ISPOINTONEDGE Test if a point belongs to an edge.
Usage
B = isPointOnEdge(POINT, EDGE)
B = isPointOnEdge(POINT, EDGE, TOL)
Description
B = isPointOnEdge(POINT, EDGE)
with POINT being [xp yp], and EDGE being [x1 y1 x2 y2], returns TRUE if
the point is located on the edge, and FALSE otherwise.
B = isPointOnEdge(POINT, EDGE, TOL)
Specify an optilonal tolerance value TOL. The tolerance is given as a
fraction of the norm of the edge direction vector. Default is 1e-14.
B = isPointOnEdge(POINTARRAY, EDGE)
B = isPointOnEdge(POINT, EDGEARRAY)
When one of the inputs has several rows, return the result of the test
for each element of the array tested against the single parameter.
B = isPointOnEdge(POINTARRAY, EDGEARRAY)
When both POINTARRAY and EDGEARRAY have the same number of rows,
returns a column vector with the same number of rows.
When the number of rows are different and both greater than 1, returns
a Np-by-Ne matrix of booleans, containing the result for each couple of
point and edge.
Examples
% create a point array
points = [10 10;15 10; 30 10];
% create an edge array
vertices = [10 10;20 10;20 20;10 20];
edges = [vertices vertices([2:end 1], :)];
% Test one point and one edge
isPointOnEdge(points(1,:), edges(1,:))
ans =
1
isPointOnEdge(points(3,:), edges(1,:))
ans =
0
% Test one point and several edges
isPointOnEdge(points(1,:), edges)'
ans =
1 0 0 1
% Test several points and one edge
isPointOnEdge(points, edges(1,:))'
ans =
1 1 0
% Test N points and N edges
isPointOnEdge(points, edges(1:3,:))'
ans =
1 0 0
% Test NP points and NE edges
isPointOnEdge(points, edges)
ans =
1 0 0 1
1 0 0 0
0 0 0 0
See also
edges2d, points2d, isPointOnLine0001 function b = isPointOnEdge(point, edge, varargin) 0002 %ISPOINTONEDGE Test if a point belongs to an edge. 0003 % 0004 % Usage 0005 % B = isPointOnEdge(POINT, EDGE) 0006 % B = isPointOnEdge(POINT, EDGE, TOL) 0007 % 0008 % Description 0009 % B = isPointOnEdge(POINT, EDGE) 0010 % with POINT being [xp yp], and EDGE being [x1 y1 x2 y2], returns TRUE if 0011 % the point is located on the edge, and FALSE otherwise. 0012 % 0013 % B = isPointOnEdge(POINT, EDGE, TOL) 0014 % Specify an optilonal tolerance value TOL. The tolerance is given as a 0015 % fraction of the norm of the edge direction vector. Default is 1e-14. 0016 % 0017 % B = isPointOnEdge(POINTARRAY, EDGE) 0018 % B = isPointOnEdge(POINT, EDGEARRAY) 0019 % When one of the inputs has several rows, return the result of the test 0020 % for each element of the array tested against the single parameter. 0021 % 0022 % B = isPointOnEdge(POINTARRAY, EDGEARRAY) 0023 % When both POINTARRAY and EDGEARRAY have the same number of rows, 0024 % returns a column vector with the same number of rows. 0025 % When the number of rows are different and both greater than 1, returns 0026 % a Np-by-Ne matrix of booleans, containing the result for each couple of 0027 % point and edge. 0028 % 0029 % Examples 0030 % % create a point array 0031 % points = [10 10;15 10; 30 10]; 0032 % % create an edge array 0033 % vertices = [10 10;20 10;20 20;10 20]; 0034 % edges = [vertices vertices([2:end 1], :)]; 0035 % 0036 % % Test one point and one edge 0037 % isPointOnEdge(points(1,:), edges(1,:)) 0038 % ans = 0039 % 1 0040 % isPointOnEdge(points(3,:), edges(1,:)) 0041 % ans = 0042 % 0 0043 % 0044 % % Test