cart2sph2

CART2SPH2 Convert cartesian coordinates to spherical coordinates.

   [THETA PHI RHO] = cart2sph2([X Y Z])
   [THETA PHI RHO] = cart2sph2(X, Y, Z)

   The following convention is used:
   THETA is the colatitude, in radians, 0 for north pole, +pi for south
   pole, pi/2 for points with z=0. 
   PHI is the azimuth, in radians, defined as matlab cart2sph: angle from
   Ox axis, counted counter-clockwise.
   RHO is the distance of the point to the origin.
   Discussion on choice for convention can be found at:
   http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf

   Example:
   cart2sph2([1 0 0])  returns [pi/2 0 1];
   cart2sph2([1 1 0])  returns [pi/2 pi/4 sqrt(2)];
   cart2sph2([0 0 1])  returns [0 0 1];

   See also:
     angles3d, sph2cart2, cart2sph, cart2sph2d

0001 function varargout = cart2sph2(varargin)
0002 %CART2SPH2 Convert cartesian coordinates to spherical coordinates.
0003 %
0004 %   [THETA PHI RHO] = cart2sph2([X Y Z])
0005 %   [THETA PHI RHO] = cart2sph2(X, Y, Z)
0006 %
0007 %   The following convention is used:
0008 %   THETA is the colatitude, in radians, 0 for north pole, +pi for south
0009 %   pole, pi/2 for points with z=0.
0010 %   PHI is the azimuth, in radians, defined as matlab cart2sph: angle from
0011 %   Ox axis, counted counter-clockwise.
0012 %   RHO is the distance of the point to the origin.
0013 %   Discussion on choice for convention can be found at:
0014 %   http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf
0015 %
0016 %   Example:
0017 %   cart2sph2([1 0 0])  returns [pi/2 0 1];
0018 %   cart2sph2([1 1 0])  returns [pi/2 pi/4 sqrt(2)];
0019 %   cart2sph2([0 0 1])  returns [0 0 1];
0020 %
0021 %   See also:
0022 %     angles3d, sph2cart2, cart2sph, cart2sph2d
0023 %
0024 
0025 %   ---------
0026 %   author : David Legland
0027 %   INRA - TPV URPOI - BIA IMASTE
0028 %   created the 18/02/2005.
0029 %
0030 
0031 %   HISTORY
0032 %   02/11/2006: update doc, and manage case RHO is empty
0033 %   03/11/2006: change convention for angle : uses order [THETA PHI RHO]
0034 %   27/06/2007: manage 2 output arguments
0035 
0036 % parse input angles based on input argument number
0037 if length(varargin) == 1
0038     xyz = varargin{1};
0039 elseif length(varargin) == 3
0040     xyz = [varargin{1} varargin{2} varargin{3}];
0041 end
0042 
0043 % ensure z coordinate is specified
0044 if size(xyz, 2) == 2
0045     xyz(:,3) = 1;
0046 end
0047 
0048 % convert to spherical coordinates
0049 [p, t, r] = cart2sph(xyz(:,1), xyz(:,2), xyz(:,3));
0050 
0051 % format output arguments
0052 if nargout == 1 || nargout == 0
0053     varargout{1} = [pi/2-t p r];
0054 elseif nargout==2
0055     varargout{1} = pi/2-t;
0056     varargout{2} = p;
0057 else
0058     varargout{1} = pi/2-t;
0059     varargout{2} = p;
0060     varargout{3} = r;
0061 end
0062