geom_utils.h

00001 /*
00002  *  This file is part of Healpix_cxx.
00003  *
00004  *  Healpix_cxx is free software; you can redistribute it and/or modify
00005  *  it under the terms of the GNU General Public License as published by
00006  *  the Free Software Foundation; either version 2 of the License, or
00007  *  (at your option) any later version.
00008  *
00009  *  Healpix_cxx is distributed in the hope that it will be useful,
00010  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
00011  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00012  *  GNU General Public License for more details.
00013  *
00014  *  You should have received a copy of the GNU General Public License
00015  *  along with Healpix_cxx; if not, write to the Free Software
00016  *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
00017  *
00018  *  For more information about HEALPix, see http://healpix.jpl.nasa.gov
00019  */
00020 
00021 /*
00022  *  Healpix_cxx is being developed at the Max-Planck-Institut fuer Astrophysik
00023  *  and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
00024  *  (DLR).
00025  */
00026 
00027 /*! \file geom_utils.h
00028  *  Geometric utility functions.
00029  *
00030  *  Copyright (C) 2003, 2006 Max-Planck-Society
00031  *  \author Martin Reinecke
00032  *  \author Reinhard Hell
00033  */
00034 
00035 #include "cxxutils.h"
00036 #include "vec3.h"
00037 
00038 /*! Returns the orientation when looking from point \a loc on the unit
00039     sphere in the direction \a dir. \a loc must be normalized. The result
00040     ranges from -pi to pi, is 0 for North and pi/2 for West, i.e. the angle
00041     is given in mathematically positive sense.
00042 
00043     If \a loc is the North or South pole, the returned angle is
00044     \a atan2(dir.y,dir.x). */
00045 inline double orientation (const vec3 &loc, const vec3 &dir)
00046   {
00047 // FIXME: here is still optimization potential
00048   if (loc.x==0 && loc.y==0)
00049     {
00050     if (loc.z>0) return safe_atan2(dir.y,-dir.x);
00051     else return safe_atan2(dir.y,dir.x);
00052     }
00053   vec3 east (-loc.y, loc.x, 0);
00054   vec3 north = crossprod(loc,east);
00055   double y = dotprod(dir,east);
00056   double x = dotprod(dir,north);
00057   return safe_atan2(-y,x);
00058   }
00059 
00060 /*! Returns the angle between \a v1 and \a v2 in radians. */
00061 inline double v_angle (const vec3 &v1, const vec3 &v2)
00062   {
00063   return atan2 (crossprod(v1,v2).Length(), dotprod(v1,v2));
00064   }