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greg |
1.1 |
#ifndef lint |
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greg |
2.22 |
static const char RCSid[] = "$Id: fvect.c,v 2.21 2014/12/08 23:51:12 greg Exp $"; |
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greg |
1.1 |
#endif |
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greg |
2.6 |
/* |
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* fvect.c - routines for floating-point vector calculations |
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*/ |
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greg |
1.1 |
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greg |
2.7 |
#include "copyright.h" |
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greg |
1.1 |
|
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greg |
2.19 |
#define _USE_MATH_DEFINES |
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greg |
2.2 |
#include <math.h> |
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greg |
1.1 |
#include "fvect.h" |
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2.20 |
#include "random.h" |
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greg |
1.1 |
|
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greg |
2.19 |
double |
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Acos(double x) /* insurance for touchy math library */ |
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{ |
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if (x <= -1.+FTINY*FTINY) |
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return(M_PI); |
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if (x >= 1.-FTINY*FTINY) |
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return(.0); |
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return(acos(x)); |
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} |
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double |
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Asin(double x) /* insurance for touchy math library */ |
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{ |
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if (x <= -1.+FTINY*FTINY) |
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return(-M_PI/2.); |
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if (x >= 1.-FTINY*FTINY) |
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return(M_PI/2); |
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return(asin(x)); |
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} |
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greg |
1.1 |
|
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double |
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greg |
2.8 |
fdot( /* return the dot product of two vectors */ |
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greg |
2.13 |
const FVECT v1, |
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const FVECT v2 |
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greg |
2.8 |
) |
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greg |
1.1 |
{ |
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return(DOT(v1,v2)); |
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} |
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double |
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greg |
2.8 |
dist2( /* return square of distance between points */ |
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greg |
2.13 |
const FVECT p1, |
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const FVECT p2 |
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2.8 |
) |
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greg |
1.1 |
{ |
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gwlarson |
2.4 |
FVECT delta; |
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greg |
1.1 |
|
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2.18 |
VSUB(delta, p2, p1); |
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gwlarson |
2.5 |
|
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greg |
1.1 |
return(DOT(delta, delta)); |
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} |
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double |
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2.8 |
dist2line( /* return square of distance to line */ |
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2.13 |
const FVECT p, /* the point */ |
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const FVECT ep1, |
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const FVECT ep2 /* points on the line */ |
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2.8 |
) |
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greg |
1.1 |
{ |
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2.11 |
double d, d1, d2; |
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1.1 |
|
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d = dist2(ep1, ep2); |
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d1 = dist2(ep1, p); |
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gwlarson |
2.5 |
d2 = d + d1 - dist2(ep2, p); |
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1.1 |
|
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gwlarson |
2.5 |
return(d1 - 0.25*d2*d2/d); |
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1.1 |
} |
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double |
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2.8 |
dist2lseg( /* return square of distance to line segment */ |
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2.13 |
const FVECT p, /* the point */ |
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const FVECT ep1, |
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const FVECT ep2 /* the end points */ |
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2.8 |
) |
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greg |
1.1 |
{ |
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2.11 |
double d, d1, d2; |
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1.1 |
|
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d = dist2(ep1, ep2); |
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d1 = dist2(ep1, p); |
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d2 = dist2(ep2, p); |
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if (d2 > d1) { /* check if past endpoints */ |
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if (d2 - d1 > d) |
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return(d1); |
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} else { |
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if (d1 - d2 > d) |
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return(d2); |
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} |
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gwlarson |
2.5 |
d2 = d + d1 - d2; |
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1.1 |
|
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gwlarson |
2.5 |
