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
|
## 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 [intersects, edgeIndices] = intersectLinePolyline(line, poly, varargin)
%INTERSECTLINEPOLYLINE Intersection points between a line and a polyline.
%
% P = intersectLinePolyline(LINE, POLY)
% Returns the intersection points of the lines LINE with polyline POLY.
% LINE is a 1-by-4 row vector containing parametric representation of the
% line (in the format [x0 y0 dx dy], see the function 'createLine' for
% details).
% POLY is a NV-by-2 array containing coordinates of the polyline vertices
% P is a K-by-2 array containing the coordinates of the K intersection
% points.
%
% P = intersectLinePolyline(LINE, POLY, TOL)
% Specifies the tolerance for geometric tests. Default is 1e-14.
%
% [P INDS] = intersectLinePolyline(...)
% Also returns the indices of edges involved in intersections. INDS is a
% K-by-1 column vector, such that P(i,:) corresponds to intersection of
% the line with the i-th edge of the polyline. If the intersection occurs
% at a polyline vertex, the index of only one of the two neighbor edges
% is returned.
% Note that due to numerical approximations, the use of function
% 'isPointOnEdge' may give results not consistent with this function.
%
%
% Examples
% % compute intersections between a square and an horizontal line
% poly = [0 0;10 0;10 10;0 10];
% line = [5 5 1 0];
% intersectLinePolyline(line, poly)
% ans =
% 10 5
% % also return indices of edges
% [inters inds] = intersectLinePolyline(line, poly)
% inters =
% 10 5
% inds =
% 2
%
% % compute intersections between a square and a diagonal line
% poly = [0 0;10 0;10 10;0 10];
% line = [5 5 1 1];
% intersectLinePolyline(line, poly)
% ans =
% 0 0
% 10 10
%
% See also
% lines2d, polylines2d, intersectLines, intersectLinePolygon
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-10-31
% Copyright 2003-2023 INRA - TPV URPOI - BIA IMASTE
% get computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% create the array of edges
N = size(poly, 1);
edges = [poly(1:N-1, :) poly(2:N, :)];
% compute intersections with supporting lines of polyline edges
supportLines = edgeToLine(edges);
intersects = intersectLines(line, supportLines, tol);
% find edges that are not parallel to the input line
inds = find(isfinite(intersects(:, 1)));
% compute position of intersection points on corresponding lines
pos = linePosition(intersects(inds, :), supportLines(inds, :), 'diag');
% and keep only intersection points located on edges
b = pos > -tol & pos < 1+tol;
inds = inds(b);
intersects = intersects(inds, :);
% remove multiple vertices (can occur for intersections located at polyline
% vertices)
[intersects, I, J] = unique(intersects, 'rows'); %#ok<ASGLU>
if nargout > 1
% return indices of edges involved in intersection
% (in case of intersection located at a vertex, only one of the
% neighbor edges is returned)
edgeIndices = inds(I);
end
|
