Volume of union and volume of intersection of convex hulls?

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Russell
Russell le 16 Avr 2014
Modifié(e) : Matt J le 31 Mar 2024 à 1:32
I apologize if the answer to this is obvious. I am a matlab and geometry noob.
Anyway, I used convhulln to compute a bunch of convex hulls. I want to know how to compute the volume of the union and the volume of the intersection of an arbitrary number of these polytopes.
Anyone have any ideas? Tried doing some googling, to no avail.

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Matt J
Matt J le 31 Mar 2024 à 1:29
Modifié(e) : Matt J le 31 Mar 2024 à 1:32
Use intersectionHull from this FEX download to find the intersection,
https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra?s_tid=srchtitle
Once you have found the vertices of the intersection, convhulln can be used to find its volume.
Once you've found the volume of the intersection, the volume of the union can be found using,
Volume(Union) = Volume(Polytope1) + Volume(Polytope2) - Volume(Intersection)

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