SUBROUTINE iau_TPORS ( XI, ETA, A, B, A01, B01, A02, B02, N ) * * - - - - - - - - - - * i a u _ T P O R S * - - - - - - - - - - * * In the tangent plane projection, given the rectangular coordinates * of a star and its spherical coordinates, determine the spherical * coordinates of the tangent point. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * XI,ETA d rectangular coordinates of star image (Note 2) * A,B d star's spherical coordinates (Note 3) * * Returned: * A01,B01 d tangent point's spherical coordinates, Soln. 1 * A02,B02 d tangent point's spherical coordinates, Soln. 2 * N i number of solutions: * 0 = no solutions returned (Note 5) * 1 = only the first solution is useful (Note 6) * 2 = both solutions are useful (Note 6) * * 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 spherical coordinates are observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the "standard * coordinates". If the spherical coordinates 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) All angular arguments are in radians. * * 4) The angles A01 and A02 are returned in the range 0-2pi. The * angles B01 and B02 are returned in the range +/-pi, but in the * usual, non-pole-crossing, case, the range is +/-pi/2. * * 5) Cases where there is no solution can arise only 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 to bring about * this combination of xi and dec. * * 6) Also near the poles, cases can arise where there are two useful * solutions. The returned value N indicates whether the second of * the two solutions returned is useful; N=1 indicates only one * useful solution, the usual case. * * 7) The basis of the algorithm is to solve the spherical triangle PSC, * where P is the north celestial pole, S is the star and C is the * tangent point. The spherical coordinates of the tangent point are * [a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c * is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be * found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and * cos(C) = eta/rho. Angle P (to be found) is the longitude * difference between star and tangent point (a-a0). * * 8) 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 * * Called: * iau_ANP normalize angle into range 0 to 2pi * * 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 XI, ETA, A, B, A01, B01, A02, B02 INTEGER N DOUBLE PRECISION XI2, R, SB, CB, RSB, RCB, W2, W, S, C DOUBLE PRECISION iau_ANP * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - XI2 = XI*XI R = SQRT(1D0+XI2+ETA*ETA) SB = SIN(B) CB = COS(B) RSB = R*SB RCB = R*CB W2 = RCB*RCB - XI2 IF ( W2 .GE. 0D0 ) THEN W = SQRT(W2) S = RSB - ETA*W C = RSB*ETA + W IF ( XI .EQ. 0D0 .AND. W .EQ. 0D0 ) W = 1D0 A01 = iau_ANP(A - ATAN2(XI,W)) B01 = ATAN2(S,C) W = -W S = RSB - ETA*W C = RSB*ETA + W A02 = iau_ANP(A - ATAN2(XI,W)) B02 = ATAN2(S,C) IF ( ABS(RSB) .LT. 1D0 ) THEN N = 1 ELSE N = 2 END IF ELSE N = 0 END IF * 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