#include "erfa.h"

void eraTpsts(double xi, double eta, double a0, double b0,
              double *a, double *b)
/*
**  - - - - - - - - -
**   e r a T p s t s
**  - - - - - - - - -
**
**  In the tangent plane projection, given the star's rectangular
**  coordinates and the spherical coordinates of the tangent point,
**  solve for the spherical coordinates of the star.
**
**  Given:
**     xi,eta    double  rectangular coordinates of star image (Note 2)
**     a0,b0     double  tangent point's spherical coordinates
**
**  Returned:
**     *a,*b     double  star's spherical coordinates
**
**  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) 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) 2013-2023, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double sb0, cb0, d;

   sb0 = sin(b0);
   cb0 = cos(b0);
   d = cb0 - eta*sb0;
   *a = eraAnp(atan2(xi,d) + a0);
   *b = atan2(sb0+eta*cb0, sqrt(xi*xi+d*d));

/* Finished. */

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2023, NumFOCUS Foundation.
**  All rights reserved.
**  
**  This library is derived, with permission, from the International
**  Astronomical Union's "Standards of Fundamental Astronomy" library,
**  available from http://www.iausofa.org.
**  
**  The ERFA version is intended to retain identical functionality to
**  the SOFA library, but made distinct through different function and
**  file names, as set out in the SOFA license conditions.  The SOFA
**  original has a role as a reference standard for the IAU and IERS,
**  and consequently redistribution is permitted only in its unaltered
**  state.  The ERFA version is not subject to this restriction and
**  therefore can be included in distributions which do not support the
**  concept of "read only" software.
**  
**  Although the intent is to replicate the SOFA API (other than
**  replacement of prefix names) and results (with the exception of
**  bugs;  any that are discovered will be fixed), SOFA is not
**  responsible for any errors found in this version of the library.
**  
**  If you wish to acknowledge the SOFA heritage, please acknowledge
**  that you are using a library derived from SOFA, rather than SOFA
**  itself.
**  
**  
**  TERMS AND CONDITIONS
**  
**  Redistribution and use in source and binary forms, with or without
**  modification, are permitted provided that the following conditions
**  are met:
**  
**  1 Redistributions of source code must retain the above copyright
**    notice, this list of conditions and the following disclaimer.
**  
**  2 Redistributions in binary form must reproduce the above copyright
**    notice, this list of conditions and the following disclaimer in
**    the documentation and/or other materials provided with the
**    distribution.
**  
**  3 Neither the name of the Standards Of Fundamental Astronomy Board,
**    the International Astronomical Union nor the names of its
**    contributors may be used to endorse or promote products derived
**    from this software without specific prior written permission.
**  
**  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
**  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
**  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
**  FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
**  COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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**  
*/
