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If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{theta}, @var{r}] =} cart2pol (@var{x}, @var{y}) ## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z}) ## @deftypefnx {} {[@var{theta}, @var{r}] =} cart2pol (@var{C}) ## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{C}) ## ## Transform Cartesian coordinates to polar or cylindrical 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 the Cartesian coordinate pair (@var{x}, @var{y}) or triplet ## (@var{x}, @var{y}, @var{z}). ## ## The outputs @var{theta}, @var{r} (, and @var{z}) will match the shape of the ## inputs. For a matrix input @var{C} the outputs will be column vectors with ## rows corresponding to the rows of the input matrix. ## ## @var{theta} describes the angle relative to the positive x-axis ## measured in the xy-plane. ## ## @var{r} is the distance to the z-axis @w{(0, 0, z)}. ## ## If present, @var{z} is unchanged by the transformation. ## ## The coordinate transformation is computed using: ## ## @tex ## $$\theta = \arctan \left ( \frac {y} {x} \right )$$ ## $$r = \sqrt{x^2 + y^2}$$ ## $$z = z$$ ## @end tex ## @ifnottex ## ## @example ## @var{theta} = arctan (@var{y} / @var{x}) ## @var{r} = sqrt (@var{x}^2 + @var{y}^2) ## @var{z} = @var{z} ## @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{pol2cart, cart2sph, sph2cart} ## @end deftypefn function [theta, r, z] = cart2pol (x, y, z = []) if (nargin < 1 || nargin > 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (x) && ismatrix (x))) error ("cart2pol: matrix input must be 2D numeric array"); endif if isvector (x) elsize = numel (x); if (elsize == 2 || elsize == 3) if (elsize == 3) z = x(3); endif y = x(2); x = x(1); else error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array"); endif else cols_x = columns(x); if (cols_x == 2 || cols_x == 3) if (cols_x == 3) z = x(:,3); endif y = x(:,2); x = x(:,1); else error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array"); endif endif elseif (nargin == 2) if (! isnumeric (x) || ! isnumeric (y)) error ("cart2pol: X, Y must be numeric arrays or scalars"); endif [err, x, y] = common_size (x, y); if (err) error ("cart2pol: X, Y must be the same size or scalars"); endif elseif (nargin == 3) if (! isnumeric (x) || ! isnumeric (y) || ! isnumeric (z)) error ("cart2pol: X, Y, Z must be numeric arrays or scalars"); endif [err, x, y, z] = common_size (x, y, z); if (err) error ("cart2pol: X, Y, Z must be the same size or scalars"); endif endif theta = atan2 (y, x); r = sqrt (x .^ 2 + y .^ 2); endfunction %!test %! x = [0, 1, 2]; %! y = 0; %! [t, r] = cart2pol (x, y); %! assert (t, [0, 0, 0]); %! assert (r, x); %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! [t, r] = cart2pol (x, y); %! assert (t, [0, pi/4, pi/4], eps); %! assert (r, sqrt (2)*[0, 1, 2], eps); %!test %! x = [0, 1, 2]'; %! y = [0, 1, 2]'; %! [t, r] = cart2pol (x, y); %! assert (t, [0; pi/4; pi/4], eps); %! assert (r, sqrt (2)*[0; 1; 2], eps); %!test %! x = [0, 1, 2]; %! y = [0, 1, 2]; %! z = [0, 1, 2]; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, pi/4, pi/4], sqrt (eps)); %! assert (r, sqrt (2)*[0, 1, 2], sqrt (eps)); %! assert (z2, z); %!test %! x = [0, 1, 2]; %! y = 0; %! z = 0; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 0, 0], eps); %! assert (r, x, eps); %! assert (z2, [0, 0, 0]); %!test %! x = 0; %! y = [0, 1, 2]; %! z = 0; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 1, 1]*pi/2, eps); %! assert (r, y, eps); %! assert (z2, [0, 0, 0]); %!test %! x = 0; %! y = 0; %! z = [0, 1, 2]; %! [t, r, z2] = cart2pol (x, y, z); %! assert (t, [0, 0, 0]); %! assert (r, [0, 0, 0]); %! assert (z2, z); %!test %! C = [0, 0; 1, 1; 2, 2]; %! [t, r] = cart2pol (C); %! assert (t, [0; 1; 1]*pi/4, eps); %! assert (r, [0; 1; 2]*sqrt(2), eps); %!test %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2]; %! [t, r, z] = cart2pol (C); %! assert (t, [0; 1; 1]*pi/4, eps); %! assert (r, [0; 1; 2]*sqrt(2), eps); %! assert (z, [0; 1; 2]); %!test %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2;1, 1, 1]; %! [t, r, z] = cart2pol (C); %! assert (t, [0; 1; 1; 1]*pi/4, eps); %! assert (r, [0; 1; 2; 1]*sqrt(2), eps); %! assert (z, [0; 1; 2; 1]); %!test %! x = zeros (1, 1, 1, 2); %! x(1, 1, 1, 2) = sqrt (2); %! y = x; %! [t, r] = cart2pol (x, y); %! T = zeros (1, 1, 1, 2); %! T(1, 1, 1, 2) = pi/4; %! R = zeros (1, 1, 1, 2); %! R(1, 1, 1, 2) = 2; %! assert (t, T, eps); %! assert (r, R, eps); %!test %! [x, y, Z] = meshgrid ([0, 1], [0, 1], [0, 1]); %! [t, r, z] = cart2pol (x, y, Z); %! T(:, :, 1) = [0, 0; pi/2, pi/4]; %! T(:, :, 2) = T(:, :, 1); %! R = sqrt (x.^2 + y.^2); %! assert (t, T, eps); %! assert (r, R, eps); %! assert (z, Z); ## Test input validation %!error cart2pol () %!error cart2pol (1,2,3,4) %!error cart2pol ({1,2,3}) %!error cart2pol (ones (3,3,2)) %!error cart2pol ([1]) %!error cart2pol ([1,2,3,4]) %!error cart2pol ({1,2,3}, [1,2,3]) %!error cart2pol ([1,2,3], {1,2,3}) %!error cart2pol (ones (3,3,3), ones (3,2,3)) %!error cart2pol ([1; 1], [2, 2]) %!error cart2pol ([1; 1], [2, 2], [3, 3]) %!error cart2pol ({1,2,3}, [1,2,3], [1,2,3]) %!error cart2pol ([1,2,3], {1,2,3}, [1,2,3]) %!error cart2pol ([1,2,3], [1,2,3], {1,2,3}) %!error cart2pol (ones (3,3,3), 1, ones (3,2,3)) %!error cart2pol (ones (3,3,3), ones (3,2,3), 1)