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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## 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.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = cart2sph2(varargin)
%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
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% parse input angles based on input argument number
if length(varargin) == 1
xyz = varargin{1};
elseif length(varargin) == 3
xyz = [varargin{1} varargin{2} varargin{3}];
end
% ensure z coordinate is specified
if size(xyz, 2) == 2
xyz(:,3) = 1;
end
% convert to spherical coordinates
[p, t, r] = cart2sph(xyz(:,1), xyz(:,2), xyz(:,3));
% format output arguments
if nargout == 1 || nargout == 0
varargout{1} = [pi/2-t p r];
elseif nargout==2
varargout{1} = pi/2-t;
varargout{2} = p;
else
varargout{1} = pi/2-t;
varargout{2} = p;
varargout{3} = r;
end
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