SLA_TPV2C - Plate centre from and

**ACTION:**- From the tangent plane coordinates of a star of known
direction cosines, determine the direction cosines
of the tangent point (single precision)
**CALL:**`CALL sla_TPV2C (XI, ETA, V, V01, V02, N)`

**GIVEN:**-

*XI,ETA***R**tangent plane coordinates of star (radians) *V***R(3)**direction cosines of star

**RETURNED:**-

*V01***R(3)**direction cosines of tangent point, solution 1 *V01***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 = there are two useful solutions (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.
- 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.
- The projection is called the
*gnomonic*projection; the Cartesian coordinates are called*standard coordinates.*The latter are in units of the distance from the tangent plane to the projection point,*i.e.*radians near the origin. - 5.
- This routine is the Cartesian equivalent of the routine sla_TPS2C.

Starlink User Note 67

P. T. Wallace

12 October 1999

E-mail:ptw@star.rl.ac.uk