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%% Copyright (c) 2011, INRA
%% 2005-2011, 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{ray} = } bisector (@var{line1}, @var{line2})
%% @deftypefnx {Function File} {@var{ray} = } bisector (@var{p1}, @var{p2}, @var{p3})
%% Return the bisector of two lines, or 3 points.
%%
%% Creates the bisector of the two lines, given as [x0 y0 dx dy].
%%
%% create the bisector of lines (@var{p2} @var{p1}) and (@var{p2} @var{p3}).
%%
%% The result has the form [x0 y0 dx dy], with [x0 y0] being the origin
%% point ans [dx dy] being the direction vector, normalized to have unit
%% norm.
%%
%% @seealso{lines2d, rays2d}
%% @end deftypefn
function ray = bisector(varargin)
if length(varargin)==2
% two lines
line1 = varargin{1};
line2 = varargin{2};
point = intersectLines(line1, line2);
elseif length(varargin)==3
% three points
p1 = varargin{1};
p2 = varargin{2};
p3 = varargin{3};
line1 = createLine(p2, p1);
line2 = createLine(p2, p3);
point = p2;
elseif length(varargin)==1
% three points, given in one array
var = varargin{1};
p1 = var(1, :);
p2 = var(2, :);
p3 = var(3, :);
line1 = createLine(p2, p1);
line2 = createLine(p2, p3);
point = p2;
end
% compute line angles
a1 = lineAngle(line1);
a2 = lineAngle(line2);
% compute bisector angle (angle of first line + half angle between lines)
angle = mod(a1 + mod(a2-a1+2*pi, 2*pi)/2, pi*2);
% create the resulting ray
ray = [point cos(angle) sin(angle)];
endfunction
%!test
%! p0 = [0 0];
%! p1 = [10 0];
%! p2 = [0 10];
%! line1 = createLine(p0, p1);
%! line2 = createLine(p0, p2);
%! ray = bisector(line1, line2);
%! assertElementsAlmostEqual([0 0], ray(1,1:2));
%! assertAlmostEqual(pi/4, lineAngle(ray));
%!test
%! p0 = [0 0];
%! p1 = [10 0];
%! p2 = [0 10];
%! ray = bisector(p1, p0, p2);
%! assertElementsAlmostEqual([0 0], ray(1,1:2));
%! assertAlmostEqual(pi/4, lineAngle(ray));
%!test
%! p0 = [0 0];
%! p1 = [10 0];
%! p2 = [0 10];
%! ray = bisector([p1; p0; p2]);
%! assertElementsAlmostEqual([0 0], ray(1,1:2));
%! assertAlmostEqual(pi/4, lineAngle(ray));
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