How to find the area of a common face of voronoi cells

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Vinit Nagda 2021-8-29

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评论： Vinit Nagda 2021-8-30

I have a set of 3D points from which I draw a Voronoi diagram using voronoin.

I want to find the area of a face common to two voronoi cells for neighbouring points. (There could possibly be more than one face common to two cells, so first to find number of common face and then their corresponding areas).

Can someone please help me with a function to calculate the same?

Thank you.

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Matt J 2021-8-29

编辑：Matt J 2021-8-29

There could possibly be more than one face common to two cells.

I don't think so. That would violate the convexity of the cells.

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Answer 1

Matt J 2021-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/1442944-how-to-find-the-area-of-a-common-face-of-voronoi-cells#answer_776674

编辑：Matt J 2021-8-29

在 MATLAB Online 中打开

The general procedure would be

Given the output [v,c]=voronoin(P) select two cells i and j
Find the vertices in comon between cells i and j using intersect(c{i},c{j})
If there are more than 2 intersecting vertices, fit a plane to them and project them into a 2D coordinate system on the plane.
Use convhull to calculate the convex area of the 2D projected points.

Step 3 can be done easily using planarFit from this File Exchange submission

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

[v,c]=voronoin(P);
V=v(intersect(c{i},c{j}), :); %intersecting vertices
if size(V,1)<=2
 Area=0;
else
  
  fitobj=planarFit(V.');
  
  [~,Area]=convhull(  (V-mean(V,1))*fitobj.R(:,2:3) );
    
end