src/common/fvect.c

#ifndef lint
static const char       RCSid[] = "$Id: fvect.c,v 2.18 2013/04/03 00:22:12 greg Exp $";
#endif
/*
 *  fvect.c - routines for floating-point vector calculations
 */

#include "copyright.h"

#define _USE_MATH_DEFINES
#include  <math.h>
#include  "fvect.h"

double
Acos(double x)                  /* insurance for touchy math library */
{
        if (x <= -1.+FTINY*FTINY)
                return(M_PI);
        if (x >= 1.-FTINY*FTINY)
                return(.0);
        return(acos(x));
}

double
Asin(double x)                  /* insurance for touchy math library */
{
        if (x <= -1.+FTINY*FTINY)
                return(-M_PI/2.);
        if (x >= 1.-FTINY*FTINY)
                return(M_PI/2);
        return(asin(x));
}

double
fdot(                           /* return the dot product of two vectors */
const FVECT v1,
const FVECT v2
)
{
        return(DOT(v1,v2));
}


double
dist2(                          /* return square of distance between points */
const FVECT p1,
const FVECT p2
)
{
        FVECT  delta;

        VSUB(delta, p2, p1);

        return(DOT(delta, delta));
}


double
dist2line(                      /* return square of distance to line */
const FVECT p,          /* the point */
const FVECT ep1,
const FVECT ep2         /* points on the line */
)
{
        double  d, d1, d2;

        d = dist2(ep1, ep2);
        d1 = dist2(ep1, p);
        d2 = d + d1 - dist2(ep2, p);

        return(d1 - 0.25*d2*d2/d);
}


double
dist2lseg(                      /* return square of distance to line segment */
const FVECT p,          /* the point */
const FVECT ep1,
const FVECT ep2         /* the end points */
)
{
        double  d, d1, d2;

        d = dist2(ep1, ep2);
        d1 = dist2(ep1, p);
        d2 = dist2(ep2, p);

        if (d2 > d1) {                  /* check if past endpoints */
                if (d2 - d1 > d)
                        return(d1);
        } else {
                if (d1 - d2 > d)
                        return(d2);
        }
        d2 = d + d1 - d2;

        return(d1 - 0.25*d2*d2/d);      /* distance to line */
}


void
fcross(                         /* vres = v1 X v2 */
FVECT vres,
const FVECT v1,
const FVECT v2
)
{
        VCROSS(vres, v1, v2);
}


void
fvsum(                          /* vres = v0 + f*v1 */
FVECT vres,
const FVECT v0,
const FVECT v1,
double f
)
{
        VSUM(vres, v0, v1, f);
}


double
normalize(                      /* normalize a vector, return old magnitude */
FVECT  v
)
{
        double  len, d;
        
        d = DOT(v, v);
        
        if (d == 0.0)
                return(0.0);
        
        if ((d <= 1.0+FTINY) & (d >= 1.0-FTINY)) {
                len = 0.5 + 0.5*d;      /* first order approximation */
                d = 2.0 - len;
        } else {
                len = sqrt(d);
                d = 1.0/len;
        }
        v[0] *= d;
        v[1] *= d;
        v[2] *= d;

        return(len);
}


int
closestapproach(                        /* closest approach of two rays */
RREAL t[2],             /* returned distances along each ray */
const FVECT rorg0,              /* first origin */
const FVECT rdir0,              /* first direction (normalized) */
const FVECT rorg1,              /* second origin */
const FVECT rdir1               /* second direction (normalized) */
)
{
        double  dotprod = DOT(rdir0, rdir1);
        double  denom = 1. - dotprod*dotprod;
        double  o1o2_d1;
        FVECT   o0o1;

        if (denom <= FTINY) {           /* check if lines are parallel */
                t[0] = t[1] = 0.0;
                return(0);
        }
        VSUB(o0o1, rorg0, rorg1);
        o1o2_d1 = DOT(o0o1, rdir1);
        t[0] = (o1o2_d1*dotprod - DOT(o0o1,rdir0)) / denom;
        t[1] = o1o2_d1 + t[0]*dotprod;
        return(1);
}


