Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / createRotation.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/createRotation.m b/octave_packages/geometry-1.5.0/geom2d/createRotation.m
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+++ b/octave_packages/geometry-1.5.0/geom2d/createRotation.m
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+%% Copyright (c) 2011, INRA
+%% 2004-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- 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);