distancePointEdge3d

DISTANCEPOINTEDGE3D Minimum distance between a 3D point and a 3D edge.

   DIST = distancePointEdge3d(POINT, EDGE);
   Return the euclidean distance between edge EDGE and point POINT. 
   EDGE has the form: [x1 y1 z1 x2 y2 z2], and POINT is [x y z].

   If EDGE is N-by-6 array, result is N-by-1 array computed for each edge.
   If POINT is a N-by-3 array, the result is computed for each point.
   If both POINT and EDGE are array, they must have the same number of
   rows, and the result is computed for each couple point(i,:);edge(i,:).

   [DIST POS] = distancePointEdge3d(POINT, EDGE);
   Also returns the position of closest point on the edge. POS is
   comprised between 0 (first point) and 1 (last point).

   See also:
   edges3d, points3d, distancePoints3d, distancePointLine3d

0001 function [dist, t] = distancePointEdge3d(point, edge)
0002 %DISTANCEPOINTEDGE3D Minimum distance between a 3D point and a 3D edge.
0003 %
0004 %   DIST = distancePointEdge3d(POINT, EDGE);
0005 %   Return the euclidean distance between edge EDGE and point POINT.
0006 %   EDGE has the form: [x1 y1 z1 x2 y2 z2], and POINT is [x y z].
0007 %
0008 %   If EDGE is N-by-6 array, result is N-by-1 array computed for each edge.
0009 %   If POINT is a N-by-3 array, the result is computed for each point.
0010 %   If both POINT and EDGE are array, they must have the same number of
0011 %   rows, and the result is computed for each couple point(i,:);edge(i,:).
0012 %
0013 %   [DIST POS] = distancePointEdge3d(POINT, EDGE);
0014 %   Also returns the position of closest point on the edge. POS is
0015 %   comprised between 0 (first point) and 1 (last point).
0016 %
0017 %   See also:
0018 %   edges3d, points3d, distancePoints3d, distancePointLine3d
0019 %
0020 
0021 %   ---------
0022 %   author : David Legland
0023 %   INRA - CEPIA URPOI - MIA MathCell
0024 %   created the 07/04/2004.
0025 %
0026 
0027 %   HISTORY
0028 %   2005-06-24 rename, and change arguments sequence
0029 %   2009-04-30 add possibility to return position of closest point
0030 %   2011-04-14 add checkup for degenerate edges, improve speed, update doc
0031 
0032 % direction vector of each edge
0033 vl = edge(:, 4:6) - edge(:, 1:3);
0034 
0035 % compute position of points projected on the supporting line
0036 % (Size of t is the max number of edges or points)
0037 t = linePosition3d(point, [edge(:,1:3) vl]);
0038 
0039 % change position to ensure projected point is located on the edge
0040 t(t < 0) = 0;
0041 t(t > 1) = 1;
0042 
0043 % difference of coordinates between projected point and base point
0044 p0 = bsxfun(@plus, edge(:,1:3), [t .* vl(:,1) t .* vl(:,2) t .* vl(:,3)]);
0045 p0 = bsxfun(@minus, point, p0);
0046 
0047 % compute distance between point and its projection on the edge
0048 dist = sqrt(sum(p0 .* p0, 2));