How to create a centroidal voronoi diagram?

How can a centroidal voronoi diagram can be implemented in matlab simply.

Answer 1

[Naga]

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:

1. Start with a set of random points within a defined region.
2. Use the built-in 'voronoin' function to compute the Voronoi diagram.
3. For each Voronoi cell, compute the centroid.
4. 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.