/usr/share/octave/packages/geometry-1.7.0/geom2d/linePosition.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## 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 AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{pos} =} linePosition (@var{point}, @var{line})
## Position of a point on a line.
##
## Computes position of point @var{point} on the line @var{line}, relative to origin
## point and direction vector of the line.
## @var{line} has the form [x0 y0 dx dy],
## @var{point} has the form [x y], and is assumed to belong to line.
##
## If @var{line} is an array of NL lines, return NL positions, corresponding to
## each line.
##
## If @var{point} is an array of NP points, return NP positions, corresponding
## to each point.
##
## If @var{point} is an array of NP points and @var{line}S is an array of NL lines,
## return an array of [NP NL] position, corresponding to each couple
## point-line.
##
## Example
##
## @example
## line = createLine([10 30], [30 90]);
## linePosition([20 60], line)
## ans =
## .5
## @end example
##
## @seealso{lines2d, createLine, projPointOnLine, isPointOnLine}
## @end deftypefn
function d = linePosition(point, lin)
# number of inputs
Nl = size(lin, 1);
Np = size(point, 1);
if Np == Nl
# if both inputs have the same size, no problem
dxl = lin(:, 3);
dyl = lin(:, 4);
dxp = point(:, 1) - lin(:, 1);
dyp = point(:, 2) - lin(:, 2);
elseif Np == 1
# one point, several lines
dxl = lin(:, 3);
dyl = lin(:, 4);
dxp = point(ones(Nl, 1), 1) - lin(:, 1);
dyp = point(ones(Nl, 1), 2) - lin(:, 2);
elseif Nl == 1
# one lin, several points
dxl = lin(ones(Np, 1), 3);
dyl = lin(ones(Np, 1), 4);
dxp = point(:, 1) - lin(1);
dyp = point(:, 2) - lin(2);
else
# expand one of the array to have the same size
dxl = repmat(lin(:,3)', Np, 1);
dyl = repmat(lin(:,4)', Np, 1);
dxp = repmat(point(:,1), 1, Nl) - repmat(lin(:,1)', Np, 1);
dyp = repmat(point(:,2), 1, Nl) - repmat(lin(:,2)', Np, 1);
end
# compute position
d = (dxp.*dxl + dyp.*dyl) ./ (dxl.^2 + dyl.^2);
endfunction
%!demo
%! point = [20 60;10 30;25 75];
%! lin = createLine([10 30], [30 90]);
%! pos = linePosition(point, lin)
%!
%! plot(point(:,1),point(:,2),'ok');
%! hold on
%! drawLine(lin,'color','r');
%! plot(lin(1)+lin(3)*pos,lin(2)+lin(4)*pos,'xb')
%! hold off
%!test
%! point = [20 60];
%! lin = createLine([10 30], [30 90]);
%! res = .5;
%! pos = linePosition(point, lin);
%! assert (res, pos);
%!test
%! point = [20 60;10 30;25 75];
%! lin = createLine([10 30], [30 90]);
%! res = [.5; 0; .75];
%! pos = linePosition(point, lin);
%! assert (res, pos);
%!test
%! point = [20 60];
%! lin1 = createLine([10 30], [30 90]);
%! lin2 = createLine([0 0], [20 60]);
%! lin3 = createLine([20 60], [40 120]);
%! lines = [lin1;lin2;lin3];
%! res = [.5; 1; 0];
%! pos = linePosition(point, lines);
%! assert (res, pos);
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