim[2]++)
                for (i = 0; i < il->nsamps; i++) {
                                        /* random direction */
                    h = ilhash(dim, 3) + i;
                    multisamp(sp, 2, urand(h));
                    r1 = (dim[1] + sp[0])/nalt;
                    r2 = (dim[2] + sp[1])/nazi;
                    flatdir(dn, r1, r2);
                    for (j = 0; j < 3; j++)
                        dir[j] = -dn[0]*u[j] - dn[1]*v[j] - dn[2]*fa->norm[j];
                                        /* random location */
                    do {
                        multisamp(sp, 2, urand(h+4862+nmisses));
                        r1 = ur[0] + (ur[1]-ur[0]) * sp[0];
                        r2 = vr[0] + (vr[1]-vr[0]) * sp[1];
                        for (j = 0; j < 3; j++)
                            org[j] = r1*u[j] + r2*v[j]
                                        + fa->offset*fa->norm[j];
                    } while (!inface(org, fa) && nmisses++ < MAXMISS);
                    if (nmisses > MAXMISS) {
                        objerror(ob, WARNING, "bad aspect");
                        rt->nrays = 0;
                        freeface(ob);
                        free((char *)distarr);
                        o_default(ob, il, rt, nm);
                        return;
                    }
                    for (j = 0; j < 3; j++)
                        org[j] += .001*fa->norm[j];
                                        /* send sample */
                    raysamp(distarr+3*(dim[1]*nazi+dim[2]), org, dir, rt);
                }
        rayflush(rt);
                                /* write out the face and its distribution */
        average(il, distarr, nalt*nazi);
        if (il->sampdens > 0)
                flatout(il, distarr, nalt, nazi, u, v, fa->norm);
        illumout(il, ob);
                                /* clean up */
        freeface(ob);
        free((char *)distarr);
#undef MAXMISS
}


o_sphere(ob, il, rt, nm)        /* make an illum sphere */
register OBJREC  *ob;
struct illum_args  *il;
struct rtproc  *rt;
char  *nm;
{
        int  dim[3];
        int  n, nalt, nazi;
        float  *distarr;
        double  sp[4], r1, r2, r3;
        FVECT  org, dir;
        FVECT  u, v;
        register int  i, j;
                                /* check arguments */
        if (ob->oargs.nfargs != 4)
                objerror(ob, USER, "bad # of arguments");
                                /* set up sampling */
        if (il->sampdens <= 0)
                nalt = nazi = 1;
        else {
                n = 4.*PI * il->sampdens;
                nalt = sqrt(n/PI) + .5;
                nazi = PI*nalt + .5;
        }
        n = nalt*nazi;
        distarr = (float *)calloc(n, 3*sizeof(float));
        if (distarr == NULL)
                error(SYSTEM, "out of memory in o_sphere");
        dim[0] = random();
                                /* sample sphere */
        for (dim[1] = 0; dim[1] < nalt; dim[1]++)
            for (dim[2] = 0; dim[2] < nazi; dim[2]++)
                for (i = 0; i < il->nsamps; i++) {
                                        /* next sample point */
                    multisamp(sp, 4, urand(ilhash(dim,3)+i));
                                        /* random direction */
                    r1 = (dim[1] + sp[0])/nalt;
                    r2 = (dim[2] + sp[1])/nazi;
                    rounddir(dir, r1, r2);
                                        /* random location */
                    mkaxes(u, v, dir);          /* yuck! */
                    r3 = sqrt(sp[2]);
                    r2 = 2.*PI*sp[3];
                    r1 = r3*ob->oargs.farg[3]*cos(r2);
                    r2 = r3*ob->oargs.farg[3]*sin(r2);
                    r3 = ob->oargs.farg[3]*sqrt(1.01-r3*r3);
                    for (j = 0; j < 3; j++) {
                        org[j] = ob->oargs.farg[j] + r1*u[j] + r2*v[j] +
                                        r3*dir[j];
                        dir[j] = -dir[j];
                    }
                                        /* send sample */
                    raysamp(distarr+3*(dim[1]*nazi+dim[2]), org, dir, rt);
                }
        rayflush(rt);
                                /* write out the sphere and its distribution */
        average(il, distarr, nalt*nazi);
        if (il->sampdens > 0)
                roundout(il, distarr, nalt, nazi);
        else
                objerror(ob, WARNING, "diffuse distribution");
        illumout(il, ob);
                                /* clean up */
        free((char *)distarr);
}


