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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{point} = } projPointOnLine (@var{pt1}, @var{line})
+%% Project of a point orthogonally onto a line
+%%
+%% Computes the (orthogonal) projection of point @var{pt1} onto the line @var{line}.
+%%
+%% Function works also for multiple points and lines. In this case, it
+%% returns multiple points.
+%% Point @var{pt1} is a [N*2] array, and @var{line} is a [N*4] array (see createLine
+%% for details). Result @var{point} is a [N*2] array, containing coordinates of
+%% orthogonal projections of @var{pt1} onto lines @var{line}.
+%%
+%% @seealso{lines2d, points2d, isPointOnLine, linePosition}
+%% @end deftypefn
+
+function point = projPointOnLine(point, line)
+
+ % ensure input arguments have same size
+ if size(line, 1)==1 && size(point, 1)>1
+ line = repmat(line, [size(point, 1) 1]);
+ end
+ if size(point, 1)==1 && size(line, 1)>1
+ point = repmat(point, [size(line, 1) 1]);
+ end
+
+ % slope of line
+ dx = line(:, 3);
+ dy = line(:, 4);
+
+ % first find relative position of projection on the line,
+ tp = ((point(:, 2) - line(:, 2)).*dy + (point(:, 1) - line(:, 1)).*dx) ./ (dx.*dx+dy.*dy);
+
+ % convert position on line to cartesian coordinate
+ point = line(:,1:2) + [tp tp].*[dx dy];
+
+endfunction