void
spinvector(                             /* rotate vector around normal */
FVECT vres,             /* returned vector (same magnitude as vorig) */
const FVECT vorig,              /* original vector */
const FVECT vnorm,              /* normalized vector for rotation */
double theta            /* right-hand radians */
)
{
        double  sint, cost, normprod;
        FVECT  vperp;
        int  i;
        
        if (theta == 0.0) {
                if (vres != vorig)
                        VCOPY(vres, vorig);
                return;
        }
        cost = cos(theta);
        sint = sin(theta);
        normprod = DOT(vorig, vnorm)*(1.-cost);
        VCROSS(vperp, vnorm, vorig);
        for (i = 0; i < 3; i++)
                vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint;
}

double
geodesic(               /* rotate vector on great circle towards target */
FVECT vres,             /* returned vector (same magnitude as vorig) */
const FVECT vorig,      /* original vector */
const FVECT vtarg,      /* vector we are rotating towards */
double t,               /* amount along arc directed towards vtarg */
int meas                /* distance measure (radians, absolute, relative) */
)
{
        FVECT   normtarg;
        double  volen, dotprod, sintr, cost;
        int     i;

        VCOPY(normtarg, vtarg);         /* in case vtarg==vres */
        if (vres != vorig)
                VCOPY(vres, vorig);
        if (t == 0.0)
                return(VLEN(vres));     /* no rotation requested */
        if ((volen = normalize(vres)) == 0.0)
                return(0.0);
        if (normalize(normtarg) == 0.0)
                return(0.0);            /* target vector is zero */
        dotprod = DOT(vres, normtarg);
                                        /* check for colinear */
        if (dotprod >= 1.0-FTINY*FTINY) {
                if (meas != GEOD_REL)
                        return(0.0);
                vres[0] *= volen; vres[1] *= volen; vres[2] *= volen;
                return(volen);
        }
        if (dotprod <= -1.0+FTINY*FTINY)
                return(0.0);
        if (meas == GEOD_ABS)
                t /= volen;
        else if (meas == GEOD_REL)
                t *= acos(dotprod);
        cost = cos(t);
        sintr = sin(t) / sqrt(1. - dotprod*dotprod);
        for (i = 0; i < 3; i++)
                vres[i] = volen*( cost*vres[i] +
                                  sintr*(normtarg[i] - dotprod*vres[i]) );

