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#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 2023-10-11
**
** Copyright (C) 2023 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) 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
**
**--------------------------------------------------------------------*/
}