function [dist t] = distancePointEdge3d(point, edge)
%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
% author : David Legland
% INRA - CEPIA URPOI - MIA MathCell
% created the 07/04/2004.
% 2005-06-24 rename, and change arguments sequence
% 2009-04-30 add possibility to return position of closest point
% 2011-04-14 add checkup for degenerate edges, improve speed, update doc
% direction vector of each edge
vl = edge(:, 4:6) - edge(:, 1:3);
% compute position of points projected on the supporting line
% (Size of t is the max number of edges or points)
t = linePosition3d(point, [edge(:,1:3) vl]);
% change position to ensure projected point is located on the edge
t(t < 0) = 0;
t(t > 1) = 1;
% difference of coordinates between projected point and base point
p0 = bsxfun(@plus, edge(:,1:3), [t .* vl(:,1) t .* vl(:,2) t .* vl(:,3)]);
p0 = bsxfun(@minus, point, p0);
% compute distance between point and its projection on the edge
dist = sqrt(sum(p0 .* p0, 2));