Hello Naveen,
Implementing a centroidal Voronoi diagram involves using an iterative process to adjust the Voronoi cells so that their centroids match the generating points. Here's a simple way to implement it:
- Start with a set of random points within a defined region.
- Use the built-in 'voronoin' function to compute the Voronoi diagram.
- For each Voronoi cell, compute the centroid.
- Replace the original points with the centroids and repeat until convergence.
% Number of points
numPoints = 20;
% Define the bounding box
bbox = [0, 1, 0, 1];
% Initialize random points
points = rand(numPoints, 2);
% Iteration parameters
maxIter = 100;
tolerance = 1e-5;
for iter = 1:maxIter
% Compute Voronoi diagram
[v, c] = voronoin(points);
newPoints = zeros(size(points));
for i = 1:numPoints
% Get the vertices of the Voronoi cell
vertIndices = c{i};
if all(vertIndices ~= 1) % Check if the cell is bounded
vert = v(vertIndices, :);
% Compute the centroid of the cell
newPoints(i, :) = mean(vert, 1);
else
% If the cell is unbounded, retain the original point
newPoints(i, :) = points(i, :);
end
end
% Check for convergence
if max(vecnorm(newPoints - points, 2, 2)) < tolerance
break;
end
% Update points
points = newPoints;
end
% Plot the final Voronoi diagram
voronoi(points(:, 1), points(:, 2));
axis equal;
xlim(bbox(1:2));
ylim(bbox(3:4));
title('Centroidal Voronoi Diagram');
This script should give you a basic centroidal Voronoi diagram. You can adjust parameters like the number of points, bounding box, and tolerance to suit your specific needs.
