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#include "copyright.h" |
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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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|
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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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FVECT delta; |
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|
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delta[0] = p2[0] - p1[0]; |
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delta[1] = p2[1] - p1[1]; |
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delta[2] = p2[2] - p1[2]; |
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VSUB(delta, p2, p1); |
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return(DOT(delta, delta)); |
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} |
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const FVECT v2 |
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) |
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{ |
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vres[0] = v1[1]*v2[2] - v1[2]*v2[1]; |
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vres[1] = v1[2]*v2[0] - v1[0]*v2[2]; |
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vres[2] = v1[0]*v2[1] - v1[1]*v2[0]; |
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VCROSS(vres, v1, v2); |
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} |
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double f |
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) |
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{ |
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vres[0] = v0[0] + f*v1[0]; |
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vres[1] = v0[1] + f*v1[1]; |
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vres[2] = v0[2] + f*v1[2]; |
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VSUM(vres, v0, v1, f); |
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} |
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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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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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void |
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spinvector( /* rotate vector around normal */ |
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FVECT vres, /* returned vector */ |
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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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cost = cos(theta); |
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sint = sin(theta); |
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normprod = DOT(vorig, vnorm)*(1.-cost); |
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fcross(vperp, vnorm, vorig); |
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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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} |