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#ifndef lint |
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static const char RCSid[] = "$Id: fvect.c,v 2.20 2014/12/04 05:26:27 greg Exp $"; |
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#endif |
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/* |
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* fvect.c - routines for floating-point vector calculations |
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*/ |
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|
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#include "copyright.h" |
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|
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#define _USE_MATH_DEFINES |
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#include <math.h> |
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#include "fvect.h" |
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#include "random.h" |
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|
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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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|
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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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|
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double |
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fdot( /* return the dot product of two vectors */ |
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const FVECT v1, |
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const FVECT v2 |
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) |
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{ |
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return(DOT(v1,v2)); |
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} |
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|
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|
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double |
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dist2( /* return square of distance between points */ |
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const FVECT p1, |
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const FVECT p2 |
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) |
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{ |
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FVECT delta; |
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|
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VSUB(delta, p2, p1); |
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|
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return(DOT(delta, delta)); |
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} |
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|
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|
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double |
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dist2line( /* return square of distance to line */ |
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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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) |
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{ |
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double d, d1, d2; |
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|
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d = dist2(ep1, ep2); |
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d1 = dist2(ep1, p); |
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d2 = d + d1 - dist2(ep2, p); |
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|
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return(d1 - 0.25*d2*d2/d); |
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} |
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|
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|
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double |
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dist2lseg( /* return square of distance to line segment */ |
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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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) |
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{ |
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double d, d1, d2; |
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|
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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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|
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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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d2 = d + d1 - d2; |
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|
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return(d1 - 0.25*d2*d2/d); /* distance to line */ |
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} |
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|
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|
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void |
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fcross( /* vres = v1 X v2 */ |
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FVECT vres, |
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const FVECT v1, |
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const FVECT v2 |
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) |
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{ |
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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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VCROSS(vres, v1, v2); |
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} |
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|
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|
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void |
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fvsum( /* vres = v0 + f*v1 */ |
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FVECT vres, |
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const FVECT v0, |
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const FVECT v1, |
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double f |
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) |
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{ |
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VSUM(vres, v0, v1, f); |
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} |
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|
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|
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double |
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normalize( /* normalize a vector, return old magnitude */ |
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FVECT v |
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) |
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{ |
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double len, d; |
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|
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d = DOT(v, v); |
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|
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if (d == 0.0) |
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return(0.0); |
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|
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if ((d <= 1.0+FTINY) & (d >= 1.0-FTINY)) { |
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len = 0.5 + 0.5*d; /* first order approximation */ |
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d = 2.0 - len; |
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} else { |
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len = sqrt(d); |
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d = 1.0/len; |
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} |
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v[0] *= d; |
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v[1] *= d; |
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v[2] *= d; |
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|
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return(len); |
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} |
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|
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|
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int |
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getperpendicular( /* choose random perpedicular direction */ |
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FVECT vp, /* returns normalized */ |
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const FVECT v /* input vector must be normalized */ |
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) |
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{ |
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FVECT v1; |
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int i; |
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/* randomize other 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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for (i = 3; i--; ) |
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if ((-0.6 < v[i]) & (v[i] < 0.6)) |
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break; |
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if (i < 0) |
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return(0); |
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v1[i] = 1.0; |
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fcross(vp, v1, v); |
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return(normalize(vp) > 0.0); |
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} |
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|
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|
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int |
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closestapproach( /* closest approach of two rays */ |
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RREAL t[2], /* returned distances along each ray */ |
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const FVECT rorg0, /* first origin */ |
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const FVECT rdir0, /* first direction (normalized) */ |
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const FVECT rorg1, /* second origin */ |
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const FVECT rdir1 /* second direction (normalized) */ |
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) |
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{ |
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double dotprod = DOT(rdir0, rdir1); |
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double denom = 1. - dotprod*dotprod; |
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double o1o2_d1; |
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FVECT o0o1; |
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|
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if (denom <= FTINY) { /* check if lines are parallel */ |
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t[0] = t[1] = 0.0; |
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return(0); |
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} |
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VSUB(o0o1, rorg0, rorg1); |
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o1o2_d1 = DOT(o0o1, rdir1); |
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t[0] = (o1o2_d1*dotprod - DOT(o0o1,rdir0)) / denom; |
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t[1] = o1o2_d1 + t[0]*dotprod; |
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return(1); |
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} |
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|
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|
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void |
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spinvector( /* rotate vector around normal */ |
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FVECT vres, /* returned vector (same magnitude as vorig) */ |
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const FVECT vorig, /* original vector */ |
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const FVECT vnorm, /* normalized vector for rotation */ |
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double theta /* right-hand radians */ |
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) |
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{ |
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double sint, cost, normprod; |
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FVECT vperp; |
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int i; |
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|
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if (theta == 0.0) { |
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if (vres != vorig) |
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VCOPY(vres, vorig); |
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return; |
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} |
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cost = cos(theta); |
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sint = sin(theta); |
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normprod = DOT(vorig, vnorm)*(1.-cost); |
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VCROSS(vperp, vnorm, vorig); |
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for (i = 0; i < 3; i++) |
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vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint; |
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} |
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|
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double |
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geodesic( /* rotate vector on great circle towards target */ |
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FVECT vres, /* returned vector (same magnitude as vorig) */ |
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const FVECT vorig, /* original vector */ |
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const FVECT vtarg, /* vector we are rotating towards */ |
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double t, /* amount along arc directed towards vtarg */ |
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int meas /* distance measure (radians, absolute, relative) */ |
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) |
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{ |
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FVECT normtarg; |
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double volen, dotprod, sintr, cost; |
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int i; |
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|
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VCOPY(normtarg, vtarg); /* in case vtarg==vres */ |
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if (vres != vorig) |
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VCOPY(vres, vorig); |
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if (t == 0.0) |
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return(VLEN(vres)); /* no rotation requested */ |
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if ((volen = normalize(vres)) == 0.0) |
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return(0.0); |
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if (normalize(normtarg) == 0.0) |
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return(0.0); /* target vector is zero */ |
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dotprod = DOT(vres, normtarg); |
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/* check for colinear */ |
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if (dotprod >= 1.0-FTINY*FTINY) { |
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if (meas != GEOD_REL) |
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return(0.0); |
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vres[0] *= volen; vres[1] *= volen; vres[2] *= volen; |
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return(volen); |
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} |
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if (dotprod <= -1.0+FTINY*FTINY) |
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return(0.0); |
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if (meas == GEOD_ABS) |
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t /= volen; |
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else if (meas == GEOD_REL) |
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t *= acos(dotprod); |
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cost = cos(t); |
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sintr = sin(t) / sqrt(1. - dotprod*dotprod); |
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for (i = 0; i < 3; i++) |
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vres[i] = volen*( cost*vres[i] + |
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sintr*(normtarg[i] - dotprod*vres[i]) ); |
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|
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return(volen); /* return vector length */ |
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} |
