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# tpors

erfa.tpors(xi, eta, a, b)

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

  Parameters
    xi double array
    eta double array
    a double array
    b double array
  Returns
    a01 double array
    b01 double array
    a02 double array
    b02 double array

  Notes

  Wraps ERFA function `eraTpors`. The ERFA documentation is:

      - - - - - - - - -
       e r a T p o r s
      - - - - - - - - -

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

      Given:
         xi,eta     double  rectangular coordinates of star image (Note 2)
         a,b        double  star's spherical coordinates (Note 3)

      Returned:
         *a01,*b01  double  tangent point's spherical coordinates, Soln. 1
         *a02,*b02  double  tangent point's spherical coordinates, Soln. 2

      Returned (function value):
                    int     number of solutions:
                            0 = no solutions returned (Note 5)
                            1 = only the first solution is useful (Note 6)
                            2 = both solutions are useful (Note 6)

      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

             eraTpxes      eraTpxev         xi,eta
             eraTpsts      eraTpstv          star
           > eraTpors <    eraTporv         origin

      Called:
         eraAnp       normalize angle into range 0 to 2pi

      References:

         Calabretta M.R. & Greisen, E.W., 2002, "Representations of
         celestial coordinates in FITS", Astron.Astrophys. 395, 1077

         Green, R.M., "Spherical Astronomy", Cambridge University Press,
         1987, Chapter 13.

      This revision:   2018 January 2

      Copyright (C) 2013-2021, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.