How to find the area of a common face of voronoi cells
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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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Accepted Answer
Matt J
on 29 Aug 2021
Edited: Matt J
on 29 Aug 2021
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
[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
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