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SUBROUTINE sla_TPV2C (XI, ETA, V, V01, V02, N)
*+
* - - - - - -
* T P V 2 C
* - - - - - -
*
* 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 sla_TPS2C.
*
* P.T.Wallace Starlink 5 June 1995
*
* Copyright (C) 1995 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
REAL XI,ETA,V(3),V01(3),V02(3)
INTEGER N
REAL X,Y,Z,RXY2,XI2,ETA2P1,SDF,R2,R,C
X=V(1)
Y=V(2)
Z=V(3)
RXY2=X*X+Y*Y
XI2=XI*XI
ETA2P1=ETA*ETA+1.0
SDF=Z*SQRT(XI2+ETA2P1)
R2=RXY2*ETA2P1-Z*Z*XI2
IF (R2.GT.0.0) THEN
R=SQRT(R2)
C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
V01(1)=C*(X*R+Y*XI)
V01(2)=C*(Y*R-X*XI)
V01(3)=(SDF-ETA*R)/ETA2P1
R=-R
C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
V02(1)=C*(X*R+Y*XI)
V02(2)=C*(Y*R-X*XI)
V02(3)=(SDF-ETA*R)/ETA2P1
IF (ABS(SDF).LT.1.0) THEN
N=1
ELSE
N=2
END IF
ELSE
N=0
END IF
END
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