#include "sofam.h" void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd) /* ** - - - - - - - - ** i a u P v 2 s ** - - - - - - - - ** ** Convert position/velocity from Cartesian to spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** 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. ** ** This revision: 2008 October 28 ** ** Copyright (C) 2008 IAU SOFA Review Board. See notes at end. */ { 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) 2008 ** Standards Of Fundamental Astronomy Review Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS ** WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Review Board ("the Board"). ** ** 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 adapt the SOFA software and its ** algorithms for your own purposes and you may copy and distribute ** a resulting "derived work" to others on a world-wide, royalty-free ** basis, provided that the derived work complies 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 contain ** software provided by SOFA or software that has been distributed ** by or endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon and/or differs from the ** original SOFA software. ** ** c) The name(s) of all routine(s) that you distribute shall differ ** from the SOFA names, even when the SOFA content has not been ** otherwise changed. ** ** d) The routine-naming prefix "iau" shall not be used. ** ** e) 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. ** ** f) 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. ** ** 4. In any published work or commercial products which includes ** results achieved by using the SOFA software, you shall acknowledge ** that the SOFA software was used in obtaining those results. ** ** 5. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or by ** inappropriate modification. ** ** 6. The SOFA software is provided "as is" and the Board makes no ** warranty as to its use or performance. The Board does not and ** cannot warrant the performance or results which the user may obtain ** by using the SOFA software. The Board 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 the Board be liable to the user for any consequential, ** incidental, or special damages, including any lost profits or lost ** savings, even if a Board representative has been advised of such ** damages, or for any claim by any third party. ** ** 7. 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. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** Internet email: sofa@rl.ac.uk ** Postal address: IAU SOFA Center ** Rutherford Appleton Laboratory ** Chilton, Didcot, Oxon OX11 0QX ** United Kingdom ** **---------------------------------------------------------------------*/ }