%% 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>
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%% -*- 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