sph2cart2d

SPH2CART2D Convert spherical coordinates to cartesian coordinates in degrees.

   C = SPH2CART2D(THETA, PHI, RHO)
   C = SPH2CART2D(THETA, PHI)       (assume rho = 1)
   C = SPH2CART2D(S)
   [X, Y, Z] = SPH2CART2D(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 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
     xyz = sph2cart2d(90, 0, 10)
     xyz =
        10    0    0

     xyz = sph2cart2d(90, 90, 10)
     xyz =
         0   10    0

     % check consistency with cart2sph2d
     cart2sph2d(sph2cart2d(30, 40, 5))
     ans =
        30.0000   40.0000    5.0000

   See also:
     angles3d, cart2sph2d, sph2cart2, eulerAnglesToRotation3d

0001 function varargout = sph2cart2d(theta, phi, rho)
0002 %SPH2CART2D Convert spherical coordinates to cartesian coordinates in degrees.
0003 %
0004 %   C = SPH2CART2D(THETA, PHI, RHO)
0005 %   C = SPH2CART2D(THETA, PHI)       (assume rho = 1)
0006 %   C = SPH2CART2D(S)
0007 %   [X, Y, Z] = SPH2CART2D(THETA, PHI, RHO);
0008 %
0009 %   S = [theta phi rho] (spherical coordinate).
0010 %   C = [X Y Z]  (cartesian coordinate)
0011 %
0012 %   The following convention is used:
0013 %   THETA is the colatitude, in degrees, 0 for north pole, +180 degrees for
0014 %   south pole, +90 degrees for points with z=0.
0015 %   PHI is the azimuth, in degrees, defined as matlab cart2sph: angle from
0016 %   Ox axis, counted counter-clockwise.
0017 %   RHO is the distance of the point to the origin.
0018 %   Discussion on choice for convention can be found at:
0019 %   http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf
0020 %
0021 %   Example
0022 %     xyz = sph2cart2d(90, 0, 10)
0023 %     xyz =
0024 %        10    0    0
0025 %
0026 %     xyz = sph2cart2d(90, 90, 10)
0027 %     xyz =
0028 %         0   10    0
0029 %
0030 %     % check consistency with cart2sph2d
0031 %     cart2sph2d(sph2cart2d(30, 40, 5))
0032 %     ans =
0033 %        30.0000   40.0000    5.0000
0034 %
0035 %   See also:
0036 %     angles3d, cart2sph2d, sph2cart2, eulerAnglesToRotation3d
0037 %
0038 
0039 % ------
0040 % Author: David Legland
0041 % e-mail: david.legland@inrae.fr
0042 % Created: 2011-06-29,    using Matlab 7.9.0.529 (R2009b)
0043 % Copyright 2011 INRA - Cepia Software Platform.
0044 
0045 % Process input arguments
0046 if nargin == 1
0047     phi     = theta(:, 2);
0048     if size(theta, 2) > 2
0049         rho = theta(:, 3);
0050     else
0051         rho = ones(size(phi));
0052     end
0053     theta   = theta(:, 1);
0054     
0055 elseif nargin == 2
0056     rho     = ones(size(theta));
0057     
0058 end
0059 
0060 % conversion
0061 rz = rho .* sind(theta);
0062 x  = rz  .* cosd(phi);
0063 y  = rz  .* sind(phi);
0064 z  = rho .* cosd(theta);
0065 
0066 % Process output arguments
0067 if nargout == 1 || nargout == 0
0068     varargout{1} = [x, y, z];
0069     
0070 else
0071     varargout{1} = x;
0072     varargout{2} = y;
0073     varargout{3} = z;
0074 end
0075