function [dist, pos] = distancePointEdge(point, edge)
%DISTANCEPOINTEDGE Minimum distance between a point and an edge
% DIST = distancePointEdge(POINT, EDGE);
% Return the euclidean distance between edge EDGE and point POINT.
% EDGE has the form: [x1 y1 x2 y2], and POINT is [x y].
% If EDGE is N-by-4 array, result is 1-by-4 array computed for each edge.
% If POINT is a N-by-2 array, the result is a N-by-1 array.
% If both POINT and EDGE are array, the result is computed for each
% point-edge couple, and stored into a NP-by-NE array.
% [DIST POS] = distancePointEdge(POINT, EDGE);
% Also returns the position of closest point on the edge. POS is
% comprised between 0 (first point) and 1 (last point).
% % Distance between a point and an edge
% distancePointEdge([3 4], [0 0 10 0])
% ans =
% % Distance between several points and one edge
% points = [10 15; 15 10; 30 10];
% edge = [10 10 20 10];
% distancePointEdge(points, edge)
% ans =
% % Distance between a point a several edges
% point = [14 33];
% edges = [10 30 20 30; 20 30 20 40;20 40 10 40;10 40 10 30];
% distancePointEdge(point, edges)
% ans =
% 3 6 7 4
% See also:
% edges2d, points2d, distancePoints, distancePointLine
% 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 (row vectors)
vx = (edge(:, 3) - edge(:,1))';
vy = (edge(:, 4) - edge(:,2))';
% squared length of edges, with a check of validity
delta = vx .* vx + vy .* vy;
invalidEdges = delta < eps;
delta(invalidEdges) = 1;
% difference of coordinates between point and edge first vertex
% (NP-by-NE arrays)
dx = bsxfun(@minus, point(:, 1), edge(:, 1)');
dy = bsxfun(@minus, point(:, 2), edge(:, 2)');
% compute position of points projected on the supporting line, by using
% normalised dot product (NP-by-NE array)
pos = bsxfun(@rdivide, bsxfun(@times, dx, vx) + bsxfun(@times, dy, vy), delta);
% ensure degenerated edges are correclty processed (consider the first
% vertex is the closest)
pos(:, invalidEdges) = 0;
% change position to ensure projected point is located on the edge
pos(pos < 0) = 0;
pos(pos > 1) = 1;
% compute distance between point and its projection on the edge
dist = hypot(bsxfun(@times, pos, vx) - dx, bsxfun(@times, pos, vy) - dy);