return(d1 - 0.25*d2*d2/d); /* distance to line */ |
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1.1 |
} |
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2.6 |
void |
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2.8 |
fcross( /* vres = v1 X v2 */ |
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2.11 |
FVECT vres, |
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2.13 |
const FVECT v1, |
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const FVECT v2 |
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2.8 |
) |
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1.1 |
{ |
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2.21 |
if ((vres == v1) | (vres == v2)) { |
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FVECT vtmp; |
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VCROSS(vtmp, v1, v2); |
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VCOPY(vres, vtmp); |
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return; |
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} |
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2.18 |
VCROSS(vres, v1, v2); |
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1.1 |
} |
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2.6 |
void |
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greg |
2.8 |
fvsum( /* vres = v0 + f*v1 */ |
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2.11 |
FVECT vres, |
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2.13 |
const FVECT v0, |
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const FVECT v1, |
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2.11 |
double f |
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2.8 |
) |
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greg |
1.4 |
{ |
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2.18 |
VSUM(vres, v0, v1, f); |
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greg |
1.4 |
} |
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greg |
1.1 |
double |
132 |
greg |
2.8 |
normalize( /* normalize a vector, return old magnitude */ |
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2.11 |
FVECT v |
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greg |
2.8 |
) |
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greg |
1.1 |
{ |
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greg |
2.11 |
double len, d; |
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1.1 |
|
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gwlarson |
2.5 |
d = DOT(v, v); |
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greg |
1.1 |
|
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greg |
2.10 |
if (d == 0.0) |
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greg |
1.1 |
return(0.0); |
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greg |
2.15 |
if ((d <= 1.0+FTINY) & (d >= 1.0-FTINY)) { |
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gwlarson |
2.5 |
len = 0.5 + 0.5*d; /* first order approximation */ |
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greg |
2.12 |
d = 2.0 - len; |
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} else { |
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gwlarson |
2.5 |
len = sqrt(d); |
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greg |
2.12 |
d = 1.0/len; |
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} |
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v[0] *= d; |
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gwlarson |
2.5 |
v[1] *= d; |
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v[2] *= d; |
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greg |
2.3 |
|
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greg |
1.1 |
return(len); |
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} |
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greg |
1.5 |
|
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greg |
2.8 |
int |
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greg |
2.22 |
getperpendicular( /* choose perpedicular direction */ |
160 |
greg |
2.21 |
FVECT vp, /* returns normalized */ |
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greg |
2.22 |
const FVECT v, /* input vector must be normalized */ |
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int randomize /* randomize orientation */ |
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greg |
2.20 |
) |
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{ |
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greg |
2.22 |
int ord[3]; |
166 |
greg |
2.20 |
FVECT v1; |
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int i; |
168 |
greg |
2.22 |
|
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if (randomize) { /* randomize coordinates? */ |
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v1[0] = 0.5 - frandom(); |
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v1[1] = 0.5 - frandom(); |
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v1[2] = 0.5 - frandom(); |
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switch (ord[0] = (int)(frandom()*2.99999)) { |
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case 0: |
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ord[1] = 1 + (frandom() > .5); |
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ord[2] = 2 - ord[1]; |
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break; |
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case 1: |
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ord[1] = 2*(frandom() > .5); |
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ord[2] = 2 - ord[1]; |
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break; |
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case 2: |
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ord[1] = (frandom() > .5); |
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ord[2] = 1 - ord[1]; |
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break; |
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} |
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} else { |
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v1[0] = v1[1] = v1[2] = .0; |
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ord[0] = 0; ord[1] = 1; ord[2] = 2; |
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} |
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greg |
2.20 |
for (i = 3; i--; ) |
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greg |
2.22 |
if ((-0.6 < v[ord[i]]) & (v[ord[i]] < 0.6)) |
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greg |
2.20 |
break; |
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if (i < 0) |
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return(0); |
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greg |
2.22 |
|
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v1[ord[i]] = 1.0; |
199 |
greg |
2.21 |
fcross(vp, v1, v); |
200 |
greg |
2.22 |
|
201 |
greg |
2.20 |
return(normalize(vp) > 0.0); |
