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
|
## 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 = hexagonalGrid(bounds, origin, size, varargin)
%HEXAGONALGRID Generate hexagonal grid of points in the plane.
%
% usage:
% PTS = hexagonalGrid(BOUNDS, ORIGIN, SIZE)
% generate points, lying in the window defined by BOUNDS (=[xmin ymin
% xmax ymax]), starting from origin with a constant step equal to size.
% SIZE is constant and is equals to the length of the sides of each
% hexagon.
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-08-06
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
size = size(1);
dx = 3*size;
dy = size*sqrt(3);
% consider two rectangular grids with shifted centers
pts1 = squareGrid(bounds, origin + [0 0], [dx dy], varargin{:});
pts2 = squareGrid(bounds, origin + [dx/3 0], [dx dy], varargin{:});
pts3 = squareGrid(bounds, origin + [dx/2 dy/2], [dx dy], varargin{:});
pts4 = squareGrid(bounds, origin + [-dx/6 dy/2], [dx dy], varargin{:});
% gather points
pts = [pts1;pts2;pts3;pts4];
% eventually compute also edges, clipped by bounds
if nargout > 1
edges = zeros([0 4]);
x0 = origin(1);
y0 = origin(2);
% find all x coordinate
x1 = bounds(1) + mod(x0-bounds(1), dx);
x2 = bounds(3) - mod(bounds(3)-x0, dx);
lx = (x1:dx:x2)';
% horizontal edges: first find y's
y1 = bounds(2) + mod(y0-bounds(2), dy);
y2 = bounds(4) - mod(bounds(4)-y0, dy);
ly = (y1:dy:y2)';
% number of points in each coord, and total number of points
ny = length(ly);
nx = length(lx);
if bounds(1)-x1+dx < size
disp('intersect bounding box');
end
if bounds(3)-x2 < size
disp('intersect 2');
edges = [edges;repmat(x2, [ny 1]) ly repmat(bounds(3), [ny 1]) ly];
x2 = x2-dx;
lx = (x1:dx:x2)';
nx = length(lx);
end
for i = 1:length(ly)
ind = (1:nx)';
tmpEdges = zeros(length(ind), 4);
tmpEdges(ind, 1) = lx;
tmpEdges(ind, 2) = ly(i);
tmpEdges(ind, 3) = lx+size;
tmpEdges(ind, 4) = ly(i);
edges = [edges; tmpEdges]; %#ok<AGROW>
end
end
% process output arguments
if nargout > 0
varargout{1} = pts;
if nargout > 1
varargout{2} = edges;
end
end
|
