How to caluclate centroid of a voronoi cell of a voronoi diagram.

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Pallov Anand 2023-1-3

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1887757-how-to-caluclate-centroid-of-a-voronoi-cell-of-a-voronoi-diagram

评论： Pallov Anand 2023-1-4

采纳的回答： Matt J

Suppose I have generated a voronoi diagram by following code:

X=[1 2 1.1 1.3 1.4 1.5 1.3 1.2 1.8 2.1 2.2];

Y=[1.5 1.3 1.5 1.8 1.4 1.6 2.5 2.3 2.4 1.1 1.8];

voronoi(X,Y)

Now, once the voronoi diagram is generated, how to find the centroid of each voronoi cell. I know there are lot of algorithms. One of them is Lloyd's Algorithm, the code of which is given here

https://www.mathworks.com/matlabcentral/fileexchange/41507-lloydsalgorithm-px-py-crs-numiterations-showplot

but after running the script , I am getting this error:

'poly2cw' requires Mapping Toolbox.

Error in lloydsAlgorithm>VoronoiBounded (line 178)

[X2, Y2] = poly2cw(V(C{ij},1),V(C{ij},2));

Error in lloydsAlgorithm (line 89)

[v,c]=VoronoiBounded(Px,Py, crs);

Can anyone help me in this.

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Bruno Luong 2023-1-3

编辑：Bruno Luong 2023-1-3

The Vorinoi cells that contain a seed on the hull are unbounded, there is no centroid for such cells.

MATLAB voronoi just cuts them with an empiric bounding box. So of you use those outer vertexes the result is randomly cut.

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Answer 1

Matt J 2023-1-3

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https://ww2.mathworks.cn/matlabcentral/answers/1887757-how-to-caluclate-centroid-of-a-voronoi-cell-of-a-voronoi-diagram#answer_1140722

编辑：Matt J 2023-1-3

在 MATLAB Online 中打开

The voronoi cells are always convex, so assuming it is bounded, you can just take the mean of all the vertices of each cell.

X=[1    2   1.1 1.3 1.4 1.5 1.3 1.2 1.8 2.1 2.2]; 
Y=[1.5  1.3 1.5 1.8 1.4 1.6 2.5 2.3 2.4 1.1 1.8];
[V,C]=voronoin([X;Y]');
centroids = cell2mat(  cellfun(@(c) mean(V(c,:),1)'  , C','uni', 0)  )
centroids = 2×11
       Inf    1.9180    1.1707    1.2800    1.1995    1.6029       Inf       Inf       Inf       Inf       Inf
       Inf    1.3544    1.4421    1.8802    0.5374    1.6873       Inf       Inf       Inf       Inf       Inf

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Matt J 2023-1-4

Because you didn't download the files at the link I gave you.

Pallov Anand 2023-1-4

Oh yes, my bad. I just downloaded voronoiPolyhedrons.m and was going through the overview given here

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra

Now, I downloaded and its working now. Thanks a lot mate.

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Answer 2

Constantino Carlos Reyes-Aldasoro 2023-1-3

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https://ww2.mathworks.cn/matlabcentral/answers/1887757-how-to-caluclate-centroid-of-a-voronoi-cell-of-a-voronoi-diagram#answer_1140492

在 MATLAB Online 中打开

This is not a trivial problem especially because the voronoi algorithm does not give you a series of closed polygons, i.e. change the axis of your current problem

X=[1 2 1.1 1.3 1.4 1.5 1.3 1.2 1.8 2.1 2.2];

Y=[1.5 1.3 1.5 1.8 1.4 1.6 2.5 2.3 2.4 1.1 1.8];

voronoi(X,Y)

axis([-2 4 -3 4])

You will see that the voronoi is finding lines that divide the points that you have provided, but it is not essentially generating polygons. Only some of these would be closed and then a centroid makes sense, but not for all of them