pv2s.c

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#include "erfa.h"

void eraPv2s(double pv[2][3],
             double *theta, double *phi, double *r,
             double *td, double *pd, double *rd)
/*
**  - - - - - - - -
**   e r a P v 2 s
**  - - - - - - - -
**
**  Convert position/velocity from Cartesian to spherical coordinates.
**
**  Given:
**     pv       double[2][3]  pv-vector
**
**  Returned:
**     theta    double        longitude angle (radians)
**     phi      double        latitude angle (radians)
**     r        double        radial distance
**     td       double        rate of change of theta
**     pd       double        rate of change of phi
**     rd       double        rate of change of r
**
**  Notes:
**
**  1) If the position part of pv is null, theta, phi, td and pd
**     are indeterminate.  This is handled by extrapolating the
**     position through unit time by using the velocity part of
**     pv.  This moves the origin without changing the direction
**     of the velocity component.  If the position and velocity
**     components of pv are both null, zeroes are returned for all
**     six results.
**
**  2) If the position is a pole, theta, td and pd are indeterminate.
**     In such cases zeroes are returned for all three.
**
**  Copyright (C) 2013-2015, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double x, y, z, xd, yd, zd, rxy2, rxy, r2, rtrue, rw, xyp;

/* Components of position/velocity vector. */
   x  = pv[0][0];
   y  = pv[0][1];
   z  = pv[0][2];
   xd = pv[1][0];
   yd = pv[1][1];
   zd = pv[1][2];

/* Component of r in XY plane squared. */
   rxy2 = x*x + y*y;

/* Modulus squared. */
   r2 = rxy2 + z*z;

/* Modulus. */
   rtrue = sqrt(r2);

/* If null vector, move the origin along the direction of movement. */
   rw = rtrue;
   if (rtrue == 0.0) {
       x = xd;
       y = yd;
       z = zd;
       rxy2 = x*x + y*y;
       r2 = rxy2 + z*z;
       rw = sqrt(r2);
   }

/* Position and velocity in spherical coordinates. */
   rxy = sqrt(rxy2);
   xyp = x*xd + y*yd;
   if (rxy2 != 0.0) {
       *theta = atan2(y, x);
       *phi = atan2(z, rxy);
       *td = (x*yd - y*xd) / rxy2;
       *pd = (zd*rxy2 - z*xyp) / (r2*rxy);
   } else {
       *theta = 0.0;
       *phi = (z != 0.0) ? atan2(z, rxy) : 0.0;
       *td = 0.0;
       *pd = 0.0;
   }
   *r = rtrue;
   *rd = (rw != 0.0) ? (xyp + z*zd) / rw : 0.0;

   return;

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2015, 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
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**    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
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*/