o_ring(ob, il, rt, nm)          /* make an illum ring */
OBJREC  *ob;
struct illum_args  *il;
struct rtproc  *rt;
char  *nm;
{
        int  dim[3];
        int  n, nalt, nazi;
        float  *distarr;
        double  sp[4], r1, r2, r3;
        FVECT  dn, org, dir;
        FVECT  u, v;
        register CONE  *co;
        register int  i, j;
                                /* get/check arguments */
        co = getcone(ob, 0);
                                /* set up sampling */
        if (il->sampdens <= 0)
                nalt = nazi = 1;
        else {
                n = PI * il->sampdens;
                nalt = sqrt(n/PI) + .5;
                nazi = PI*nalt + .5;
        }
        n = nalt*nazi;
        distarr = (float *)calloc(n, 3*sizeof(float));
        if (distarr == NULL)
                error(SYSTEM, "out of memory in o_ring");
        mkaxes(u, v, co->ad);
        dim[0] = random();
                                /* sample disk */
        for (dim[1] = 0; dim[1] < nalt; dim[1]++)
            for (dim[2] = 0; dim[2] < nazi; dim[2]++)
                for (i = 0; i < il->nsamps; i++) {
                                        /* next sample point */
                    multisamp(sp, 4, urand(ilhash(dim,3)+i));
                                        /* random direction */
                    r1 = (dim[1] + sp[0])/nalt;
                    r2 = (dim[2] + sp[1])/nalt;
                    flatdir(dn, r1, r2);
                    for (j = 0; j < 3; j++)
                        dir[j] = -dn[0]*u[j] - dn[1]*v[j] - dn[2]*co->ad[j];
                                        /* random location */
                    r3 = sqrt(CO_R0(co)*CO_R0(co) +
                            sp[2]*(CO_R1(co)*CO_R1(co) - CO_R0(co)*CO_R0(co)));
                    r2 = 2.*PI*sp[3];
                    r1 = r3*cos(r2);
                    r2 = r3*sin(r2);
                    for (j = 0; j < 3; j++)
                        org[j] = CO_P0(co)[j] + r1*u[j] + r1*v[j] +
                                        .001*co->ad[j];

                                        /* send sample */
                    raysamp(distarr+3*(dim[1]*nazi+dim[2]), org, dir, rt);
                }
        rayflush(rt);
                                /* write out the ring and its distribution */
        average(il, distarr, nalt*nazi);
        if (il->sampdens > 0)
                flatout(il, distarr, nalt, nazi, u, v, co->ad);
        illumout(il, ob);
                                /* clean up */
        freecone(ob);
        free((char *)distarr);
}


raysamp(res, org, dir, rt)      /* compute a ray sample */
float  res[3];
FVECT  org, dir;
register struct rtproc  *rt;
{
        register float  *fp;

        if (rt->nrays == rt->bsiz)
                rayflush(rt);
        rt->dest[rt->nrays] = res;
        fp = rt->buf + 6*rt->nrays++;
        *fp++ = org[0]; *fp++ = org[1]; *fp++ = org[2];
        *fp++ = dir[0]; *fp++ = dir[1]; *fp = dir[2];
}


rayflush(rt)                    /* flush buffered rays */
register struct rtproc  *rt;
{
        register int  i;

