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#include "erfa.h"
int eraTpxev(double v[3], double v0[3], double *xi, double *eta)
/*
** - - - - - - - - -
** e r a 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.
**
** 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
**
** eraTpxes > eraTpxev < xi,eta
** eraTpsts eraTpstv star
** eraTpors eraTporv 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
**
** Copyright (C) 2013-2021, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
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) 2013-2021, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/