TPSTV Subroutine

public subroutine TPSTV(xi, eta, v0, v)

In the tangent plane projection, given the star's rectangular coordinates and the direction cosines of the tangent point, solve for the direction cosines of the star.

Status: support routine.

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 complete the star vector in the (xi,eta) based triad and normalize it, then rotate the triad to put the tangent point at the pole with the x-axis aligned to zero longitude. Writing (a0,b0) for the celestial spherical coordinates of the tangent point, the sequence of rotations is (b0-pi/2) around the x-axis followed by (-a0-pi/2) around the z-axis.

4. If vector V0 is not of unit length, the returned vector V will be wrong.

5. If vector V0 points at a pole, the returned vector V 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
   
    TPXES      TPXEV      xi,eta
    TPSTS    > TPSTV <     star
    TPORS      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.

History

• IAU SOFA revision: 2018 January 2

Arguments

    subroutine TPSTV ( xi, eta, v0, v )

    implicit none

    real(wp),intent(in) :: xi !! rectangular coordinates of star image (Note 2)
    real(wp),intent(in) :: eta !! rectangular coordinates of star image (Note 2)
    real(wp),dimension(3),intent(in) :: v0 !! tangent point's direction cosines (Note 4)
    real(wp),dimension(3),intent(out) :: v !! star's direction cosines

    real(wp) :: x, y, z, r, f

    !  Tangent point.
    x = v0(1)
    y = v0(2)
    z = v0(3)

    !  Deal with polar case.
    r = sqrt(x*x+y*y)
    if ( r == 0.0_wp ) then
       r = 1e-20_wp
       x = r
    end if

    !  Star vector length to tangent plane.
    f = sqrt(1.0_wp+xi*xi+eta*eta)

    !  Apply the transformation and normalize.
    v(1) = ( x - (xi*y+eta*x*z) / r ) / f
    v(2) = ( y + (xi*x-eta*y*z) / r ) / f
    v(3) = ( z + eta*r ) / f

    end subroutine TPSTV