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## Copyright (C) 2024 David Legland
## 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
## documentation and/or other materials provided with the distribution.
##
## 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
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function mat = createRotation90(varargin)
%CREATEROTATION90 Matrix of a rotation for 90 degrees multiples.
%
% MAT = createRotation90
% Returns the 3-by-3 matrix corresponding to a rotation by 90 degrees.
% As trigonometric functions are explicitley converted to +1 or -1, the
% resulting matrix obtained with this function is more precise than
% the one obtained with createRotation.
%
% MAT = createRotation90(NUM)
% Specifies the number of rotations to performs. NUM should be an integer
% (possibly negative).
%
% Example
% poly = [10 0;20 0;10 10];
% rot = createRotation90;
% poly2 = transformPoint(poly, rot);
% figure; hold on; axis equal;
% drawPolygon(poly);
% drawPolygon(poly2, 'm');
% legend('original', 'rotated');
%
% % specify number of rotations, and center
% rot = createRotation90(2, [10 10]);
% poly3 = transformPoint(poly, rot);
% drawPolygon(poly3, 'g');
%
% See also
% transforms2d, createRotation
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-06-20, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
% default values
num = 1;
center = [0 0];
% process input arguments
while ~isempty(varargin)
var = varargin{1};
if isnumeric(var) && isscalar(var)
% extract number of rotations
num = mod(mod(var, 4) + 4, 4);
elseif isnumeric(var) && length(var) == 2
% extract rotation center
center = var;
else
% unknown argument
error('MatGeom:createRotation90', ...
'Unable to parse input arguments');
end
varargin(1) = [];
end
% determine rotation parameters
switch num
case 0
ct = 1;
st = 0;
case 1
ct = 0;
st = 1;
case 2
ct = -1;
st = 0;
case 3
ct = 0;
st = -1;
end
% compute transform matrix
mat = [ ...
ct -st 0; ...
st ct 0; ...
0 0 1];
% change center if needed
if sum(center ~= [0 0]) > 0
tra = createTranslation(center);
mat = tra * mat / tra;
end
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