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#include "sofa.h"
int iauTpxev(double v[3], double v0[3], double *xi, double *eta)
/*
** - - - - - - - - -
** 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 function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** v double[3] direction cosines of star (Note 4)
** v0 double[3] direction cosines of tangent point (Note 4)
**
** Returned:
** *xi,*eta double tangent plane coordinates of star
**
** Returned (function value):
** int 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 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 2020-07-21
**
** Copyright (C) 2020 IAU SOFA Board. See notes at end.
*/
{
const double TINY = 1e-6;
int j;
double x, y, z, x0, y0, z0, r2, r, w, d;
/* Star and tangent point. */
x = v[0];
y = v[1];
z = v[2];
x0 = v0[0];
y0 = v0[1];
z0 = v0[2];
/* Deal with polar case. */
r2 = x0*x0 + y0*y0;
r = sqrt(r2);
if ( r == 0.0 ) {
r = 1e-20;
x0 = r;
}
/* Reciprocal of star vector length to tangent plane. */
w = x*x0 + y*y0;
d = w + z*z0;
/* Check for error cases. */
if ( d > TINY ) {
j = 0;
} else if ( d >= 0.0 ) {
j = 1;
d = TINY;
} else if ( d > -TINY ) {
j = 2;
d = -TINY;
} else {
j = 3;
}
/* Return the tangent plane coordinates (even in dubious cases). */
d *= r;
*xi = (y*x0 - x*y0) / d;
*eta = (z*r2 - z0*w) / d;
/* Return the status. */
return j;
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2020
** 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
**
**--------------------------------------------------------------------*/
}