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 % E-mail: david.legland@inrae.fr
0024 % Created: 2004-04-07
0025 % Copyright 2004-2024 INRA - CEPIA URPOI - MIA MathCell
0026 
0027 % direction vector of each edge
0028 vl = edge(:, 4:6) - edge(:, 1:3);
0029 
0030 % compute position of points projected on the supporting line
0031 % (Size of t is the max number of edges or points)
0032 t = line3dPosition(point, [edge(:,1:3) vl]);
0033 
0034 % change position to ensure projected point is located on the edge
0035 t(t < 0) = 0;
0036 t(t > 1) = 1;
0037 
0038 % difference of coordinates between projected point and base point
0039 p0 = bsxfun(@plus, edge(:,1:3), [t .* vl(:,1) t .* vl(:,2) t .* vl(:,3)]);
0040 p0 = bsxfun(@minus, point, p0);
0041 
0042 % compute distance between point and its projection on the edge
0043 dist = sqrt(sum(p0 .* p0, 2));