one point and several edges 0045 % isPointOnEdge(points(1,:), edges)' 0046 % ans = 0047 % 1 0 0 1 0048 % 0049 % % Test several points and one edge 0050 % isPointOnEdge(points, edges(1,:))' 0051 % ans = 0052 % 1 1 0 0053 % 0054 % % Test N points and N edges 0055 % isPointOnEdge(points, edges(1:3,:))' 0056 % ans = 0057 % 1 0 0 0058 % 0059 % % Test NP points and NE edges 0060 % isPointOnEdge(points, edges) 0061 % ans = 0062 % 1 0 0 1 0063 % 1 0 0 0 0064 % 0 0 0 0 0065 % 0066 % 0067 % See also 0068 % edges2d, points2d, isPointOnLine 0069 % 0070 0071 % --------- 0072 % author : David Legland 0073 % INRA - TPV URPOI - BIA IMASTE 0074 % created the 31/10/2003. 0075 % 0076 0077 % HISTORY 0078 % 11/03/2004 change input format: edge is [x1 y1 x2 y2]. 0079 % 17/01/2005 if test N edges with N points, return N boolean. 0080 % 21/01/2005 normalize test for colinearity, so enhance precision 0081 % 22/05/2009 rename to isPointOnEdge, add psb to specify tolerance 0082 % 26/01/2010 fix bug in precision computation 0083 % 04/10/2010 fix a bug, and clean up code 0084 % 28/10/2010 fix bug to have N results when input is N points and N 0085 % edges, add support for arrays with different numbers of rows, and 0086 % update doc. 0087 % 2011-06-15 rewrites by using less memory, and avoiding repmat when psb 0088 0089 0090 % extract computation tolerance 0091 tol = 1e-14; 0092 if ~isempty(varargin) 0093 tol = varargin{1}; 0094 end 0095 0096 % number of edges and of points 0097 nPoints = size(point, 1); 0098 nEdges = size(edge, 1); 0099 0100 % adapt size of inputs if needed, and extract elements for computation 0101 if nPoints == nEdges 0102 % When the number of points and edges is the same, the one-to-one test 0103 % will be computed, so there is no need to repeat matrices 0104 dx = edge(:,3) - edge(:,1); 0105 dy = edge(:,4) - edge(:,2); 0106 lx = point(:,1) - edge(:,1); 0107 ly = point(:,2) - edge(:,2); 0108 0109 elseif nPoints == 1 0110 % one point, several edges 0111 dx = edge(:, 3) - edge(:, 1); 0112 dy = edge(:, 4) - edge(:, 2); 0113 lx = point(ones(nEdges, 1), 1) - edge(:, 1); 0114 ly = point(ones(nEdges, 1), 2) - edge(:, 2); 0115 0116 elseif nEdges == 1 0117 % several points, one edge 0118 dx = (edge(3) - edge(1)) * ones(nPoints, 1); 0119 dy = (edge(4) - edge(2)) * ones(nPoints, 1); 0120 lx = point(:, 1) - edge(1); 0121 ly = point(:, 2) - edge(2); 0122 0123 else 0124 % Np points and Ne edges: 0125 % Create an array for each parameter, so that the result will be a 0126 % Np-by-Ne matrix of booleans (requires more memory, and uses repmat) 0127 0128 x0 = repmat(edge(:, 1)', nPoints, 1); 0129 y0 = repmat(edge(:, 2)', nPoints, 1); 0130 dx = repmat(edge(:, 3)', nPoints, 1) - x0; 0131 dy = repmat(edge(:, 4)', nPoints, 1) - y0; 0132 0133 lx = repmat(point(:, 1), 1, nEdges) - x0; 0134 ly = repmat(point(:, 2), 1, nEdges) - y0; 0135 end 0136 0137 % test if point is located on supporting line 0138 b1 = abs(lx.*dy - ly.*dx) ./ (dx.*dx + dy.*dy) < tol; 0139 0140 % compute position of point with respect to edge bounds 0141 % use different tests depending on line angle 0142 ind = abs(dx) > abs(dy); 0143 t = zeros(size(dx)); 0144 t(ind) = lx( ind) ./ dx( ind); 0145 t(~ind) = ly(~ind) ./ dy(~ind); 0146 0147 % check if point is located between edge bounds 0148 b = t >- tol & t-1 < tol & b1;