How to find the area of voronoi shapes

clc
clear all
close all  
n= 60;
  x=720*rand(1,n);
  y=360*rand(1,n);
  voronoi(x,y)
  [vx,vy] =voronoi(x,y);
  plot(x,y,'r+',vx,vy,'b-'); 
  axis equal;
With this example of a voronoi diagram, is it possible to find the areas of each respective voronoi shape?  If so, how?

[Sean]

figure(2)
for j=1:length(vx(1,:))
   line([vx(1,j) vx(2,j)],[vy(1,j) vy(2,j)])
  end
  axis equal

Outlines the voronoi diagram.

Answer 1

[Ronit]

Hello Sean,

To find the areas of each respective Voronoi cell in a Voronoi diagram, this can be accomplished using the "voronoin" function, which provides the vertices of the Voronoi cells. You can then calculate the area of each cell using these vertices. Please refer to the following code for implementation:

% Create the Voronoi diagram
[v, c] = voronoin([x(:), y(:)]);

% Plot the Voronoi diagram
figure(1);
voronoi(x, y);
hold on;
plot(x, y, 'r+');
axis equal;

% Calculate the area of each Voronoi cell
areas = zeros(1, n);
for i = 1:length(c)
    if all(c{i} ~= 1)   % If the cell is not infinite
        % Get the vertices of the Voronoi cell
        vertices = v(c{i}, :);
        
        % Calculate the area using the polyarea function
        areas(i) = polyarea(vertices(:, 1), vertices(:, 2));
    else
        areas(i) = NaN; % Infinite cell, area is undefined
    end
end

For more information regarding the MATLAB functions used above, please refer to the following documenation pages:

1. voronoin: https://www.mathworks.com/help/matlab/ref/voronoin.html
2. polyarea: https://www.mathworks.com/help/matlab/ref/polyarea.html

I hope it resolves your query!