        return(volen);                  /* return vector length */
}
Revision:	2.19
Committed:	Sat Jun 29 21:03:44 2013 UTC (12 years, 4 months ago) by greg
Content type:	text/plain
Branch:	MAIN
CVS Tags:	rad4R2, rad4R2P1, rad4R2P2
Changes since 2.18:	+21 -1 lines
Log Message:	Fixed problem with acos(1) returning NaN
#	User	Rev	Content
1	greg	1.1	#ifndef lint
2	greg	2.19	static const char RCSid[] = "$Id: fvect.c,v 2.18 2013/04/03 00:22:12 greg Exp $";
3	greg	1.1	#endif
4	greg	2.6	/*
5			* fvect.c - routines for floating-point vector calculations
6			*/
7	greg	1.1
8	greg	2.7	#include "copyright.h"
9	greg	1.1
10	greg	2.19	#define _USE_MATH_DEFINES
11	greg	2.2	#include <math.h>
12	greg	1.1	#include "fvect.h"
13
14	greg	2.19	double
15			Acos(double x) /* insurance for touchy math library */
16			{
17			if (x <= -1.+FTINY*FTINY)
18			return(M_PI);
19			if (x >= 1.-FTINY*FTINY)
20			return(.0);
21			return(acos(x));
22			}
23
24			double
25			Asin(double x) /* insurance for touchy math library */
26			{
27			if (x <= -1.+FTINY*FTINY)
28			return(-M_PI/2.);
29			if (x >= 1.-FTINY*FTINY)
30			return(M_PI/2);
31			return(asin(x));
32			}
33	greg	1.1
34			double
35	greg	2.8	fdot( /* return the dot product of two vectors */
36	greg	2.13	const FVECT v1,
37			const FVECT v2
38	greg	2.8	)
39	greg	1.1	{
40			return(DOT(v1,v2));
41			}
42
43
44			double
45	greg	2.8	dist2( /* return square of distance between points */
46	greg	2.13	const FVECT p1,
47			const FVECT p2
48	greg	2.8	)
49	greg	1.1	{
50	gwlarson	2.4	FVECT delta;
51	greg	1.1
52	greg	2.18	VSUB(delta, p2, p1);
53	gwlarson	2.5
54	greg	1.1	return(DOT(delta, delta));
55			}
56
57
58			double
59	greg	2.8	dist2line( /* return square of distance to line */
60	greg	2.13	const FVECT p, /* the point */
61			const FVECT ep1,
62			const FVECT ep2 /* points on the line */
63	greg	2.8	)
64	greg	1.1	{
65	greg	2.11	double d, d1, d2;
66	greg	1.1
67			d = dist2(ep1, ep2);
68			d1 = dist2(ep1, p);
69	gwlarson	2.5	d2 = d + d1 - dist2(ep2, p);
70	greg	1.1
71	gwlarson	2.5	return(d1 - 0.25d2d2/d);
72	greg	1.1	}
73
74
75			double
76	greg	2.8	dist2lseg( /* return square of distance to line segment */
77	greg	2.13	const FVECT p, /* the point */
78			const FVECT ep1,
79			const FVECT ep2 /* the end points */
80	greg	2.8	)
81	greg	1.1	{
82	greg	2.11	double d, d1, d2;
83	greg	1.1
84			d = dist2(ep1, ep2);
85			d1 = dist2(ep1, p);
86			d2 = dist2(ep2, p);
87
88			if (d2 > d1) { /* check if past endpoints */
89			if (d2 - d1 > d)
90			return(d1);
91			} else {
92			if (d1 - d2 > d)
93			return(d2);
94			}
95	gwlarson	2.5	d2 = d + d1 - d2;
96	greg	1.1
97	gwlarson	2.5	return(d1 - 0.25d2d2/d); /* distance to line */
98	greg	1.1	}
99
100
101	greg	2.6	void
102	greg	2.8	fcross( /* vres = v1 X v2 */
103	greg	2.11	FVECT vres,
104	greg	2.13	const FVECT v1,
105			const FVECT v2
106	greg	2.8	)
107	greg	1.1	{
108	greg	2.18	VCROSS(vres, v1, v2);
109	greg	1.1	}
110
111
112	greg	2.6	void
113	greg	2.8	fvsum( /* vres = v0 + fv1 /
114	greg	2.11	FVECT vres,
115	greg	2.13	const FVECT v0,
116			const FVECT v1,
117	greg	2.11	double f
118	greg	2.8	)
119	greg	1.4	{
120	greg	2.18	VSUM(vres, v0, v1, f);
121	greg	1.4	}
122
123
124	greg	1.1	double
125	greg	2.8	normalize( /* normalize a vector, return old magnitude */
126	greg	2.11	FVECT v
127	greg	2.8	)
128	greg	1.1	{
129	greg	2.11	double len, d;
130	greg	1.1
131	gwlarson	2.5	d = DOT(v, v);
132	greg	1.1
133	greg	2.10	if (d == 0.0)
134	greg	1.1	return(0.0);
135
136	greg	2.15	if ((d <= 1.0+FTINY) & (d >= 1.0-FTINY)) {
