function varargout = cart2sph2d(x, y, z)
%CART2SPH2D Convert cartesian coordinates to spherical coordinates in degrees.
%
%   [THETA PHI RHO] = cart2sph2d([X Y Z])
%   [THETA PHI RHO] = cart2sph2d(X, Y, Z)
%
%   The following convention is used:
%   THETA is the colatitude, in degrees, 0 for north pole, 180 degrees for
%   south pole, 90 degrees for points with z=0.
%   PHI is the azimuth, in degrees, 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:
%     cart2sph2d([1 0 0])
%     ans =
%       90   0   1
%
%     cart2sph2d([1 1 0])
%     ans =
%       90   45   1.4142
%
%     cart2sph2d([0 0 1])
%     ans =
%       0    0    1
%
%     % check consistency with sph2cart2d
%     sph2cart2d(cart2sph2d(30, 40, 5))
%     ans =
%         30.0000   40.0000    5.0000
%
%   See also 
%     angles3d, sph2cart2d, cart2sph, cart2sph2
%

% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-06-29, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2024 INRA - Cepia Software Platform

% if data are grouped, extract each coordinate
if nargin == 1
    y = x(:, 2);
    z = x(:, 3);
    x = x(:, 1);
end

% cartesian to spherical conversion
hxy     = hypot(x, y);
rho     = hypot(hxy, z);
theta   = 90 - atan2(z, hxy) * 180 / pi;
phi     = atan2(y, x) * 180 / pi;

% format output
if nargout <= 1
    varargout{1} = [theta phi rho];
    
elseif nargout == 2
    varargout{1} = theta;
    varargout{2} = phi;
    
else
    varargout{1} = theta;
    varargout{2} = phi;
    varargout{3} = rho;
end
    
