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########################################################################
##
## Copyright (C) 2019-2024 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
## @code{@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 T = roty (angle)
if (nargin < 1 || ! isscalar (angle))
print_usage ();
endif
angle *= pi / 180;
s = sin (angle);
c = cos (angle);
T = [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 <Invalid call> roty ()
%!error <Invalid call> roty ([1 2 3])
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