Mercurial > jwe > octave
view scripts/geometry/roty.m @ 29363:0a5b15007766 stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 09:52:15 -0500 |
parents | 9f9ac219896d |
children | 7854d5752dd2 |
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######################################################################## ## ## Copyright (C) 2019-2021 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{T} =} roty (@var{angle}) ## ## @code{roty} returns the 3x3 transformation matrix corresponding to an active ## rotation of a vector about the y-axis by the specified @var{angle}, given in ## degrees, where a positive angle corresponds to a counterclockwise ## rotation when viewing the z-x plane from the positive y side. ## ## The form of the transformation matrix is: ## @tex ## $$ ## T = \left[\matrix{ \cos(angle) & 0 & \sin(angle) \cr ## 0 & 1 & 0 \cr ## -\sin(angle) & 0 & \cos(angle)}\right]. ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## | cos(@var{angle}) 0 sin(@var{angle}) | ## T = | 0 1 0 | ## | -sin(@var{angle}) 0 cos(@var{angle}) | ## @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 z-axis, rotated ## 90-degrees about the y-axis, will result in a vector pointing along the ## positive x-axis: ## ## @example ## @group ## >> u = [0 0 1]' ## u = ## 0 ## 0 ## 1 ## ## >> T = roty (90) ## T = ## 0.00000 0.00000 1.00000 ## 0.00000 1.00000 0.00000 ## -1.00000 0.00000 0.00000 ## ## >> v = T*u ## v = ## 1.00000 ## 0.00000 ## 0.00000 ## @end group ## @end example ## ## @seealso{rotx, rotz} ## @end deftypefn function retmat = roty (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 0 s; 0 1 0; -s 0 c]; endfunction ## Function output tests %!assert (roty (0), [1 0 0; 0 1 0; 0 0 1]); %!assert (roty (45), [sqrt(2) 0 sqrt(2); 0 2 0; -sqrt(2) 0 sqrt(2)]./2, 1e-12); %!assert (roty (90), [0 0 1; 0 1 0; -1 0 0], 1e-12); %!assert (roty (180), [-1 0 0; 0 1 0; 0 0 -1], 1e-12); ## Test input validation %!error roty () %!error roty (1, 2) %!error roty ([1 2 3])