/usr/share/octave/packages/geometry-1.7.0/geom3d/distancePointLine3d.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
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{d} =} distancePointLine3d (@var{point}, @var{line})
## Euclidean distance between 3D point and line
##
## Returns the distance between point POINT and the line LINE, given as:
## POINT : [x0 y0 z0]
## LINE : [x0 y0 z0 dx dy dz]
## D : (positive) scalar
##
## Run @command{demo distancePointLine3d} to see examples.
##
## References
## http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
##
## @seealso{lines3d, distancePointLine, distancePointEdge3d, projPointOnLine3d}
## @end deftypefn
function d = distancePointLine3d(point, lin)
[np nd] = size (point);
[nl ndl] = size (lin);
if ndl < 4
error("geometry:InvalidInput","second argument must be a line. See lines3d.");
end
# Compare everything to everything
if np != nl
# Order the lines such that all points are compared against 1st line, then
# secoind and so on. --JPi
idx = reshape (1:np*nl,nl,np)'(:);
lin = repmat (lin, np, 1)(idx,:);
point = repmat (point, nl, 1);
end
d = vectorNorm ( cross ( lin(:,4:6), lin(:,1:3)-point, 2)) ./ ...
vectorNorm (lin(:,4:6));
endfunction
%!demo
%! point = [0 0 1];
%! lin = [0 0 0 1 1 1];
%! d = distancePointLine3d (point,lin);
%!
%! # Orthogonal and Parallel projectors
%! dl = normalizeVector (lin(4:end))';
%! V = dl*dl';
%! P = eye(3) - dl*dl';
%! pv = P*point';
%! vv = V*point';
%!
%! # Compare
%! disp([d vectorNorm(pv)])
%!
%! figure(1);
%! clf
%! plot3 (point(1),point(2),point(3),'.k');
%! line ([0 point(1)],[0 point(2)],[0 point(3)],'color','k');
%! line (dl(1)*[-2 2],dl(2)*[-2 2],dl(3)*[-2 2],'color','r');
%! line ([0 vv(1)],[0 vv(2)],[0 vv(3)],'color','g');
%! line (vv(1)+[0 pv(1)],vv(2)+[0 pv(2)],vv(3)+[0 pv(3)],'color','b');
%! axis square equal
%!
%! # -------------------------------------------------------------------------
%! # Distance between a line and a point, the distance is verified against the
%! # vector form the point to the line, orthogonal to the line.
%!demo
%! point = 2*rand(4,3)-1;
%! lin = [0 0 0 1 1 1; 0 0 0 1 1 0];
%! d = distancePointLine3d (point,lin)
%!
%! # Organize as matrix point vs lines
%! reshape (d,4,2)
%!
%! # -------------------------------------------------------------------------
%! # Distance between 4 points and two lines. The result can be arrange as a
%! # distance matrix.
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