1## Copyright (C) 2021 David Legland
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27
28function varargout = sph2cart2(theta, phi, rho)
29%SPH2CART2 Convert spherical coordinates to cartesian coordinates.
30%
31%   C = SPH2CART2(S)
32%   C = SPH2CART2(THETA, PHI)       (assume rho = 1)
33%   C = SPH2CART2(THETA, PHI, RHO)
34%   [X, Y, Z] = SPH2CART2(THETA, PHI, RHO);
35%
36%   S = [phi theta rho] (spherical coordinate).
37%   C = [X Y Z]  (cartesian coordinate)
38%
39%   The following convention is used:
40%   THETA is the colatitude, in radians, 0 for north pole, +pi for south
41%   pole, pi/2 for points with z=0.
42%   PHI is the azimuth, in radians, defined as matlab cart2sph: angle from
43%   Ox axis, counted counter-clockwise.
44%   RHO is the distance of the point to the origin.
45%   Discussion on choice for convention can be found at:
46%   http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf
47%
48%   See also:
49%   angles3d, cart2sph2, sph2cart, sph2cart2d
50%
51%   ---------
52%   author : David Legland
53%   INRA - TPV URPOI - BIA IMASTE
54%   created the 18/02/2005.
55%
56
57%   HISTORY
58%   22/03/2005: make test for 2 args, and add radius if not specified for
59%       1 arg.
60%   03/11/2006: change convention for angle: uses order [THETA PHI RHO]
61
62% Process input arguments
63if nargin == 1
64    phi     = theta(:, 2);
65    if size(theta, 2) > 2
66        rho = theta(:, 3);
67    else
68        rho = ones(size(phi));
69    end
70    theta   = theta(:, 1);
71
72elseif nargin == 2
73    rho     = ones(size(theta));
74
75end
76
77% conversion
78rz = rho .* sin(theta);
79x  = rz  .* cos(phi);
80y  = rz  .* sin(phi);
81z  = rho .* cos(theta);
82
83if nargout <= 1
84    varargout{1} = [x, y, z];
85else
86    varargout{1} = x;
87    varargout{2} = y;
88    varargout{3} = z;
89end
90
91