#include "sofa.h"

Include dependency graph for tpors.c:

Functions
int	iauTpors (double xi, double eta, double a, double b, double a01, double b01, double a02, double b02)
	In the tangent plane projection, determine the spherical coordinates of the tangent point. More...

Function Documentation

◆ iauTpors()

int iauTpors	(	double	xi,
		double	eta,
		double	a,
		double	b,
		double *	a01,
		double *	b01,
		double *	a02,
		double *	b02
	)

In the tangent plane projection, determine the spherical coordinates of the tangent point.

In the tangent plane projection, given the rectangular coordinates of a star and its spherical coordinates, determine the spherical coordinates of the tangent point.

Notes:

1) The tangent plane projection is also called the "gnomonic projection" and the "central projection".

2) The eta axis points due north in the adopted coordinate system. If the spherical coordinates are observed (RA,Dec), the tangent plane coordinates (xi,eta) are conventionally called the "standard coordinates". If the spherical coordinates are with respect to a right-handed triad, (xi,eta) are also right-handed. The units of (xi,eta) are, effectively, radians at the tangent point.

3) All angular arguments are in radians.

4) The angles a01 and a02 are returned in the range 0-2pi. The angles b01 and b02 are returned in the range +/-pi, but in the usual, non-pole-crossing, case, the range is +/-pi/2.

5) Cases where there is no solution can arise only near the poles. For example, it is clearly impossible for a star at the pole itself to have a non-zero xi value, and hence it is meaningless to ask where the tangent point would have to be to bring about this combination of xi and dec.

6) Also near the poles, cases can arise where there are two useful solutions. The return value indicates whether the second of the two solutions returned is useful; 1 indicates only one useful solution, the usual case.

7) The basis of the algorithm is to solve the spherical triangle PSC, where P is the north celestial pole, S is the star and C is the tangent point. The spherical coordinates of the tangent point are [a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and cos(C) = eta/rho. Angle P (to be found) is the longitude difference between star and tangent point (a-a0).

8) This function is a member of the following set:

         spherical      vector         solve for

         iauTpxes      iauTpxev         xi,eta
         iauTpsts      iauTpstv          star
       > iauTpors <    iauTporv         origin

Parameters

[in]	xi	rectangular coordinates of star image
[in]	eta	rectangular coordinates of star image
[out]	a01	tangent point's spherical coordinates soln 1
[out]	b01	tangent point's spherical coordinates soln 1
[out]	a02	tangent point's spherical coordinates soln 2
[out]	b02	tangent point's spherical coordinates soln 2

Returns: number of solutions: 0= no solutions returnd, 1 = only the first solution is useful, 2= both solutions are useful.

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Function Documentation

◆ iauTpors()