137	gwlarson	2.5	len = 0.5 + 0.5d; / first order approximation */
138	greg	2.12	d = 2.0 - len;
139			} else {
140	gwlarson	2.5	len = sqrt(d);
141	greg	2.12	d = 1.0/len;
142			}
143			v[0] *= d;
144	gwlarson	2.5	v[1] *= d;
145			v[2] *= d;
146	greg	2.3
147	greg	1.1	return(len);
148			}
149	greg	1.5
150
151	greg	2.8	int
152			closestapproach( /* closest approach of two rays */
153			RREAL t[2], /* returned distances along each ray */
154	greg	2.13	const FVECT rorg0, /* first origin */
155			const FVECT rdir0, /* first direction (normalized) */
156			const FVECT rorg1, /* second origin */
157			const FVECT rdir1 /* second direction (normalized) */
158	greg	2.8	)
159			{
160			double dotprod = DOT(rdir0, rdir1);
161			double denom = 1. - dotprod*dotprod;
162			double o1o2_d1;
163			FVECT o0o1;
164
165			if (denom <= FTINY) { /* check if lines are parallel */
166			t[0] = t[1] = 0.0;
167			return(0);
168			}
169			VSUB(o0o1, rorg0, rorg1);
170			o1o2_d1 = DOT(o0o1, rdir1);
171			t[0] = (o1o2_d1*dotprod - DOT(o0o1,rdir0)) / denom;
172			t[1] = o1o2_d1 + t[0]*dotprod;
173			return(1);
174			}
175
176
177	greg	2.6	void
178	greg	2.8	spinvector( /* rotate vector around normal */
179	greg	2.15	FVECT vres, /* returned vector (same magnitude as vorig) */
180	greg	2.13	const FVECT vorig, /* original vector */
181			const FVECT vnorm, /* normalized vector for rotation */
182	greg	2.14	double theta /* right-hand radians */
183	greg	2.8	)
184	greg	1.5	{
185	greg	1.6	double sint, cost, normprod;
186	greg	1.5	FVECT vperp;
187	greg	2.11	int i;
188	greg	1.5
189			if (theta == 0.0) {
190	greg	1.6	if (vres != vorig)
191			VCOPY(vres, vorig);
192	greg	1.5	return;
193			}
194	greg	1.6	cost = cos(theta);
195	greg	1.5	sint = sin(theta);
196	greg	1.6	normprod = DOT(vorig, vnorm)*(1.-cost);
197	greg	2.18	VCROSS(vperp, vnorm, vorig);
198	greg	1.5	for (i = 0; i < 3; i++)
199	greg	1.6	vres[i] = vorig[i]cost + vnorm[i]normprod + vperp[i]*sint;
200	greg	1.5	}
201	greg	2.15
202			double
203			geodesic( /* rotate vector on great circle towards target */
204			FVECT vres, /* returned vector (same magnitude as vorig) */
205			const FVECT vorig, /* original vector */
206			const FVECT vtarg, /* vector we are rotating towards */
207			double t, /* amount along arc directed towards vtarg */
208			int meas /* distance measure (radians, absolute, relative) */
209			)
210			{
211			FVECT normtarg;
212	greg	2.17	double volen, dotprod, sintr, cost;
213	greg	2.15	int i;
214
215	greg	2.16	VCOPY(normtarg, vtarg); /* in case vtarg==vres */
216	greg	2.15	if (vres != vorig)
217			VCOPY(vres, vorig);
218			if (t == 0.0)
219			return(VLEN(vres)); /* no rotation requested */
220			if ((volen = normalize(vres)) == 0.0)
221			return(0.0);
222			if (normalize(normtarg) == 0.0)
223			return(0.0); /* target vector is zero */
224			dotprod = DOT(vres, normtarg);
225			/* check for colinear */
226			if (dotprod >= 1.0-FTINY*FTINY) {
227			if (meas != GEOD_REL)
228			return(0.0);
229			vres[0] = volen; vres[1] = volen; vres[2] *= volen;
230			return(volen);
231			}
232			if (dotprod <= -1.0+FTINY*FTINY)
233			return(0.0);
234			if (meas == GEOD_ABS)
235			t /= volen;
236			else if (meas == GEOD_REL)
237			t *= acos(dotprod);
238			cost = cos(t);
239	greg	2.17	sintr = sin(t) / sqrt(1. - dotprod*dotprod);
240	greg	2.15	for (i = 0; i < 3; i++)
241			vres[i] = volen( costvres[i] +
242	greg	2.17	sintr(normtarg[i] - dotprodvres[i]) );
243	greg	2.15
244			return(volen); /* return vector length */
245			}