Mercurial > octave
view scripts/general/sph2cart.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2000-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- 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 represent a spherical coordinate triplet (@var{theta}, @var{phi}, ## @var{r}). ## ## The outputs @var{x}, @var{y}, @var{z} match the shape of the inputs. For a ## matrix input @var{S} the outputs are 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 ## @group ## @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 group ## @end example ## ## @end ifnottex ## @c FIXME: Remove this note in Octave 9.1 (two releases after 7.1). ## Note: For @sc{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 2-D numeric array"); endif if (columns (theta) != 3 && numel (theta) != 3) error ("sph2cart: matrix input must be a 3-element vector or 3-column array"); endif if (numel (theta) == 3) r = theta(3); phi = theta(2); theta = theta(1); else r = theta(:,3); phi = theta(:,2); theta = theta(:,1); 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 <Invalid call> sph2cart () %!error <Invalid call> sph2cart (1,2) %!error <matrix input must be a 2-D numeric array> sph2cart ({1,2,3}) %!error <matrix input must be a 2-D numeric array> sph2cart (ones (3,3,2)) %!error <matrix input must be a 3-element> sph2cart ([1,2,3,4]) %!error <matrix input must be a 3-element> sph2cart ([1,2,3,4; 1,2,3,4; 1,2,3,4]) %!error <must be numeric arrays or scalars> sph2cart ({1,2,3}, [1,2,3], [1,2,3]) %!error <must be numeric arrays or scalars> sph2cart ([1,2,3], {1,2,3}, [1,2,3]) %!error <must be numeric arrays or scalars> sph2cart ([1,2,3], [1,2,3], {1,2,3}) %!error <must be the same size or scalars> sph2cart ([1,2,3], [1,2,3], [1,2,3]') %!error <must be the same size or scalars> sph2cart (ones (3,3,3), 1, ones (3,2,3)) %!error <must be the same size or scalars> sph2cart (ones (3,3,3), ones (3,2,3), 1)