--- /dev/null
+%% Copyright (c) 2011, INRA
+%% 2007-2011, 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{alpha} =} vectorAngle (@var{v1})
+%% Angle of a vector, or between 2 vectors
+%%
+%% A = vectorAngle(V);
+%% Returns angle between Ox axis and vector direction, in Counter
+%% clockwise orientation.
+%% The result is normalised between 0 and 2*PI.
+%%
+%% A = vectorAngle(V1, V2);
+%% Returns the angle from vector V1 to vector V2, in counter-clockwise
+%% order, and in radians.
+%%
+%% A = vectorAngle(..., 'cutAngle', CUTANGLE);
+%% A = vectorAngle(..., CUTANGLE); % (deprecated syntax)
+%% Specifies convention for angle interval. CUTANGLE is the center of the
+%% 2*PI interval containing the result. See <a href="matlab:doc
+%% ('normalizeAngle')">normalizeAngle</a> for details.
+%%
+%% Example:
+%% rad2deg(vectorAngle([2 2]))
+%% ans =
+%% 45
+%% rad2deg(vectorAngle([1 sqrt(3)]))
+%% ans =
+%% 60
+%% rad2deg(vectorAngle([0 -1]))
+%% ans =
+%% 270
+%%
+%% @seealso{vectors2d, angles2d, normalizeAngle}
+%% @end deftypefn
+
+function alpha = vectorAngle(v1, varargin)
+
+ %% Initializations
+
+ % default values
+ v2 = [];
+ cutAngle = pi;
+
+ % process input arguments
+ while ~isempty(varargin)
+ var = varargin{1};
+ if isnumeric(var) && isscalar(var)
+ % argument is normalization constant
+ cutAngle = varargin{1};
+ varargin(1) = [];
+
+ elseif isnumeric(var) && size(var, 2) == 2
+ % argument is second vector
+ v2 = varargin{1};
+ varargin(1) = [];
+
+ elseif ischar(var) && length(varargin) >= 2
+ % argument is option given as string + value
+ if strcmpi(var, 'cutAngle')
+ cutAngle = varargin{2};
+ varargin(1:2) = [];
+
+ else
+ error(['Unknown option: ' var]);
+ end
+
+ else
+ error('Unable to parse inputs');
+ end
+ end
+
+
+ %% Case of one vector
+
+ % If only one vector is provided, computes its angle
+ if isempty(v2)
+ % compute angle and format result in a 2*pi interval
+ alpha = atan2(v1(:,2), v1(:,1));
+
+ % normalize within a 2*pi interval
+ alpha = normalizeAngle(alpha + 2*pi, cutAngle);
+
+ return;
+ end
+
+
+ %% Case of two vectors
+
+ % compute angle of each vector
+ alpha1 = atan2(v1(:,2), v1(:,1));
+ alpha2 = atan2(v2(:,2), v2(:,1));
+
+ % difference
+ alpha = bsxfun(@minus, alpha2, alpha1);
+
+ % normalize within a 2*pi interval
+ alpha = normalizeAngle(alpha + 2*pi, cutAngle);
+
+endfunction
+
+%!test
+%! ang = vectorAngle([1 0]);
+%! assert(0, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 1]);
+%! assert(pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([-1 0]);
+%! assert(pi, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 -1]);
+%! assert(3*pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([-1 1]);
+%! assert(3*pi/4, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([1 0], pi);
+%! assert(0, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 1], pi);
+%! assert(pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([-1 0], pi);
+%! assert(pi, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 -1], pi);
+%! assert(3*pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([-1 1], pi);
+%! assert(3*pi/4, ang, 1e-6);
+
+%!test
+%! vecs = [1 0;0 1;-1 0;0 -1;1 1];
+%! angs = [0;pi/2;pi;3*pi/2;pi/4];
+%! assert(angs, vectorAngle(vecs));
+%! assert(angs, vectorAngle(vecs, pi));
+
+%!test
+%! ang = vectorAngle([1 0], 0);
+%! assert(0, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 1], 0);
+%! assert(pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([0 -1], 0);
+%! assert(-pi/2, ang, 1e-6);
+
+%!test
+%! ang = vectorAngle([-1 1], 0);
+%! assert(3*pi/4, ang, 1e-6);
+
+%!test
+%! vecs = [1 0;0 1;0 -1;1 1;1 -1];
+%! angs = [0;pi/2;-pi/2;pi/4;-pi/4];
+%! assert(angs, vectorAngle(vecs, 0), 1e-6);
+
+%!test
+%! v1 = [1 0];
+%! v2 = [0 1];
+%! ang = pi /2 ;
+%! assert(ang, vectorAngle(v1, v2), 1e-6);
+
+%!test
+%! v1 = [1 0];
+%! v2 = [0 1; 0 1; 1 1; -1 1];
+%! ang = [pi / 2 ;pi / 2 ;pi / 4 ; 3 * pi / 4];
+%! assert(ang, vectorAngle(v1, v2), 1e-6);
+
+%!test
+%! v1 = [0 1; 0 1; 1 1; -1 1];
+%! v2 = [-1 0];
+%! ang = [pi / 2 ;pi / 2 ; 3 * pi / 4 ; pi / 4];
+%! assert(ang, vectorAngle(v1, v2), 1e-6);
+
+%!test
+%! v1 = [1 0; 0 1; 1 1; -1 1];
+%! v2 = [0 1; 1 0; -1 1; -1 0];
+%! ang = [pi / 2 ;3 * pi / 2 ;pi / 2 ; pi / 4];
+%! assert(ang, vectorAngle(v1, v2), 1e-6);
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