/usr/share/octave/packages/geometry-1.7.0/geom2d/createRotation.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{T} = } createRotation (@var{theta})
## @deftypefnx {Function File} {@var{T} = } createRotation (@var{point}, @var{theta})
## @deftypefnx {Function File} {@var{T} = } createRotation (@var{x0}, @var{y0}, @var{theta})
## Create the 3*3 matrix of a rotation.
##
## Returns the rotation corresponding to angle @var{theta} (in radians)
## The returned matrix has the form :
## [cos(theta) -sin(theta) 0]
## [sin(theta) cos(theta) 0]
## [0 0 1]
##
## @var{point} or (@var{x0},@var{y0}), specifies origin of rotation. The result is similar as performing
## translation(-@var{x0},-@var{y0}), rotation(@var{theta}), and translation(@var{x0},@var{y0}).
##
##
## @seealso{transforms2d, transformPoint, createTranslation, createScaling}
## @end deftypefn
function trans = createRotation(varargin)
# default values
cx = 0;
cy = 0;
theta = 0;
# get input values
if length(varargin)==1
# only angle
theta = varargin{1};
elseif length(varargin)==2
# origin point (as array) and angle
var = varargin{1};
cx = var(1);
cy = var(2);
theta = varargin{2};
elseif length(varargin)==3
# origin (x and y) and angle
cx = varargin{1};
cy = varargin{2};
theta = varargin{3};
end
# compute coefs
cot = cos(theta);
sit = sin(theta);
tx = cy*sit - cx*cot + cx;
ty = -cy*cot - cx*sit + cy;
# create transformation matrix
trans = [cot -sit tx; sit cot ty; 0 0 1];
endfunction
%!test
%! trans = createRotation(0);
%! assert (trans, [1 0 0;0 1 0;0 0 1], 1e-6);
%!test
%! trans = createRotation(pi/2);
%! assert (trans, [0 -1 0; 1 0 0; 0 0 1], 1e-6);
%!test
%! trans = createRotation(pi);
%! assert (trans, [-1 0 0;0 -1 0;0 0 1], 1e-6);
%!test
%! trans = createRotation(3*pi/2);
%! assert (trans, [0 1 0; -1 0 0; 0 0 1], 1e-6);
%!test
%! p0 = [3 5];
%! theta = pi/3;
%! trans1 = createRotation(p0, theta);
%! t1 = createTranslation(-p0);
%! rot = createRotation(theta);
%! t2 = createTranslation(p0);
%! trans2 = t2*rot*t1;
%! assert (trans1, trans2, 1e-6);
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