| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaDtpv2c ( double xi, double eta, double v[3], double v01[3],
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| 4 | double v02[3], int *n )
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| 5 | /*
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| 6 | ** - - - - - - - - - -
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| 7 | ** s l a D t p v 2 c
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| 8 | ** - - - - - - - - - -
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| 9 | **
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| 10 | ** Given the tangent-plane coordinates of a star and its direction
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| 11 | ** cosines, determine the direction cosines of the tangent-point.
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| 12 | **
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| 13 | ** (double precision)
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| 14 | **
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| 15 | ** Given:
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| 16 | ** xi,eta double tangent plane coordinates of star
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| 17 | ** v double[3] direction cosines of star
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| 18 | **
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| 19 | ** Returned:
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| 20 | ** v01 double[3] direction cosines of TP, solution 1
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| 21 | ** v02 double[3] direction cosines of TP, solution 2
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| 22 | ** *n int number of solutions:
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| 23 | ** 0 = no solutions returned (note 2)
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| 24 | ** 1 = only the first solution is useful (note 3)
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| 25 | ** 2 = both solutions are useful (note 3)
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| 26 | **
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| 27 | ** Notes:
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| 28 | **
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| 29 | ** 1 The vector v must be of unit length or the result will be wrong.
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| 30 | **
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| 31 | ** 2 Cases where there is no solution can only arise near the poles.
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| 32 | ** For example, it is clearly impossible for a star at the pole
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| 33 | ** itself to have a non-zero xi value, and hence it is meaningless
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| 34 | ** to ask where the tangent point would have to be.
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| 35 | **
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| 36 | ** 3 Also near the poles, cases can arise where there are two useful
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| 37 | ** solutions. The argument n indicates whether the second of the
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| 38 | ** two solutions returned is useful; n=1 indicates only one useful
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| 39 | ** solution, the usual case. Under these circumstances, the second
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| 40 | ** solution can be regarded as valid if the vector v02 is interpreted
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| 41 | ** as the "over-the-pole" case.
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| 42 | **
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| 43 | ** 4 This routine is the Cartesian equivalent of the routine slaDtps2c.
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| 44 | **
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| 45 | ** Last revision: 5 June 1995
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| 46 | **
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| 47 | ** Copyright P.T.Wallace. All rights reserved.
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| 48 | */
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| 49 | {
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| 50 | double x, y, z, rxy2, xi2, eta2p1, sdf, r2, r, c;
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| 51 |
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| 52 |
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| 53 | x = v[0];
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| 54 | y = v[1];
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| 55 | z = v[2];
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| 56 | rxy2 = x * x + y * y;
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| 57 | xi2 = xi * xi;
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| 58 | eta2p1 = eta*eta + 1.0;
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| 59 | sdf = z * sqrt ( xi2 + eta2p1 );
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| 60 | r2 = rxy2 * eta2p1 - z * z * xi2;
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| 61 | if ( r2 > 0.0 ) {
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| 62 | r = sqrt( r2 );
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| 63 | c = ( sdf * eta + r ) / ( eta2p1 * sqrt ( rxy2 * ( r2 + xi2 ) ) );
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| 64 | v01[0] = c * ( x * r + y * xi );
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| 65 | v01[1] = c * ( y * r - x * xi );
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| 66 | v01[2] = ( sdf - eta * r ) / eta2p1;
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| 67 | r = - r;
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| 68 | c = ( sdf * eta + r ) / ( eta2p1 * sqrt ( rxy2 * ( r2 + xi2 ) ) );
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| 69 | v02[0] = c * ( x * r + y * xi );
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| 70 | v02[1] = c * ( y * r - x * xi );
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| 71 | v02[2] = ( sdf - eta * r ) / eta2p1;
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| 72 | *n = ( fabs ( sdf ) < 1.0 ) ? 1 : 2;
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| 73 | } else {
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| 74 | *n = 0;
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| 75 | }
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| 76 | }
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