Hello Muhammet,
To calculate the areas of the Voronoi cells, you can use the vertices of each cell and apply a polygon area calculation method. Since you already have the Voronoi vertices (V) and the regions (R) from the 'voronoiDiagram' function, you can compute the area of each cell by iterating over the regions and using the vertices to calculate the area of the polygons. Please refer the code below:
% Compute the Voronoi diagram
dt = delaunayTriangulation(X(:, 1), X(:, 2));
[V, R] = voronoiDiagram(dt);
% Initialize an array for areas
areas = zeros(length(R), 1);
% Calculate the area of each Voronoi cell
for i = 1:length(R)
regionIndices = R{i};
if all(regionIndices ~= 1) % Check if the region is finite
vertices = V(regionIndices, :);
areas(i) = polyarea(vertices(:, 1), vertices(:, 2));
else
areas(i) = NaN; % Assign NaN for unbounded regions
end
end
% Display the areas
disp('Areas of the Voronoi cells:');
disp(areas);
- Use 'delaunayTriangulation' and 'voronoiDiagram' to obtain Voronoi vertices and regions.
- Check each region to ensure it is bounded (i.e., does not include the point at infinity).
- Compute the area of each bounded region using 'polyarea' function, which applies the shoelace formula.
- If a region is unbounded, you can assign a placeholder value like NaN.
This approach assumes that all relevant Voronoi cells are bounded. If you have unbounded regions that you want to handle differently, you will need to adjust the logic accordingly.
Refer to the below documentation page for more information on 'polyarea' function:
Hope this helps!
