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If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{x}, @var{y}] =} pol2cart (@var{theta}, @var{r}) ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{theta}, @var{r}, @var{z}) ## @deftypefnx {} {[@var{x}, @var{y}] =} pol2cart (@var{P}) ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{P}) ## Transform polar or cylindrical coordinates to Cartesian coordinates. ## ## The inputs @var{theta}, @var{r}, (and @var{z}) must be the same shape, or ## scalar. If called with a single matrix argument then each row of @var{P} ## represents the polar/(cylindrical) coordinate pair (@var{theta}, @var{r}) or ## triplet (@var{theta}, @var{r}, @var{z}). ## ## The outputs @var{x}, @var{y} (, and @var{z}) will match the shape of the ## inputs. For a matrix input @var{P} 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 ## $$x = r \cos \theta$$ ## $$y = r \sin \theta$$ ## $$z = z$$ ## @end tex ## @ifnottex ## ## @example ## @var{x} = @var{r} * cos (@var{theta}) ## @var{y} = @var{r} * sin (@var{theta}) ## @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{cart2pol, sph2cart, cart2sph} ## @end deftypefn function [x, y, z] = pol2cart (theta, r, z = []) if (nargin < 1 || nargin > 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (theta) && ismatrix (theta))) error ("cart2pol: matrix input must be 2D numeric array"); endif if isvector (theta) elsize = numel (theta); if (elsize == 2 || elsize == 3) if (elsize == 3) z = theta(3); endif r = theta(2); theta = theta(1); else error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array"); endif else cols_theta = columns(theta); if (cols_theta == 2 || cols_theta == 3) if (cols_theta == 3) z = theta(:,3); endif r = theta(:,2); theta = theta(:,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 (theta) || ! isnumeric (r)) error ("pol2cart: THETA, R must be numeric arrays or scalars"); endif [err, theta, r] = common_size (theta, r); if (err) error ("pol2cart: THETA, R must be the same size or scalars"); endif elseif (nargin == 3) if (! isnumeric (theta) || ! isnumeric (r) || ! isnumeric (z)) error ("pol2cart: THETA, R, Z must be numeric arrays or scalars"); endif [err, theta, r, z] = common_size (theta, r, z); if (err) error ("pol2cart: THETA, R, Z must be the same size or scalars"); endif endif x = r .* cos (theta); y = r .* sin (theta); endfunction %!test %! t = [0, 0.5, 1] * pi; %! r = 1; %! [x, y] = pol2cart (t, r); %! assert (x, [1, 0, -1], eps); %! assert (y, [0, 1, 0], eps); %!test %! t = [0, 1, 1] * pi/4; %! r = sqrt (2) * [0, 1, 2]; %! [x, y] = pol2cart (t, r); %! assert (x, [0, 1, 2], 2*eps); %! assert (y, [0, 1, 2], 2*eps); %!test %! t = [0, 1, 1] * pi/4; %! r = sqrt (2) * [0, 1, 2]; %! z = [0, 1, 2]; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [0, 1, 2], 2*eps); %! assert (y, [0, 1, 2], 2*eps); %! assert (z2, z); %!test %! t = [0; 1; 1] * pi/4; %! r = sqrt (2) * [0; 1; 2]; %! z = [0; 1; 2]; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [0; 1; 2], 2*eps); %! assert (y, [0; 1; 2], 2*eps); %! assert (z2, z); %!test %! t = 0; %! r = [0, 1, 2]; %! z = [0, 1, 2]; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [0, 1, 2], eps); %! assert (y, [0, 0, 0], eps); %! assert (z2, z); %!test %! t = [1, 1, 1]*pi/4; %! r = 1; %! z = [0, 1, 2]; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [1, 1, 1] / sqrt (2), eps); %! assert (y, [1, 1, 1] / sqrt (2), eps); %! assert (z2, z); %!test %! t = 0; %! r = [1, 2, 3]; %! z = 1; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [1, 2, 3], eps); %! assert (y, [0, 0, 0] / sqrt (2), eps); %! assert (z2, [1, 1, 1]); %!test %! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)]; %! [x, y] = pol2cart(P); %! assert (x, [0; 1; 2], 2*eps); %! assert (y, [0; 1; 2], 2*eps); %!test %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2]; %! [x, y, z] = pol2cart(P); %! assert (x, [0; 1; 2], 2*eps); %! assert (y, [0; 1; 2], 2*eps); %! assert (z, P(:,3), 2*eps); %!test %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2; 0, 0, 0]; %! [x, y, z] = pol2cart(P); %! assert (x, [0; 1; 2; 0], 2*eps); %! assert (y, [0; 1; 2; 0], 2*eps); %! assert (z, P(:,3), 2*eps); %!test %! r = ones (1, 1, 1, 2); %! r(1, 1, 1, 2) = 2; %! t = pi/2 * r; %! [x, y] = pol2cart (t, r); %! X = zeros (1, 1, 1, 2); %! X(1, 1, 1, 2) = -2; %! Y = zeros (1, 1, 1, 2); %! Y(1, 1, 1, 1) = 1; %! assert (x, X, 2*eps); %! assert (y, Y, 2*eps); %!test %! [t, r, Z] = meshgrid ([0, pi/2], [1, 2], [0, 1]); %! [x, y, z] = pol2cart (t, r, Z); %! X = zeros(2, 2, 2); %! X(:, 1, 1) = [1; 2]; %! X(:, 1, 2) = [1; 2]; %! Y = zeros(2, 2, 2); %! Y(:, 2, 1) = [1; 2]; %! Y(:, 2, 2) = [1; 2]; %! assert (x, X, eps); %! assert (y, Y, eps); %! assert (z, Z); ## Test input validation %!error pol2cart () %!error pol2cart (1,2,3,4) %!error pol2cart ({1,2,3}) %!error pol2cart (ones (3,3,2)) %!error pol2cart ([1]) %!error pol2cart ([1,2,3,4]) %!error pol2cart ({1,2,3}, [1,2,3]) %!error pol2cart ([1,2,3], {1,2,3}) %!error pol2cart (ones (3,3,3), ones (3,2,3)) %!error pol2cart ([1; 1], [2, 2]) %!error pol2cart ([1; 1], [2, 2], [3, 3]) %!error pol2cart ({1,2,3}, [1,2,3], [1,2,3]) %!error pol2cart ([1,2,3], {1,2,3}, [1,2,3]) %!error pol2cart ([1,2,3], [1,2,3], {1,2,3}) %!error pol2cart (ones (3,3,3), 1, ones (3,2,3)) %!error pol2cart (ones (3,3,3), ones (3,2,3), 1)