        if (rt->nrays <= 0)
                return;
        bzero(rt->buf+6*rt->nrays, 6*sizeof(float));
        if ( process(rt->pd, (char *)rt->buf, (char *)rt->buf,
                        3*sizeof(float)*rt->nrays,
                        6*sizeof(float)*(rt->nrays+1)) <
                        3*sizeof(float)*rt->nrays )
                error(SYSTEM, "error reading from rtrace process");
        i = rt->nrays;
        while (i--) {
                rt->dest[i][0] += rt->buf[3*i];
                rt->dest[i][1] += rt->buf[3*i+1];
                rt->dest[i][2] += rt->buf[3*i+2];
        }
        rt->nrays = 0;
}


mkaxes(u, v, n)                 /* compute u and v to go with n */
FVECT  u, v, n;
{
        register int  i;

        v[0] = v[1] = v[2] = 0.0;
        for (i = 0; i < 3; i++)
                if (n[i] < 0.6 && n[i] > -0.6)
                        break;
        v[i] = 1.0;
        fcross(u, v, n);
        normalize(u);
        fcross(v, n, u);
}


rounddir(dv, alt, azi)          /* compute uniform spherical direction */
register FVECT  dv;
double  alt, azi;
{
        double  d1, d2;

        dv[2] = 1. - 2.*alt;
        d1 = sqrt(1. - dv[2]*dv[2]);
        d2 = 2.*PI * azi;
        dv[0] = d1*cos(d2);
        dv[1] = d1*sin(d2);
}


flatdir(dv, alt, azi)           /* compute uniform hemispherical direction */
register FVECT  dv;
double  alt, azi;
{
        double  d1, d2;

