edgePosition

EDGEPOSITION Return position of a point on an edge.

   POS = edgePosition(POINT, EDGE);
   Computes position of point POINT on the edge EDGE, relative to the
   position of edge vertices.
   EDGE has the form [x1 y1 x2 y2],
   POINT has the form [x y], and is assumed to belong to edge supporting
   line. The result POS has the following meaning:
     POS < 0:      POINT is located before the first vertex
     POS = 0:      POINT is located on the first vertex
     0 < POS < 1:  POINT is located between the 2 vertices (on the edge)
     POS = 1:      POINT is located on the second vertex
     POS > 1:      POINT is located after the second vertex

   POS = edgePosition(POINT, EDGES);
   If EDGES is an array of NL edges, return NE positions, corresponding to
   each edge.

   POS = edgePosition(POINTS, EDGE);
   If POINTS is an array of NP points, return NP positions, corresponding
   to each point.

   POS = edgePosition(POINTS, EDGES);
   If POINTS is an array of NP points and EDGES is an array of NE edges,
   return an array of [NP NE] position, corresponding to each couple
   point-edge.

   POS = edgePosition(POINTS, EDGES, 'diag');
   When POINTS and EDGES are two arrays with same number of rows, returns
   single column vector corresponding to each pair of point-edge.

   See also
     edges2d, createEdge, isPointOnEdge, edgeToLine

0001 function pos = edgePosition(point, edge, varargin)
0002 %EDGEPOSITION Return position of a point on an edge.
0003 %
0004 %   POS = edgePosition(POINT, EDGE);
0005 %   Computes position of point POINT on the edge EDGE, relative to the
0006 %   position of edge vertices.
0007 %   EDGE has the form [x1 y1 x2 y2],
0008 %   POINT has the form [x y], and is assumed to belong to edge supporting
0009 %   line. The result POS has the following meaning:
0010 %     POS < 0:      POINT is located before the first vertex
0011 %     POS = 0:      POINT is located on the first vertex
0012 %     0 < POS < 1:  POINT is located between the 2 vertices (on the edge)
0013 %     POS = 1:      POINT is located on the second vertex
0014 %     POS > 1:      POINT is located after the second vertex
0015 %
0016 %   POS = edgePosition(POINT, EDGES);
0017 %   If EDGES is an array of NL edges, return NE positions, corresponding to
0018 %   each edge.
0019 %
0020 %   POS = edgePosition(POINTS, EDGE);
0021 %   If POINTS is an array of NP points, return NP positions, corresponding
0022 %   to each point.
0023 %
0024 %   POS = edgePosition(POINTS, EDGES);
0025 %   If POINTS is an array of NP points and EDGES is an array of NE edges,
0026 %   return an array of [NP NE] position, corresponding to each couple
0027 %   point-edge.
0028 %
0029 %   POS = edgePosition(POINTS, EDGES, 'diag');
0030 %   When POINTS and EDGES are two arrays with same number of rows, returns
0031 %   single column vector corresponding to each pair of point-edge.
0032 %
0033 %   See also
0034 %     edges2d, createEdge, isPointOnEdge, edgeToLine
0035 %
0036 
0037 % ------
0038 % Author: David Legland
0039 % E-mail: david.legland@inrae.fr
0040 % Created: 2004-05-25
0041 % Copyright 2004-2024 INRA - Cepia Software Platform
0042 
0043 % parse input options
0044 diag = false;
0045 if ~isempty(varargin) && strcmp(varargin{1}, 'diag')
0046     diag = true;
0047 end
0048 
0049 % number of points and of edges
0050 nEdges = size(edge, 1);
0051 nPoints = size(point, 1);
0052 
0053 if nPoints == nEdges && diag
0054     % reshape into N-by-1 arrays
0055     dxe = (edge(:,3) - edge(:,1));
0056     dye = (edge(:,4) - edge(:,2));
0057     dxp = point(:,1) - edge(:,1);
0058     dyp = point(:,2) - edge(:,2);
0059 else
0060     % reshape arrays to result in NP-by-NE arrays
0061     dxe = (edge(:,3) - edge(:,1))';
0062     dye = (edge(:,4) - edge(:,2))';
0063     dxp = bsxfun(@minus, point(:,1), edge(:,1)');
0064     dyp = bsxfun(@minus, point(:,2), edge(:,2)');
0065 end
0066 
0067 % compute position
0068 pos = (dxp .* dxe + dyp .* dye) ./ (dxe .* dxe + dye .* dye);