#include "sofa.h" int iauTporv(double xi, double eta, double v[3], double v01[3], double v02[3]) /* ** - - - - - - - - - ** i a u T p o r v ** - - - - - - - - - ** ** In the tangent plane projection, given the rectangular coordinates ** of a star and its direction cosines, determine the direction ** cosines of the tangent point. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** xi,eta double rectangular coordinates of star image (Note 2) ** v double[3] star's direction cosines (Note 3) ** ** Returned: ** v01 double[3] tangent point's direction cosines, Solution 1 ** v02 double[3] tangent point's direction cosines, Solution 2 ** ** Returned (function value): ** int number of solutions: ** 0 = no solutions returned (Note 4) ** 1 = only the first solution is useful (Note 5) ** 2 = both solutions are useful (Note 5) ** ** 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 vector v must be of unit length or the result will be wrong. ** ** 4) 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. ** ** 5) Also near the poles, cases can arise where there are two useful ** solutions. The return value indicates whether the second of the ** two solutions returned is useful; 1 indicates only one useful ** solution, the usual case. ** ** 6) 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. Calling the celestial spherical coordinates ** of the star and tangent point (a,b) and (a0,b0) respectively, and ** writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), and ** transforming the vector v into (a,b) in the normal way, 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), while angle C is given by sin(C) = xi/rho ** and cos(C) = eta/rho; angle P (to be found) is (a-a0). After ** solving the spherical triangle, the result (a0,b0) can be ** expressed in vector form as v0. ** ** 7) This function is a member of the following set: ** ** spherical vector solve for ** ** iauTpxes iauTpxev xi,eta ** iauTpsts iauTpstv star ** iauTpors > iauTporv < 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 2019-07-22 ** ** Copyright (C) 2019 IAU SOFA Board. See notes at end. */ { double x, y, z, rxy2, xi2, eta2p1, r, rsb, rcb, w2, w, c; x = v[0]; y = v[1]; z = v[2]; rxy2 = x*x + y*y; xi2 = xi*xi; eta2p1 = eta*eta + 1.0; r = sqrt(xi2 + eta2p1); rsb = r*z; rcb = r*sqrt(x*x + y*y); w2 = rcb*rcb - xi2; if ( w2 > 0.0 ) { w = sqrt(w2); c = (rsb*eta + w) / (eta2p1*sqrt(rxy2*(w2+xi2))); v01[0] = c * (x*w + y*xi); v01[1] = c * (y*w - x*xi); v01[2] = (rsb - eta*w) / eta2p1; w = - w; c = (rsb*eta + w) / (eta2p1*sqrt(rxy2*(w2+xi2))); v02[0] = c * (x*w + y*xi); v02[1] = c * (y*w - x*xi); v02[2] = (rsb - eta*w) / eta2p1; return (fabs(rsb) < 1.0) ? 1 : 2; } else { return 0; } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2019 ** 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 ** **--------------------------------------------------------------------*/ }