SUBROUTINE iau_TPXES ( A, B, A0, B0, XI, ETA, J )
*+
*  - - - - - - - - - -
*   i a u _ T P X E S
*  - - - - - - - - - -
*
*  In the tangent plane projection, given celestial spherical
*  coordinates for a star and the tangent point, solve for the star's
*  rectangular coordinates in the tangent plane.
*
*  This routine is part of the International Astronomical Union's
*  SOFA (Standards of Fundamental Astronomy) software collection.
*
*  Status:  support routine.
*
*  Given:
*     A,B       d       star's spherical coordinates
*     A0,B0     d       tangent point's spherical coordinates
*
*  Returned:
*     XI,ETA    d       rectangular coordinates of star image (Note 2)
*     J         i       status:  0 = OK
*                                1 = star too far from axis
*                                2 = antistar on tangent plane
*                                3 = antistar too far from axis
*
*  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".  For right-handed spherical coordinates, (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 routine is a member of the following set:
*
*         spherical       vector       solve for
*
*       > iau_TPXES <    iau_TPXEV       xi,eta
*         iau_TPSTS      iau_TPSTV        star
*         iau_TPORS      iau_TPORV       origin
*
*  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
*
*  SOFA release 2020-07-21
*
*  Copyright (C) 2020 IAU SOFA Board.  See notes at end.
*
*-----------------------------------------------------------------------

      IMPLICIT NONE

      DOUBLE PRECISION A, B, A0, B0, XI, ETA
      INTEGER J

      DOUBLE PRECISION TINY
      PARAMETER ( TINY = 1D-6 )

      DOUBLE PRECISION SB0, SB, CB0, CB, DA, SDA, CDA, D

* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*  Functions of the spherical coordinates.
      SB0 = SIN(B0)
      SB = SIN(B)
      CB0 = COS(B0)
      CB = COS(B)
      DA = A - A0
      SDA = SIN(DA)
      CDA = COS(DA)

*  Reciprocal of star vector length to tangent plane.
      D = SB*SB0 + CB*CB0*CDA

*  Check for error cases.
      IF ( D .GT. TINY ) THEN
         J = 0
      ELSE IF ( D .GE. 0D0 ) THEN
         J = 1
         D = TINY
      ELSE IF ( D .GT. -TINY ) THEN
         J = 2
         D = -TINY
      ELSE
         J = 3
      END IF

*  Return the tangent plane coordinates (even in dubious cases).
      XI = CB*SDA / D
      ETA = ( SB*CB0 - CB*SB0*CDA ) / D

*  Finished.

*+----------------------------------------------------------------------
*
*  Copyright (C) 2020
*  Standards Of Fundamental Astronomy Board
*  of the International Astronomical Union.
*
*  =====================
*  SOFA Software License
*  =====================
*
*  NOTICE TO USER:
*
*  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
*  CONDITIONS WHICH APPLY TO ITS USE.
*
*  1. The Software is owned by the IAU SOFA Board ("SOFA").
*
*  2. Permission is granted to anyone to use the SOFA software for any
*     purpose, including commercial applications, free of charge and
*     without payment of royalties, subject to the conditions and
*     restrictions listed below.
*
*  3. You (the user) may copy and distribute SOFA source code to others,
*     and use and adapt its code and algorithms in your own software,
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*     of SOFA source code files is a "derived work" that must comply
*     with the following requirements:
*
*     a) Your work shall be marked or carry a statement that it
*        (i) uses routines and computations derived by you from
*        software provided by SOFA under license to you; and
*        (ii) does not itself constitute software provided by and/or
*        endorsed by SOFA.
*
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*
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*
*  In any published work or commercial product which uses the SOFA
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*
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*  follows:
*
*      By email:  sofa@ukho.gov.uk
*      By post:   IAU SOFA Center
*                 HM Nautical Almanac Office
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*
*-----------------------------------------------------------------------

      END