How to find the area of voronoi shapes

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Sean
Sean 2014-6-25
回答： Ronit 2024-11-8，9:51
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?
  1 个评论
Sean
Sean 2014-6-25
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.

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回答（1 个）

Ronit
Ronit 2024-11-8，9:51
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!

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