Mercurial > octave
view scripts/geometry/rotz.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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## Copyright (C) 2017-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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{T} =} rotz (@var{angle}) ## ## @code{rotz} returns the 3x3 transformation matrix corresponding to an active ## rotation of a vector about the z-axis by the specified @var{angle}, given in ## degrees, where a positive angle corresponds to a counterclockwise ## rotation when viewing the x-y plane from the positive z side. ## ## The form of the transformation matrix is: ## @tex ## $$ ## T = \left[\matrix{ \cos(angle) & -\sin(angle) & 0 \cr ## \sin(angle) & \cos(angle) & 0 \cr ## 0 & 0 & 1}\right]. ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## | cos(@var{angle}) -sin(@var{angle}) 0 | ## T = | sin(@var{angle}) cos(@var{angle}) 0 | ## | 0 0 1 | ## @end group ## @end example ## @end ifnottex ## ## This rotation matrix is intended to be used as a left-multiplying matrix ## when acting on a column vector, using the notation @var{v} = @var{T}@var{u}. ## For example, a vector, @var{u}, pointing along the positive x-axis, rotated ## 90-degrees about the z-axis, will result in a vector pointing along the ## positive y-axis: ## ## @example ## @group ## >> u = [1 0 0]' ## u = ## 1 ## 0 ## 0 ## ## >> T = rotz (90) ## T = ## 0.00000 -1.00000 0.00000 ## 1.00000 0.00000 0.00000 ## 0.00000 0.00000 1.00000 ## ## >> v = T*u ## v = ## 0.00000 ## 1.00000 ## 0.00000 ## @end group ## @end example ## ## @seealso{rotx, roty} ## @end deftypefn ## Author: Nicholas Jankowski <jankowskin@asme.org> ## Created: 2017-04-09 function retmat = rotz (angle_in_deg) if ((nargin != 1) || ! isscalar (angle_in_deg)) print_usage (); endif angle_in_rad = angle_in_deg * pi / 180; s = sin (angle_in_rad); c = cos (angle_in_rad); retmat = [c -s 0; s c 0; 0 0 1]; endfunction ## Function output tests %!assert (rotz (0), [1 0 0; 0 1 0; 0 0 1]); %!assert (rotz (45), [(sqrt(2)/2).*[1 -1; 1 1] ,[0; 0]; 0, 0, 1], 1e-12); %!assert (rotz (90), [0 -1 0; 1 0 0; 0 0 1], 1e-12); %!assert (rotz (180), [-1 0 0; 0 -1 0; 0 0 1], 1e-12); ## Test input validation %!error rotz () %!error rotz (1, 2) %!error rotz ([1 2 3])