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
|
## 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 varargout = polygonSelfIntersections(poly, varargin)
%POLYGONSELFINTERSECTIONS Find self-intersection points of a polygon.
%
% PTS = polygonSelfIntersections(POLY)
% Return the position of self intersection points
%
% [PTS, POS1, POS2] = polygonSelfIntersections(POLY)
% Also return the 2 positions of each intersection point (the position
% when meeting point for first time, then position when meeting point
% for the second time).
%
% [...] = polygonSelfIntersections(POLY, 'tolerance', TOL)
% Specifies an additional parameter to decide whether two intersection
% points should be considered the same, based on their euclidean
% distance.
%
%
% Example
% % use a '8'-shaped polygon
% poly = [10 0;0 0;0 10;20 10;20 20;10 20];
% polygonSelfIntersections(poly)
% ans =
% 10 10
%
% See also
% polygons2d, polylineSelfIntersections
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2009-06-15, using Matlab 7.7.0.471 (R2008b)
% Copyright 2009-2023 INRA - Cepia Software Platform
tol = 1e-14;
% parse optional arguments
while length(varargin) > 1
pname = varargin{1};
if ~ischar(pname)
error('Expect optional arguments as name-value pairs');
end
if strcmpi(pname, 'tolerance')
tol = varargin{2};
else
error(['Unknown parameter name: ' pname]);
end
varargin(1:2) = [];
end
% ensure the last point equals the first one
if sum(abs(poly(end, :)-poly(1,:)) < tol) ~= 2
poly = [poly; poly(1,:)];
end
% compute intersections by calling algo for polylines
[points, pos1, pos2] = polylineSelfIntersections(poly, 'closed', 'tolerance', tol);
% It may append that first vertex of polygon is detected as intersection,
% the following tries to detect this.
% (pos1 < pos2 by construction)
n = size(poly, 1) - 1;
inds = abs(pos1) < tol & abs(pos2 - n) < tol;
points(inds, :) = [];
pos1(inds) = [];
pos2(inds) = [];
%% Post-processing
% process output arguments
if nargout <= 1
varargout = {points};
elseif nargout == 3
varargout = {points, pos1, pos2};
end
|
