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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 [gnodes, gedges] = relativeNeighborhoodGraph(points)
%RELATIVENEIGHBORHOODGRAPH Relative Neighborhood Graph of a set of points.
%
% [NODES, EDGES] = relativeNeighborhoodGraph(POINTS)
% EDGES = relativeNeighborhoodGraph(POINTS)
%
% The Relative Neighborhood Graph (RNG) is a subgraph of the Delaunay
% Triangulation computed from the same set of points. The Gabriel graph
% and the euclidean minimal spanning tree (EMST) are subgraphs of the
% RNG.
%
% Example
% nodes = rand(100, 2) * 100;
% edges = relativeNeighborhoodGraph(nodes);
% figure; drawGraph(nodes, edges);
%
% See also
% gabrielGraph, euclideanMST
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2016-03-02, using Matlab 8.6.0.267246 (R2015b)
% Copyright 2016-2023 INRA - Cepia Software Platform
% first compute Delaunay triangulation to reduce further computations
DT = delaunayTriangulation(points);
E = edges(DT);
% compute edge lengths
nEdges = size(E, 1);
edgeLengths = zeros(nEdges, 1);
for i = 1:nEdges
edgeLengths(i) = distancePoints(points(E(i,1),:), points(E(i,2),:));
end
% identify indices of faces attached to each vertex
vertexFaces = vertexAttachments(DT);
% iterate over edges to check if the should be kept
keepEdge = true(nEdges, 1);
for iEdge = 1:nEdges
iVertex1 = E(iEdge, 1);
iVertex2 = E(iEdge, 2);
vertex1 = points(iVertex1, :);
vertex2 = points(iVertex2, :);
% compute indices of faces containing one of the two vertices
inds = [vertexFaces{iVertex1} vertexFaces{iVertex2}];
localFaces = DT.ConnectivityList(inds, :);
% compute indices of vertices is the first neighborhood of the edge
inds = unique(localFaces);
inds(ismember(inds, [iVertex1 iVertex2])) = [];
% compute max of distances to both original vertices
dists1 = distancePoints(vertex1, points(inds, :));
dists2 = distancePoints(vertex2, points(inds, :));
distsMax = max(dists1, dists2);
% keep edge if all points are outside the "lunule" defined by the edge
if edgeLengths(iEdge) > min(distsMax)
keepEdge(iEdge) = false;
end
end
% filter edges
gedges = E(keepEdge, :);
% format output
gnodes = points;
if nargin == 1
gnodes = gedges;
end
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