        d1 = sqrt(alt);
        d2 = 2.*PI * azi;
        dv[0] = d1*cos(d2);
        dv[1] = d1*sin(d2);
        dv[2] = sqrt(1. - alt);
}
Revision:	1.11
Committed:	Thu Aug 22 12:12:23 1991 UTC (32 years, 8 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 1.10:	+39 -19 lines
Log Message:	interpret d=0 to mean diffuse source changed peano() calls to multisamp()
#	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	greg	1.4	* Routines to do the actual calculation for mkillum
9	greg	1.1	*/
10
11			#include "mkillum.h"
12
13			#include "face.h"
14
15			#include "cone.h"
16
17	greg	1.2	#include "random.h"
18	greg	1.1
19	greg	1.2
20			o_default(ob, il, rt, nm) /* default illum action */
21	greg	1.1	OBJREC *ob;
22			struct illum_args *il;
23			struct rtproc *rt;
24	greg	1.2	char *nm;
25	greg	1.1	{
26	greg	1.2	sprintf(errmsg, "(%s): cannot make illum for %s \"%s\"",
27			nm, ofun[ob->otype].funame, ob->oname);
28			error(WARNING, errmsg);
29			if (!(il->flags & IL_LIGHT))
30	greg	1.4	printobj(il->altmat, ob);
31	greg	1.2	}
32
33
34			o_face(ob, il, rt, nm) /* make an illum face */
35			OBJREC *ob;
36			struct illum_args *il;
37			struct rtproc *rt;
38			char *nm;
39			{
40	greg	1.3	#define MAXMISS (5nil->nsamps)
41	greg	1.10	int dim[3];
42			int n, nalt, nazi, h;
43	greg	1.3	float *distarr;
44	greg	1.10	double sp[2], r1, r2;
45	greg	1.4	FVECT dn, org, dir;
46	greg	1.3	FVECT u, v;
47			double ur[2], vr[2];
48			int nmisses;
49			register FACE *fa;
50			register int i, j;
51			/* get/check arguments */
52			fa = getface(ob);
53			if (fa->area == 0.0) {
54			freeface(ob);
55			o_default(ob, il, rt, nm);
56			return;
57			}
58			/* set up sampling */
59	greg	1.11	if (il->sampdens <= 0)
60			nalt = nazi = 1;
61			else {
62			n = PI * il->sampdens;
63			nalt = sqrt(n/PI) + .5;
64			nazi = PI*nalt + .5;
65			}
66	greg	1.3	n = nalt*nazi;
67			distarr = (float )calloc(n, 3sizeof(float));
68			if (distarr == NULL)
69			error(SYSTEM, "out of memory in o_face");
70			mkaxes(u, v, fa->norm);
71			ur[0] = vr[0] = FHUGE;
72			ur[1] = vr[1] = -FHUGE;
73			for (i = 0; i < fa->nv; i++) {
74			r1 = DOT(VERTEX(fa,i),u);
75			if (r1 < ur[0]) ur[0] = r1;
76			if (r1 > ur[1]) ur[1] = r1;
77			r2 = DOT(VERTEX(fa,i),v);
78			if (r2 < vr[0]) vr[0] = r2;
79			if (r2 > vr[1]) vr[1] = r2;
80			}
81			dim[0] = random();
82			/* sample polygon */
83			nmisses = 0;
84			for (dim[1] = 0; dim[1] < nalt; dim[1]++)
85			for (dim[2] = 0; dim[2] < nazi; dim[2]++)
86			for (i = 0; i < il->nsamps; i++) {
87			/* random direction */
88	greg	1.10	h = ilhash(dim, 3) + i;
89	greg	1.11	multisamp(sp, 2, urand(h));
90	greg	1.10	r1 = (dim[1] + sp[0])/nalt;
91			r2 = (dim[2] + sp[1])/nazi;
92	greg	1.3	flatdir(dn, r1, r2);
93			for (j = 0; j < 3; j++)
94	greg	1.5	dir[j] = -dn[0]u[j] - dn[1]v[j] - dn[2]*fa->norm[j];
95	greg	1.3	/* random location */
96			do {
97	greg	1.11	multisamp(sp, 2, urand(h+4862+nmisses));
98	greg	1.10	r1 = ur[0] + (ur[1]-ur[0]) * sp[0];
99			r2 = vr[0] + (vr[1]-vr[0]) * sp[1];
100	greg	1.3	for (j = 0; j < 3; j++)
101			org[j] = r1u[j] + r2v[j]
102			+ fa->offset*fa->norm[j];
103			} while (!inface(org, fa) && nmisses++ < MAXMISS);
104			if (nmisses > MAXMISS) {
105			objerror(ob, WARNING, "bad aspect");
106			rt->nrays = 0;
107			freeface(ob);
108			free((char *)distarr);
109			o_default(ob, il, rt, nm);
110			return;
111			}
