.help tpv2c Jun99 "Slalib Package"
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      SUBROUTINE slTPVC (XI, ETA, V, V01, V02, N)

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      T P V C
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  Given the tangent-plane coordinates of a star and its direction
  cosines, determine the direction cosines of the tangent-point.

  (single precision)

  Given:
     XI,ETA    r       tangent plane coordinates of star
     V         r(3)    direction cosines of star

  Returned:
     V01       r(3)    direction cosines of tangent point, solution 1
     V02       r(3)    direction cosines of tangent point, solution 2
     N         i       number of solutions:
                         0 = no solutions returned (note 2)
                         1 = only the first solution is useful (note 3)
                         2 = both solutions are useful (note 3)

  Notes:

  1  The vector V must be of unit length or the result will be wrong.

  2  Cases where there is no solution can only arise 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.

  3  Also near the poles, cases can arise where there are two useful
     solutions.  The argument N indicates whether the second of the
     two solutions returned is useful.  N=1 indicates only one useful
     solution, the usual case;  under these circumstances, the second
     solution can be regarded as valid if the vector V02 is interpreted
     as the "over-the-pole" case.

  4  This routine is the Cartesian equivalent of the routine slTPSC.

  P.T.Wallace   Starlink   5 June 1995

  Copyright (C) 1995 Rutherford Appleton Laboratory
  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.

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