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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 [nodes, edges, faces] = boundedVoronoi2d(box, germs)
%BOUNDEDVORONOI2D Computes a bounded voronoi diagram as a graph structure.
%
% [NODES, EDGES, FACES] = boundedVoronoi2d(BOX, GERMS)
% GERMS an array of points with dimension 2
% NODES, EDGES, FACES: usual graph representation, FACES as cell array
%
% Example
% % clip a graph with
% box = [0 100 0 100];
% [n, e, f] = boundedVoronoi2d(box, rand(100, 2)*100);
% [n, e, f] = clipGraph(n, e, f, box);
% drawGraph(n, e);
%
% See also
% graphs, boundedCentroidalVoronoi2d, clipGraph, clipGraphPolygon
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-01-12
% Copyright 2007-2023 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas
% uniformize input for box.
box = box';
box = box(:);
% add points far enough
boxSizeX = box(2) - box(1);
boxSizeY = box(4) - box(3);
farPoints = [...
box(2)+2*boxSizeX box(4)+3*boxSizeY;...
box(1)-3*boxSizeX box(4)+2*boxSizeY;...
box(1)-2*boxSizeX box(3)-3*boxSizeY;...
box(2)+3*boxSizeX box(3)-2*boxSizeY;...
];
% extract voronoi vertices and face structure
[V, C] = voronoin([germs ; farPoints]);
% initialize graph structure, without edges and without faces
nodes = V(2:end, :);
edges = zeros(0, 2);
faces = cell(1, size(germs, 1));
% for each cell associated to a germ, we retrieve the nodes of the Voronoi
% diagram, remove 1 because first vertex at infinity is removed, keep the
% list of vertices that constitute the face, and generate the set of edges
% around face.
for i = 1:size(germs, 1)
face = C{i};
face = face-1;
faces{i} = face;
edges = [edges; sort([face' face([2:end 1])'], 2)]; %#ok<AGROW>
end
% remove duplicate edges as they were created twice (once for each face)
edges = unique(edges, 'rows');
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