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If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z}) ## @deftypefnx {} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{C}) ## Transform Cartesian coordinates to spherical coordinates. ## ## The inputs @var{x}, @var{y}, and @var{z} must be the same shape, or scalar. ## If called with a single matrix argument then each row of @var{C} ## represents a Cartesian coordinate (@var{x}, @var{y}, @var{z}). ## ## @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 ## $$\theta = \arctan \left (\frac{y}{x} \right )$$ ## $$\phi = \arctan \left (\frac{z}{\sqrt{x^2+y^2}} \right )$$ ## $$r = \sqrt{x^2+y^2 + z^2}$$ ## @end tex ## @ifnottex ## ## @example ## @var{theta} = arctan (@var{y} / @var{x}) ## @var{phi} = arctan (@var{z} / sqrt (@var{x}^2 + @var{y}^2)) ## @var{r} = sqrt (@var{x}^2 + @var{y}^2 + @var{z}^2) ## @end example ## ## @end ifnottex ## Note: To improve Matlab compatibility, this function no longer returns a ## full single coordinate matrix when called with a single return argument. ## @seealso{sph2cart, cart2pol, pol2cart} ## @end deftypefn function [theta, phi, r] = cart2sph (x, y, z) if (nargin != 1 && nargin != 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (x) && ismatrix (x))) error ("cart2sph: matrix input must be a 2D numeric array"); endif if (numel (x) == 3) z = x(3); y = x(2); x = x(1); elseif (size (x, 2) == 3) z = x(:,3); y = x(:,2); x = x(:,1); else error ("cart2sph: matrix input must be a 3 element vector or 3 column array"); endif else if (! isnumeric (x) || ! isnumeric (y) || ! isnumeric (z)) error ("cart2sph: X, Y, Z must be numeric arrays of the same size, or scalar"); endif [err, x, y, z] = common_size (x, y, z); if (err) error ("cart2sph: X, Y, Z must be numeric arrays of the same size, or scalar"); endif endif theta = atan2 (y, x); phi = atan2 (z, sqrt (x .^ 2 + y .^ 2)); r = sqrt (x .^ 2 + y .^ 2 + z .^ 2); endfunction %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! z = [0, 1, 2]; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0, pi/4, pi/4], eps); %! assert (p, [0, 1, 1]*atan (sqrt (0.5)), eps); %! assert (r, [0, 1, 2]*sqrt (3), eps); %!test %! x = [0; 1; 2]; %! y = [0; 1; 2]; %! z = [0; 1; 2]; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0; pi/4; pi/4], eps); %! assert (p, [0; 1; 1] * atan (sqrt (0.5)), eps); %! assert (r, [0; 1; 2] * sqrt (3), eps); %!test %! x = 0; %! y = [0, 1, 2]; %! z = [0, 1, 2]; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0; 1; 1] * pi/2, eps); %! assert (p, [0; 1; 1] * pi/4, eps); %! assert (r, [0; 1; 2] * sqrt (2), eps); %!test %! x = [0, 1, 2]; %! y = 0; %! z = [0, 1, 2]; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0, 0, 0]); %! assert (p, [0, 1, 1] * pi/4, eps); %! assert (r, [0, 1, 2] * sqrt (2), eps); %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! z = 0; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0, 1, 1] * pi/4, eps); %! assert (p, [0, 0, 0]); %! assert (r, [0, 1, 2] * sqrt (2), eps); %!test %! x = 0; %! y = 0; %! z = [0, 1, 2]; %! [t, p, r] = cart2sph (x, y, z); %! assert (t, [0, 0, 0]); %! assert (p, [0, 1, 1] * pi/2, eps); %! assert (r, [0, 1, 2]); %!test %! C = [0, 0, 0; 1, 0, 1; 2, 0, 2]; %! [t, p, r] = cart2sph (C); %! assert (t, [0; 0; 0]); %! assert (p, [0; 1; 1] * pi/4, eps); %! assert (r, [0; 1; 2] * sqrt (2), eps); %!test %! C = [0, 0, 0; 1, 0, 1; 2, 0, 2; 1, 0, 1]; %! [t, p, r] = cart2sph (C); %! assert (t, [0; 0; 0; 0]); %! assert (p, [0; 1; 1; 1] * pi/4, eps); %! assert (r, [0; 1; 2; 1] * sqrt (2), eps); %!test %! [x, y, z] = meshgrid ([0, 1], [0, 1], [0, 1]); %! [t, p, r] = cart2sph (x, y, z); %! T(:, :, 1) = [0, 0; pi/2, pi/4]; %! T(:, :, 2) = T(:, :, 1); %! P(:, :, 1) = zeros (2, 2); %! P(:, :, 2) = [pi/2, pi/4; pi/4, acos(sqrt(2/3))]; %! R = sqrt (x .^ 2 + y .^ 2 + z .^ 2); %! assert (t, T, eps); %! assert (p, P, eps); %! assert (r, R, eps); ## Test input validation %!error cart2sph () %!error cart2sph (1,2) %!error cart2sph (1,2,3,4) %!error cart2sph ({1,2,3}) %!error cart2sph (ones (3,3,2)) %!error cart2sph ([1,2,3,4]) %!error cart2sph ([1,2,3,4; 1,2,3,4; 1,2,3,4]) %!error cart2sph ({1,2,3}, [1,2,3], [1,2,3]) %!error cart2sph ([1,2,3], {1,2,3}, [1,2,3]) %!error cart2sph ([1,2,3], [1,2,3], {1,2,3}) %!error cart2sph ([1,2,3], [1,2,3], [1,2,3]') %!error cart2sph (ones (3,3,3), 1, ones (3,2,3)) %!error cart2sph (ones (3,3,3), ones (3,2,3), 1)