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 2023-10-11 * * Copyright (C) 2023 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) 2023 * Standards of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END