1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function b = isPointOnEdge(point, edge, varargin)
%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, isPointOnLine
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-10-31
% Copyright 2003-2023 INRA - TPV URPOI - BIA IMASTE
% extract computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% number of edges and of points
nPoints = size(point, 1);
nEdges = size(edge, 1);
% adapt size of inputs if needed, and extract elements for computation
if nPoints == nEdges
% When the number of points and edges is the same, the one-to-one test
% will be computed, so there is no need to repeat matrices
dx = edge(:,3) - edge(:,1);
dy = edge(:,4) - edge(:,2);
lx = point(:,1) - edge(:,1);
ly = point(:,2) - edge(:,2);
elseif nPoints == 1
% one point, several edges
dx = edge(:, 3) - edge(:, 1);
dy = edge(:, 4) - edge(:, 2);
lx = point(ones(nEdges, 1), 1) - edge(:, 1);
ly = point(ones(nEdges, 1), 2) - edge(:, 2);
elseif nEdges == 1
% several points, one edge
dx = (edge(3) - edge(1)) * ones(nPoints, 1);
dy = (edge(4) - edge(2)) * ones(nPoints, 1);
lx = point(:, 1) - edge(1);
ly = point(:, 2) - edge(2);
else
% Np points and Ne edges:
% Create an array for each parameter, so that the result will be a
% Np-by-Ne matrix of booleans (requires more memory, and uses repmat)
x0 = repmat(edge(:, 1)', nPoints, 1);
y0 = repmat(edge(:, 2)', nPoints, 1);
dx = repmat(edge(:, 3)', nPoints, 1) - x0;
dy = repmat(edge(:, 4)', nPoints, 1) - y0;
lx = repmat(point(:, 1), 1, nEdges) - x0;
ly = repmat(point(:, 2), 1, nEdges) - y0;
end
% test if point is located on supporting line
b1 = abs(lx.*dy - ly.*dx) ./ (dx.*dx + dy.*dy) < tol;
% compute position of point with respect to edge bounds
% use different tests depending on line angle
ind = abs(dx) > abs(dy);
t = zeros(size(dx));
t(ind) = lx( ind) ./ dx( ind);
t(~ind) = ly(~ind) ./ dy(~ind);
% check if point is located between edge bounds
b = t >- tol & t-1 < tol & b1;
|
