SUBROUTINE iau_TPXEV ( V, V0, XI, ETA, J )
*+
*  - - - - - - - - - -
*   i a u _ T P X E V
*  - - - - - - - - - -
*
*  In the tangent plane projection, given celestial direction cosines
*  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:
*     V         d(3)       direction cosines of star (Note 4)
*     V0        d(3)       direction cosines of tangent point (Note 4)
*
*  Returned:
*     XI,ETA    d          tangent plane coordinates of star
*     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 direction cosines represent observed (RA,Dec), the tangent
*     plane coordinates (xi,eta) are conventionally called the "standard
*     coordinates".  If the direction cosines 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) The method used is to extend the star vector to the tangent
*     plane and then rotate the triad so that (x,y) becomes (xi,eta).
*     Writing (a,b) for the celestial spherical coordinates of the
*     star, the sequence of rotations is (a+pi/2) around the z-axis
*     followed by (pi/2-b) around the x-axis.
*
*  4) If vector V0 is not of unit length, or if vector V is of zero
*     length, the results will be wrong.
*
*  5) If V0 points at a pole, the returned (XI,ETA) will be based on the
*     arbitrary assumption that the longitude coordinate of the tangent
*     point is zero.
*
*  6) 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 V(3), V0(3), XI, ETA
      INTEGER J

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

      DOUBLE PRECISION X, Y, Z, X0, Y0, Z0, R2, R, W, D

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

*  Star and tangent point.
      X = V(1)
      Y = V(2)
      Z = V(3)
      X0 = V0(1)
      Y0 = V0(2)
      Z0 = V0(3)

*  Deal with polar case.
      R2 = X0*X0 + Y0*Y0
      R = SQRT(R2)
      IF ( R .EQ. 0D0 ) THEN
         R = 1D-20
         X0 = R
      END IF

*  Reciprocal of star vector length to tangent plane.
      W = X*X0 + Y*Y0
      D = W + Z*Z0

*  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).
      D = R*D
      XI = ( Y*X0 - X*Y0 ) / D
      ETA = ( Z*R2 - Z0*W ) / D

*  Finished.

*+----------------------------------------------------------------------
*
*  Copyright (C) 2020
*  Standards Of Fundamental Astronomy Board
*  of the International Astronomical Union.
*
*  =====================
*  SOFA Software License
*  =====================
*
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*
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*
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*-----------------------------------------------------------------------

      END