distancePointEdge

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).

   Eaxmple
     % Distance between a point and an edge
     distancePointEdge([3 4], [0 0 10 0])
     ans =
         4

     % Distance between several points and one edge
     points = [10 15; 15 10; 30 10];
     edge   = [10 10 20 10];
     distancePointEdge(points, edge)
     ans = 
         5 
         0
        10

     % 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

0001 function [dist, pos] = distancePointEdge(point, edge)
0002 %DISTANCEPOINTEDGE Minimum distance between a point and an edge.
0003 %
0004 %   DIST = distancePointEdge(POINT, EDGE);
0005 %   Return the euclidean distance between edge EDGE and point POINT.
0006 %   EDGE has the form: [x1 y1 x2 y2], and POINT is [x y].
0007 %
0008 %   If EDGE is N-by-4 array, result is 1-by-4 array computed for each edge.
0009 %   If POINT is a N-by-2 array, the result is a N-by-1 array.
0010 %   If both POINT and EDGE are array, the result is computed for each
0011 %   point-edge couple, and stored into a NP-by-NE array.
0012 %
0013 %   [DIST POS] = distancePointEdge(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 %   Eaxmple
0018 %     % Distance between a point and an edge
0019 %     distancePointEdge([3 4], [0 0 10 0])
0020 %     ans =
0021 %         4
0022 %
0023 %     % Distance between several points and one edge
0024 %     points = [10 15; 15 10; 30 10];
0025 %     edge   = [10 10 20 10];
0026 %     distancePointEdge(points, edge)
0027 %     ans =
0028 %         5
0029 %         0
0030 %        10
0031 %
0032 %     % Distance between a point a several edges
0033 %     point = [14 33];
0034 %     edges  = [10 30 20 30; 20 30 20 40;20 40 10 40;10 40 10 30];
0035 %     distancePointEdge(point, edges)
0036 %     ans =
0037 %         3    6    7    4
0038 %
0039 %
0040 %   See also:
0041 %   edges2d, points2d, distancePoints, distancePointLine
0042 %
0043 
0044 % ------
0045 % Author: David Legland
0046 % e-mail: david.legland@nantes.inra.fr
0047 % Created: 2004-04-07
0048 % Copyright 2016 INRA - BIA-BIBS.
0049 %
0050 
0051 %   HISTORY
0052 %   2005-06-24 rename, and change arguments sequence
0053 %   2009-04-30 add possibility to return position of closest point
0054 %   2011-04-14 add checkup for degenerate edges, improve speed, update doc
0055 
0056 
0057 % direction vector of each edge (row vectors)
0058 vx = (edge(:, 3) - edge(:,1))';
0059 vy = (edge(:, 4) - edge(:,2))';
0060 
0061 % squared length of edges, with a check of validity
0062 delta = vx .* vx + vy .* vy;
0063 invalidEdges = delta < eps;
0064 delta(invalidEdges) = 1; 
0065 
0066 % difference of coordinates between point and edge first vertex
0067 % (NP-by-NE arrays)
0068 dx  = bsxfun(@minus, point(:, 1), edge(:, 1)');
0069 dy  = bsxfun(@minus, point(:, 2), edge(:, 2)');
0070 
0071 % compute position of points projected on the supporting line, by using
0072 % normalised dot product (NP-by-NE array)
0073 pos = bsxfun(@rdivide, bsxfun(@times, dx, vx) + bsxfun(@times, dy, vy), delta);
0074 
0075 % ensure degenerated edges are correclty processed (consider the first
0076 % vertex is the closest)
0077 pos(:, invalidEdges) = 0;
0078 
0079 % change position to ensure projected point is located on the edge
0080 pos(pos < 0) = 0;
0081 pos(pos > 1) = 1;
0082 
0083 % compute distance between point and its projection on the edge
0084 dist = hypot(bsxfun(@times, pos, vx) - dx, bsxfun(@times, pos, vy) - dy);