112			for (j = 0; j < 3; j++)
113			org[j] += .001*fa->norm[j];
114			/* send sample */
115	greg	1.7	raysamp(distarr+3(dim[1]nazi+dim[2]), org, dir, rt);
116	greg	1.3	}
117			rayflush(rt);
118	greg	1.11	/* write out the face and its distribution */
119			average(il, distarr, nalt*nazi);
120			if (il->sampdens > 0)
121			flatout(il, distarr, nalt, nazi, u, v, fa->norm);
122	greg	1.4	illumout(il, ob);
123	greg	1.3	/* clean up */
124			freeface(ob);
125			free((char *)distarr);
126			#undef MAXMISS
127	greg	1.2	}
128
129
130			o_sphere(ob, il, rt, nm) /* make an illum sphere */
131	greg	1.3	register OBJREC *ob;
132	greg	1.2	struct illum_args *il;
133			struct rtproc *rt;
134			char *nm;
135			{
136	greg	1.10	int dim[3];
137	greg	1.2	int n, nalt, nazi;
138			float *distarr;
139	greg	1.10	double sp[4], r1, r2, r3;
140	greg	1.4	FVECT org, dir;
141	greg	1.2	FVECT u, v;
142			register int i, j;
143			/* check arguments */
144			if (ob->oargs.nfargs != 4)
145			objerror(ob, USER, "bad # of arguments");
146			/* set up sampling */
147	greg	1.11	if (il->sampdens <= 0)
148			nalt = nazi = 1;
149			else {
150			n = 4.PI il->sampdens;
151			nalt = sqrt(n/PI) + .5;
152			nazi = PI*nalt + .5;
153			}
154	greg	1.2	n = nalt*nazi;
155			distarr = (float )calloc(n, 3sizeof(float));
156			if (distarr == NULL)
157			error(SYSTEM, "out of memory in o_sphere");
158			dim[0] = random();
159			/* sample sphere */
160			for (dim[1] = 0; dim[1] < nalt; dim[1]++)
161	greg	1.8	for (dim[2] = 0; dim[2] < nazi; dim[2]++)
162	greg	1.2	for (i = 0; i < il->nsamps; i++) {
163	greg	1.10	/* next sample point */
164	greg	1.11	multisamp(sp, 4, urand(ilhash(dim,3)+i));
165	greg	1.2	/* random direction */
166	greg	1.10	r1 = (dim[1] + sp[0])/nalt;
167			r2 = (dim[2] + sp[1])/nazi;
168	greg	1.2	rounddir(dir, r1, r2);
169			/* random location */
170	greg	1.8	mkaxes(u, v, dir); /* yuck! */
171	greg	1.10	r3 = sqrt(sp[2]);
172			r2 = 2.PIsp[3];
173	greg	1.5	r1 = r3ob->oargs.farg[3]cos(r2);
174			r2 = r3ob->oargs.farg[3]sin(r2);
175			r3 = ob->oargs.farg[3]sqrt(1.01-r3r3);
176			for (j = 0; j < 3; j++) {
177			org[j] = ob->oargs.farg[j] + r1u[j] + r2v[j] +
178			r3*dir[j];
179			dir[j] = -dir[j];
180			}
181	greg	1.2	/* send sample */
182	greg	1.7	raysamp(distarr+3(dim[1]nazi+dim[2]), org, dir, rt);
183	greg	1.2	}
184			rayflush(rt);
185	greg	1.11	/* write out the sphere and its distribution */
186			average(il, distarr, nalt*nazi);
187			if (il->sampdens > 0)
188			roundout(il, distarr, nalt, nazi);
189			else
190			objerror(ob, WARNING, "diffuse distribution");
191	greg	1.4	illumout(il, ob);
192	greg	1.2	/* clean up */
193			free((char *)distarr);
194			}
195
196
197			o_ring(ob, il, rt, nm) /* make an illum ring */
198			OBJREC *ob;
199			struct illum_args *il;
200			struct rtproc *rt;
201			char *nm;
202			{
203	greg	1.10	int dim[3];
204	greg	1.3	int n, nalt, nazi;
205			float *distarr;
206	greg	1.10	double sp[4], r1, r2, r3;
207	greg	1.4	FVECT dn, org, dir;
208	greg	1.3	FVECT u, v;
209			register CONE *co;
210			register int i, j;
211			/* get/check arguments */
212			co = getcone(ob, 0);
213			/* set up sampling */
214	greg	1.11	if (il->sampdens <= 0)
215			nalt = nazi = 1;
216			else {
217			n = PI * il->sampdens;
218			nalt = sqrt(n/PI) + .5;
219			nazi = PI*nalt + .5;
220			}
221	greg	1.3	n = nalt*nazi;
222			distarr = (float )calloc(n, 3sizeof(float));
223			if (distarr == NULL)
