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tpors.c
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tpors.c
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#include "erfa.h"
int eraTpors(double xi, double eta, double a, double b,
double *a01, double *b01, double *a02, double *b02)
/*
** - - - - - - - - -
** e r a 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.
**
** Given:
** xi,eta double rectangular coordinates of star image (Note 2)
** a,b double star's spherical coordinates (Note 3)
**
** Returned:
** *a01,*b01 double tangent point's spherical coordinates, Soln. 1
** *a02,*b02 double tangent point's spherical coordinates, Soln. 2
**
** Returned (function value):
** int 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 return value indicates whether the second of the
** two solutions returned is useful; 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 function is a member of the following set:
**
** spherical vector solve for
**
** eraTpxes eraTpxev xi,eta
** eraTpsts eraTpstv star
** > eraTpors < eraTporv origin
**
** Called:
** eraAnp 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
**
** Copyright (C) 2013-2023, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double xi2, r, sb, cb, rsb, rcb, w2, w, s, c;
xi2 = xi*xi;
r = sqrt(1.0 + xi2 + eta*eta);
sb = sin(b);
cb = cos(b);
rsb = r*sb;
rcb = r*cb;
w2 = rcb*rcb - xi2;
if ( w2 >= 0.0 ) {
w = sqrt(w2);
s = rsb - eta*w;
c = rsb*eta + w;
if ( xi == 0.0 && w == 0.0 ) w = 1.0;
*a01 = eraAnp(a - atan2(xi,w));
*b01 = atan2(s,c);
w = -w;
s = rsb - eta*w;
c = rsb*eta + w;
*a02 = eraAnp(a - atan2(xi,w));
*b02 = atan2(s,c);
return (fabs(rsb) < 1.0) ? 1 : 2;
} else {
return 0;
}
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2023, 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.
**
*/