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} |
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greg |
2.21 |
|
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greg |
2.20 |
int |
206 |
greg |
2.8 |
closestapproach( /* closest approach of two rays */ |
207 |
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RREAL t[2], /* returned distances along each ray */ |
208 |
greg |
2.13 |
const FVECT rorg0, /* first origin */ |
209 |
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const FVECT rdir0, /* first direction (normalized) */ |
210 |
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const FVECT rorg1, /* second origin */ |
211 |
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const FVECT rdir1 /* second direction (normalized) */ |
212 |
greg |
2.8 |
) |
213 |
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{ |
214 |
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double dotprod = DOT(rdir0, rdir1); |
215 |
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double denom = 1. - dotprod*dotprod; |
216 |
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double o1o2_d1; |
217 |
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FVECT o0o1; |
218 |
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219 |
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if (denom <= FTINY) { /* check if lines are parallel */ |
220 |
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t[0] = t[1] = 0.0; |
221 |
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return(0); |
222 |
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} |
223 |
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VSUB(o0o1, rorg0, rorg1); |
224 |
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o1o2_d1 = DOT(o0o1, rdir1); |
225 |
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t[0] = (o1o2_d1*dotprod - DOT(o0o1,rdir0)) / denom; |
226 |
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t[1] = o1o2_d1 + t[0]*dotprod; |
227 |
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return(1); |
228 |
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} |
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greg |
2.6 |
void |
232 |
greg |
2.8 |
spinvector( /* rotate vector around normal */ |
233 |
greg |
2.15 |
FVECT vres, /* returned vector (same magnitude as vorig) */ |
234 |
greg |
2.13 |
const FVECT vorig, /* original vector */ |
235 |
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const FVECT vnorm, /* normalized vector for rotation */ |
236 |
greg |
2.14 |
double theta /* right-hand radians */ |
237 |
greg |
2.8 |
) |
238 |
greg |
1.5 |
{ |
239 |
greg |
1.6 |
double sint, cost, normprod; |
240 |
greg |
1.5 |
FVECT vperp; |
241 |
greg |
2.11 |
int i; |
242 |
greg |
1.5 |
|
243 |
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if (theta == 0.0) { |
244 |
greg |
1.6 |
if (vres != vorig) |
245 |
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VCOPY(vres, vorig); |
246 |
greg |
1.5 |
return; |
247 |
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} |
248 |
greg |
1.6 |
cost = cos(theta); |
249 |
greg |
1.5 |
sint = sin(theta); |
250 |
greg |
1.6 |
normprod = DOT(vorig, vnorm)*(1.-cost); |
251 |
greg |
2.18 |
VCROSS(vperp, vnorm, vorig); |
252 |
greg |
1.5 |
for (i = 0; i < 3; i++) |
253 |
greg |
1.6 |
vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint; |
254 |
greg |
1.5 |
} |
255 |
greg |
2.15 |
|
256 |
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double |
257 |
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geodesic( /* rotate vector on great circle towards target */ |
258 |
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FVECT vres, /* returned vector (same magnitude as vorig) */ |
259 |
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const FVECT vorig, /* original vector */ |
260 |
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const FVECT vtarg, /* vector we are rotating towards */ |
261 |
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double t, /* amount along arc directed towards vtarg */ |
262 |
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int meas /* distance measure (radians, absolute, relative) */ |
263 |
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) |
264 |
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{ |
265 |
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FVECT normtarg; |
266 |
greg |
2.17 |
double volen, dotprod, sintr, cost; |
267 |
greg |
2.15 |
int i; |
268 |
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|
269 |
greg |
2.16 |
VCOPY(normtarg, vtarg); /* in case vtarg==vres */ |
270 |
greg |
2.15 |
if (vres != vorig) |
271 |
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VCOPY(vres, vorig); |
272 |
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if (t == 0.0) |
273 |
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return(VLEN(vres)); /* no rotation requested */ |
274 |
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if ((volen = normalize(vres)) == 0.0) |
275 |
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return(0.0); |
276 |
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if (normalize(normtarg) == 0.0) |
277 |
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return(0.0); /* target vector is zero */ |
278 |
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dotprod = DOT(vres, normtarg); |
279 |
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/* check for colinear */ |
280 |
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if (dotprod >= 1.0-FTINY*FTINY) { |
281 |
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if (meas != GEOD_REL) |
282 |
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return(0.0); |
283 |
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vres[0] *= volen; vres[1] *= volen; vres[2] *= volen; |
284 |
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return(volen); |
285 |
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} |
286 |
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if (dotprod <= -1.0+FTINY*FTINY) |
287 |
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return(0.0); |
288 |
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if (meas == GEOD_ABS) |
289 |
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t /= volen; |
290 |
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else if (meas == GEOD_REL) |
291 |
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t *= acos(dotprod); |
292 |
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cost = cos(t); |
293 |
greg |
2.17 |
sintr = sin(t) / sqrt(1. - dotprod*dotprod); |
294 |
greg |
2.15 |
for (i = 0; i < 3; i++) |
295 |
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vres[i] = volen*( cost*vres[i] + |
296 |
greg |
2.17 |
sintr*(normtarg[i] - dotprod*vres[i]) ); |
297 |
greg |
2.15 |
|
298 |
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return(volen); /* return vector length */ |
299 |
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} |