224			error(SYSTEM, "out of memory in o_ring");
225			mkaxes(u, v, co->ad);
226			dim[0] = random();
227			/* sample disk */
228			for (dim[1] = 0; dim[1] < nalt; dim[1]++)
229			for (dim[2] = 0; dim[2] < nazi; dim[2]++)
230			for (i = 0; i < il->nsamps; i++) {
231	greg	1.10	/* next sample point */
232	greg	1.11	multisamp(sp, 4, urand(ilhash(dim,3)+i));
233	greg	1.3	/* random direction */
234	greg	1.10	r1 = (dim[1] + sp[0])/nalt;
235			r2 = (dim[2] + sp[1])/nalt;
236	greg	1.3	flatdir(dn, r1, r2);
237			for (j = 0; j < 3; j++)
238	greg	1.5	dir[j] = -dn[0]u[j] - dn[1]v[j] - dn[2]*co->ad[j];
239	greg	1.3	/* random location */
240	greg	1.5	r3 = sqrt(CO_R0(co)*CO_R0(co) +
241	greg	1.10	sp[2](CO_R1(co)CO_R1(co) - CO_R0(co)*CO_R0(co)));
242			r2 = 2.PIsp[3];
243	greg	1.5	r1 = r3*cos(r2);
244			r2 = r3*sin(r2);
245	greg	1.3	for (j = 0; j < 3; j++)
246	greg	1.5	org[j] = CO_P0(co)[j] + r1u[j] + r1v[j] +
247			.001*co->ad[j];
248	greg	1.3
249			/* send sample */
250	greg	1.7	raysamp(distarr+3(dim[1]nazi+dim[2]), org, dir, rt);
251	greg	1.3	}
252			rayflush(rt);
253	greg	1.11	/* write out the ring and its distribution */
254			average(il, distarr, nalt*nazi);
255			if (il->sampdens > 0)
256			flatout(il, distarr, nalt, nazi, u, v, co->ad);
257	greg	1.4	illumout(il, ob);
258	greg	1.3	/* clean up */
259			freecone(ob);
260			free((char *)distarr);
261	greg	1.2	}
262
263
264			raysamp(res, org, dir, rt) /* compute a ray sample */
265			float res[3];
266			FVECT org, dir;
267			register struct rtproc *rt;
268			{
269			register float *fp;
270
271			if (rt->nrays == rt->bsiz)
272			rayflush(rt);
273			rt->dest[rt->nrays] = res;
274			fp = rt->buf + 6*rt->nrays++;
275			fp++ = org[0]; fp++ = org[1]; *fp++ = org[2];
276			fp++ = dir[0]; fp++ = dir[1]; *fp = dir[2];
277			}
278
279
280			rayflush(rt) /* flush buffered rays */
281			register struct rtproc *rt;
282			{
283			register int i;
284
285			if (rt->nrays <= 0)
286			return;
287	greg	1.9	bzero(rt->buf+6rt->nrays, 6sizeof(float));
288	greg	1.2	if ( process(rt->pd, (char )rt->buf, (char )rt->buf,
289			3sizeof(float)rt->nrays,
290			6sizeof(float)(rt->nrays+1)) <
291			3sizeof(float)rt->nrays )
292			error(SYSTEM, "error reading from rtrace process");
293			i = rt->nrays;
294			while (i--) {
295			rt->dest[i][0] += rt->buf[3*i];
296			rt->dest[i][1] += rt->buf[3*i+1];
297			rt->dest[i][2] += rt->buf[3*i+2];
298			}
299			rt->nrays = 0;
300	greg	1.4	}
301
302
303			mkaxes(u, v, n) /* compute u and v to go with n */
304			FVECT u, v, n;
305			{
306			register int i;
307
308			v[0] = v[1] = v[2] = 0.0;
309			for (i = 0; i < 3; i++)
310			if (n[i] < 0.6 && n[i] > -0.6)
311			break;
312			v[i] = 1.0;
313			fcross(u, v, n);
314			normalize(u);
315			fcross(v, n, u);
316			}
317
318
319			rounddir(dv, alt, azi) /* compute uniform spherical direction */
320			register FVECT dv;
321			double alt, azi;
322			{
323			double d1, d2;
324
325			dv[2] = 1. - 2.*alt;
326			d1 = sqrt(1. - dv[2]*dv[2]);
327			d2 = 2.PI azi;
328			dv[0] = d1*cos(d2);
329			dv[1] = d1*sin(d2);
330			}
331
332
333			flatdir(dv, alt, azi) /* compute uniform hemispherical direction */
334			register FVECT dv;
335			double alt, azi;
336			{
337			double d1, d2;
338
339			d1 = sqrt(alt);
340			d2 = 2.PI azi;
341			dv[0] = d1*cos(d2);
342			dv[1] = d1*sin(d2);
343	greg	1.6	dv[2] = sqrt(1. - alt);
344	greg	1.1	}