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-/* arcdot.c
- *
- * Angle between two vectors
- *
- *
- *
- *
- * SYNOPSIS:
- *
- * double p[3], q[3], arcdot();
- *
- * y = arcdot( p, q );
- *
- *
- *
- * DESCRIPTION:
- *
- * For two vectors p, q, the angle A between them is given by
- *
- * p.q / (|p| |q|) = cos A .
- *
- * where "." represents inner product, "|x|" the length of vector x.
- * If the angle is small, an expression in sin A is preferred.
- * Set r = q - p. Then
- *
- * p.q = p.p + p.r ,
- *
- * |p|^2 = p.p ,
- *
- * |q|^2 = p.p + 2 p.r + r.r ,
- *
- * p.p^2 + 2 p.p p.r + p.r^2
- * cos^2 A = ----------------------------
- * p.p (p.p + 2 p.r + r.r)
- *
- * p.p + 2 p.r + p.r^2 / p.p
- * = --------------------------- ,
- * p.p + 2 p.r + r.r
- *
- * sin^2 A = 1 - cos^2 A
- *
- * r.r - p.r^2 / p.p
- * = --------------------
- * p.p + 2 p.r + r.r
- *
- * = (r.r - p.r^2 / p.p) / q.q .
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -1, 1 10^6 1.7e-16 4.2e-17
- *
- */
-
-/*
-Cephes Math Library Release 2.3: November, 1995
-Copyright 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double acos ( double );
-extern double asin ( double );
-extern double atan ( double );
-#else
-double sqrt(), acos(), asin(), atan();
-#endif
-extern double PI;
-
-double arcdot(p,q)
-double p[], q[];
-{
-double pp, pr, qq, rr, rt, pt, qt, pq;
-int i;
-
-pq = 0.0;
-qq = 0.0;
-pp = 0.0;
-pr = 0.0;
-rr = 0.0;
-for (i=0; i<3; i++)
- {
- pt = p[i];
- qt = q[i];
- pq += pt * qt;
- qq += qt * qt;
- pp += pt * pt;
- rt = qt - pt;
- pr += pt * rt;
- rr += rt * rt;
- }
-if (rr == 0.0 || pp == 0.0 || qq == 0.0)
- return 0.0;
-rt = (rr - (pr * pr) / pp) / qq;
-if (rt <= 0.75)
- {
- rt = sqrt(rt);
- qt = asin(rt);
- if (pq < 0.0)
- qt = PI - qt;
- }
-else
- {
- pt = pq / sqrt(pp*qq);
- qt = acos(pt);
- }
-return qt;
-}