Mercurial > octave
view scripts/general/pol2cart.m @ 21178:3be6a07e8bad
maint: Periodic merge of stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 02 Feb 2016 17:06:11 -0500 |
parents | 516bb87ea72e 5f62b5dae8b1 |
children | 1e88747417e6 |
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## Copyright (C) 2000-2016 Kai Habel ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- 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}) ## @deftypefnx {} {@var{C} =} pol2cart (@dots{}) ## 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 (@var{theta}, @var{r} ## (, @var{z})). ## ## @var{theta} describes the angle relative to the positive x-axis. ## ## @var{r} is the distance to the z-axis (0, 0, z). ## ## If only a single return argument is requested then return a matrix @var{C} ## where each row represents one Cartesian coordinate ## (@var{x}, @var{y} (, @var{z})). ## @seealso{cart2pol, sph2cart, cart2sph} ## @end deftypefn ## Author: Kai Habel <kai.habel@gmx.de> ## Adapted-by: jwe function [x, y, z] = pol2cart (theta, r, z = []) if (nargin < 1 || nargin > 3) print_usage (); endif if (nargin == 1) if (! (isnumeric (theta) && ismatrix (theta) && (columns (theta) == 2 || columns (theta) == 3))) error ("pol2cart: matrix input must have 2 or 3 columns [THETA, R (, Z)]"); endif if (columns (theta) == 3) z = theta(:,3); endif r = theta(:,2); theta = theta(:,1); elseif (nargin == 2) if (! ((isnumeric (theta) && isnumeric (r)) && (size_equal (theta, r) || isscalar (theta) || isscalar (r)))) error ("pol2cart: THETA, R must be numeric arrays of the same size, or scalar"); endif elseif (nargin == 3) if (! ((isnumeric (theta) && isnumeric (r) && isnumeric (z)) && (size_equal (theta, r) || isscalar (theta) || isscalar (r)) && (size_equal (theta, z) || isscalar (theta) || isscalar (z)) && (size_equal (r, z) || isscalar (r) || isscalar (z)))) error ("pol2cart: THETA, R, Z must be numeric arrays of the same size, or scalar"); endif endif x = r .* cos (theta); y = r .* sin (theta); if (nargout <= 1) x = [x(:), y(:), z(:)]; endif endfunction %!test %! t = [0, 0.5, 1] * pi; %! r = 1; %! [x, y] = pol2cart (t, r); %! assert (x, [1, 0, -1], sqrt (eps)); %! assert (y, [0, 1, 0], sqrt (eps)); %!test %! t = [0, 1, 1] * pi/4; %! r = sqrt (2) * [0, 1, 2]; %! C = pol2cart (t, r); %! assert (C(:,1), [0; 1; 2], sqrt (eps)); %! assert (C(:,2), [0; 1; 2], sqrt (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], sqrt (eps)); %! assert (y, [0, 1, 2], sqrt (eps)); %! assert (z, z2); %!test %! t = 0; %! r = [0, 1, 2]; %! z = [0, 1, 2]; %! [x, y, z2] = pol2cart (t, r, z); %! assert (x, [0, 1, 2], sqrt (eps)); %! assert (y, [0, 0, 0], sqrt (eps)); %! assert (z, z2); %!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 (z, z2); %!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 (z, z2); %!test %! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)]; %! C = [0, 0; 1, 1; 2, 2]; %! assert (pol2cart (P), C, sqrt (eps)); %!test %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2]; %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2]; %! assert (pol2cart (P), C, sqrt (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 <matrix input must have 2 or 3 columns> pol2cart ({1,2,3}) %!error <matrix input must have 2 or 3 columns> pol2cart (ones (3,3,2)) %!error <matrix input must have 2 or 3 columns> pol2cart ([1]) %!error <matrix input must have 2 or 3 columns> pol2cart ([1,2,3,4]) %!error <numeric arrays of the same size> pol2cart ({1,2,3}, [1,2,3]) %!error <numeric arrays of the same size> pol2cart ([1,2,3], {1,2,3}) %!error <numeric arrays of the same size> pol2cart (ones (3,3,3), ones (3,2,3)) %!error <numeric arrays of the same size> pol2cart ({1,2,3}, [1,2,3], [1,2,3]) %!error <numeric arrays of the same size> pol2cart ([1,2,3], {1,2,3}, [1,2,3]) %!error <numeric arrays of the same size> pol2cart ([1,2,3], [1,2,3], {1,2,3}) %!error <numeric arrays of the same size> pol2cart (ones (3,3,3), 1, ones (3,2,3)) %!error <numeric arrays of the same size> pol2cart (ones (3,3,3), ones (3,2,3), 1)