1## Copyright (C) 2021 David Legland
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27
28function loops = expandPolygon(poly, dist, varargin)
29%EXPANDPOLYGON Expand a polygon by a given (signed) distance.
30%
31%   POLY2 = expandPolygon(POLY, DIST);
32%   Associates to each edge of the polygon POLY the parallel line located
33%   at distance DIST from the current edge, and compute intersections with
34%   neighbor parallel lines. The input polygon POLY must be oriented
35%   counter-clockwise. Otherwise, distance is computed inside the polygon.
36%   The resulting polygon is simplified to remove inner "loops", and can
37%   eventually be disconnected.
38%   The result POLY2 is a cell array, each cell containing a simple linear
39%   ring.
40%
41%   This is a kind of dilation, but behaviour on corners is different.
42%   This function keeps angles of polygons, but there is no direct relation
43%   between the lengths of each polygon.
44%
45%   It is also possible to specify negative distance, and get all points
46%   inside the polygon. If the polygon is convex, the result equals
47%   morphological erosion of polygon by a ball with radius equal to the
48%   given distance.
49%
50%   Example:
51%   % Computes the negative offset of a non-convex polygon
52%     poly = [10 10;30 10;30 30;20 20;10 30];
53%     poly2 = expandPolygon(poly, -3);
54%     figure;
55%     drawPolygon(poly, 'linewidth', 2);
56%     hold on; drawPolygon(poly2, 'm')
57%     axis equal; axis([0 40 0 40]);
58%
59%   See also:
60%   polygons2d, polygonLoops, polygonSelfIntersections
61%
62
63%   ---------
64%   author : David Legland
65%   INRA - TPV URPOI - BIA IMASTE
66%   created the 14/05/2005.
67%
68
69%   HISTORY:
70%   31-07-2005 change algo for negative distance: use clipping of polygon
71%   by half-planes
72
73% default options
74cleanupLoops = false;
75
76% process input argument
77while length(varargin) > 1
78    paramName = varargin{1};
79    switch lower(paramName)
80        case 'cleanuploops'
81            cleanupLoops = varargin{2};
82        otherwise
83            error(['Unknown parameter name: ' paramName]);
84    end
85    varargin(1:2) = [];
86end
87
88% eventually copy first point at the end to ensure closed polygon
89if sum(poly(end, :) == poly(1,:)) ~= 2
90    poly = [poly; poly(1,:)];
91end
92
93% number of vertices of the polygon
94N = size(poly, 1)-1;
95
96% find lines parallel to polygon edges located at distance DIST
97lines = zeros(N, 4);
98for i = 1:N
99    side = createLine(poly(i,:), poly(i+1,:));
100    lines(i, 1:4) = parallelLine(side, dist);
101end
102
103% compute intersection points of consecutive lines
104lines = [lines;lines(1,:)];
105poly2 = zeros(N, 2);
106for i = 1:N
107    poly2(i,1:2) = intersectLines(lines(i,:), lines(i+1,:));
108end
109
110% split result polygon into set of loops (simple polygons)
111loops = polygonLoops(poly2);
112
113% keep only loops whose distance to original polygon is correct
114if cleanupLoops
115    distLoop = zeros(length(loops), 1);
116    for i = 1:length(loops)
117        distLoop(i) = distancePolygons(loops{i}, poly);
118    end
119    loops = loops(abs(distLoop-abs(dist)) < abs(dist)/1000);
120end
121