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If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{theta}, @var{phi}, @var{r}) ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{S}) ## Transform spherical coordinates to Cartesian coordinates. ## ## The inputs @var{theta}, @var{phi}, and @var{r} must be the same shape, or ## scalar. If called with a single matrix argument then each row of @var{S} must ## represents a spherical coordinate triplet (@var{theta}, @var{phi}, @var{r}). ## ## The outputs @var{x}, @var{y}, @var{z} will match the shape of the inputs. For ## a matrix input @var{S} the outputs will be column vectors with rows ## corresponding to the rows of the input matrix. ## ## @var{theta} describes the azimuth angle relative to the positive x-axis ## measured in the xy-plane. ## ## @var{phi} is the elevation angle measured relative to the xy-plane. ## ## @var{r} is the distance to the origin @w{(0, 0, 0)}. ## ## The coordinate transformation is computed using: ## ## @tex ## $$ x = r \cos \phi \cos \theta $$ ## $$ y = r \cos \phi \sin \theta $$ ## $$ z = r \sin \phi $$ ## @end tex ## @ifnottex ## ## @example ## @var{x} = r * cos (@var{phi}) * cos (@var{theta}) ## @var{y} = r * cos (@var{phi}) * sin (@var{theta}) ## @var{z} = r * sin (@var{phi}) ## @end example ## ## @end ifnottex ## Note: To improve Matlab compatibility, this function no longer returns a ## full coordinate matrix when called with a single return argument. ## @seealso{cart2sph, pol2cart, cart2pol} ## @end deftypefn function [x, y, z] = sph2cart (theta, phi, r) if (nargin != 1 && nargin != 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (theta) && ismatrix (theta))) error ("sph2cart: matrix input must be a 2D numeric array"); endif if (numel (theta) == 3) r = theta(3); phi = theta(2); theta = theta(1); elseif (size (theta, 2) == 3) r = theta(:,3); phi = theta(:,2); theta = theta(:,1); else error ("sph2cart: matrix input must be a 3 element vector or 3 column array"); endif else if (! isnumeric (theta) || ! isnumeric (phi) || ! isnumeric (r)) error ("sph2cart: THETA, PHI, R must be numeric arrays or scalars"); endif [err, theta, phi, r] = common_size (theta, phi, r); if (err) error ("sph2cart: THETA, PHI, R must be the same size or scalars"); endif endif x = r .* cos (phi) .* cos (theta); y = r .* cos (phi) .* sin (theta); z = r .* sin (phi); endfunction %!test %! t = [0, 0, 0]; %! p = [0, 0, 0]; %! r = [0, 1, 2]; %! [x, y, z] = sph2cart (t, p, r); %! assert (x, r); %! assert (y, [0, 0, 0]); %! assert (z, [0, 0, 0]); %!test %! t = [0; 0; 0]; %! p = [0; 0; 0]; %! r = [0; 1; 2]; %! [x, y, z] = sph2cart (t, p, r); %! assert (x, [0; 1; 2]); %! assert (y, [0; 0; 0]); %! assert (z, [0; 0; 0]); %!test %! t = 0; %! p = [0, 0, 0]; %! r = [0, 1, 2]; %! [x, y, z] = sph2cart (t, p, r); %! assert (x, [0, 1, 2]); %! assert (y, [0, 0, 0]); %! assert (z, [0, 0, 0]); %!test %! t = [0, 0, 0]; %! p = 0; %! r = [0, 1, 2]; %! [x, y, z] = sph2cart (t, p, r); %! assert (x, r); %! assert (y, [0, 0, 0]); %! assert (z, [0, 0, 0]); %!test %! t = [0, 0.5, 1]*pi; %! p = [0, 0, 0]; %! r = 1; %! [x, y, z] = sph2cart (t, p, r); %! assert (x, [1, 0, -1], eps); %! assert (y, [0, 1, 0], eps); %! assert (z, [0, 0, 0], eps); %!test %! [x, y, z] = sph2cart ([0 0 0], 0, 1); %! assert (x, [1, 1, 1], eps); %! assert (y, [0, 0, 0], eps); %! assert (z, [0, 0, 0], eps); %!test %! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1]; %! [x, y, z] = sph2cart (S); %! assert (x, [1; 0; -1], eps); %! assert (y, [0; 1; 0], eps); %! assert (z, [0; 0; 0], eps); %!test %! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1; pi, pi, 1]; %! [x, y, z] = sph2cart (S); %! assert (x, [1; 0; -1; 1], eps); %! assert (y, [0; 1; 0; 0], eps); %! assert (z, [0; 0; 0; 0], eps); %!test %! [t, p, r] = meshgrid ([0, pi/2], [0, pi/2], [0, 1]); %! [x, y, z] = sph2cart (t, p, r); %! X = zeros(2, 2, 2); %! X(1, 1, 2) = 1; %! Y = zeros(2, 2, 2); %! Y(1, 2, 2) = 1; %! Z = zeros(2, 2, 2); %! Z(2, :, 2) = [1 1]; %! assert (x, X, eps); %! assert (y, Y, eps); %! assert (z, Z); ## Test input validation %!error sph2cart () %!error sph2cart (1,2) %!error sph2cart (1,2,3,4) %!error sph2cart ({1,2,3}) %!error sph2cart (ones (3,3,2)) %!error sph2cart ([1,2,3,4]) %!error sph2cart ([1,2,3,4; 1,2,3,4; 1,2,3,4]) %!error sph2cart ({1,2,3}, [1,2,3], [1,2,3]) %!error sph2cart ([1,2,3], {1,2,3}, [1,2,3]) %!error sph2cart ([1,2,3], [1,2,3], {1,2,3}) %!error sph2cart ([1,2,3], [1,2,3], [1,2,3]') %!error sph2cart (ones (3,3,3), 1, ones (3,2,3)) %!error sph2cart (ones (3,3,3), ones (3,2,3), 1)