/
sph2cart2.m
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sph2cart2.m
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function varargout = sph2cart2(theta, phi, rho)
%SPH2CART2 Convert spherical coordinates to cartesian coordinates.
%
% C = SPH2CART2(S)
% C = SPH2CART2(THETA, PHI) (assuming rho = 1)
% C = SPH2CART2(THETA, PHI, RHO)
% [X, Y, Z] = SPH2CART2(THETA, PHI, RHO);
%
% S = [theta phi rho] (spherical coordinate).
% C = [X Y Z] (cartesian coordinate)
%
% 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
% xyz = sph2cart2(pi/2, 0, 10)
% xyz =
% 10.0000 0 0.0000
%
% xyz = sph2cart2(pi/2, pi/2, 10)
% xyz =
% 0.0000 10.0000 0.0000
%
% % check consistency with cart2sph2
% sph2cart2(cart2sph2(0.7, 0.8, 5))
% ans =
% 0.7000 0.8000 5.0000
%
% See also:
% angles3d, cart2sph2, sph2cart, sph2cart2d, eulerAnglesToRotation3d
%
% ------
% Author: David Legland
% e-mail: david.legland@inrae.fr
% INRAE - BIA Research Unit - BIBS Platform (Nantes)
% created the 18/02/2005.
%
% HISTORY
% 22/03/2005: make test for 2 args, and add radius if not specified for
% 1 arg.
% 03/11/2006: change convention for angle: uses order [THETA PHI RHO]
% Process input arguments
if nargin == 1
phi = theta(:, 2);
if size(theta, 2) > 2
rho = theta(:, 3);
else
rho = ones(size(phi));
end
theta = theta(:, 1);
elseif nargin == 2
rho = ones(size(theta));
end
% conversion
rz = rho .* sin(theta);
x = rz .* cos(phi);
y = rz .* sin(phi);
z = rho .* cos(theta);
% format output
if nargout <= 1
varargout{1} = [x, y, z];
else
varargout{1} = x;
varargout{2} = y;
varargout{3} = z;
end