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

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Vinit Nagda on 29 Aug 2021
Commented: Vinit Nagda on 30 Aug 2021
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).
Thank you.
Matt J on 29 Aug 2021
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.

Matt J on 29 Aug 2021
Edited: Matt J on 29 Aug 2021
The general procedure would be
1. Given the output [v,c]=voronoin(P) select two cells i and j
2. Find the vertices in comon between cells i and j using intersect(c{i},c{j})
3. If there are more than 2 intersecting vertices, fit a plane to them and project them into a 2D coordinate system on the plane.
4. 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
Vinit Nagda on 30 Aug 2021
@Matt J Thank you very much for your response. I should now be able to calculate the area of common face with your code.
I am not sure about the number of common faces but I will check that and let you know.
Thanks for your time and support.

R2020b

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