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## 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 = boundedCentroidalVoronoi2d(germs, box, varargin)
%BOUNDEDCENTROIDALVORONOI2D Create a 2D Centroidal Voronoi Tesselation in a box.
%
% [N, E, F] = boundedCentroidalVoronoi2d(GERMS, BOX)
% GERMS are N-by-2 point array, BOX is given as [xmin xmax ymin ymax].
% Algorithm is an iteration of voronoi diagram computations, using at
% each steps the centroids of previous diagram as germs for the new
% diagram.
%
% [N, E, F] = boundedCentroidalVoronoi2d(GERMS, BOX, NITER)
% Specifies the number of iterations. Default is 10.
%
% [N, E, F, G] = boundedCentroidalVoronoi2d(...)
% also returns the positions of germs/centroids for each face. If the
% number of iteration was sufficient, location of germs should correspond
% to centroids of faces 'fc' computed using:
% fc(i,:) = polygonCentroid(n(f{i}, :));
%
% Example
% [n, e, f] = boundedCentroidalVoronoi2d(rand(20, 2)*100, [0 100 0 100]);
% drawGraph(n, e, f);
%
% See also
% graphs, boundedVoronoi2d, centroidalVoronoi2d, clipGraph
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-01-12
% Copyright 2007-2023 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas
% number of iteration
nIter = 10;
if ~isempty(varargin)
nIter = varargin{1};
end
% limits and size of the box
x0 = box(1); x1 = box(2);
y0 = box(3); y1 = box(4);
dx = x1 - x0; dy = y1 - y0;
% far points to bound the voronoi diagram
farPoints = [...
x1 + 10 * dx, y1 + 10 * dy;...
x0 - 10 * dx, y1 + 10 * dy;...
x0 - 10 * dx, y0 - 10 * dy;...
x1 + 10 * dx, y0 - 10 * dy];
% iterate bounded voronoi tesselation
for i = 1:nIter
% generate Voronoi diagram, and clip with the box
[n, e, f] = voronoi2d([germs ; farPoints]);
[n, e, f] = clipGraph(n, e, f, box);
% centroid of each face will be used as germs for next iteration
for j = 1:length(f)
face = n(f{j}, :);
germs(j, 1:2) = polygonCentroid(face);
end
end
% result is given in n, e, and f, eventually germs
varargout{1} = n;
varargout{2} = e;
varargout{3} = f;
if nargout > 3
varargout{4} = germs;
end
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