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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 = 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 2011-2023 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
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