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#include "erfa.h"
int eraTporv(double xi, double eta, double v[3],
double v01[3], double v02[3])
/*
** - - - - - - - - -
** e r a 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.
**
** 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
**
** 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.
*/
{
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) 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.
**
*/