Volume of union and volume of intersection of convex hulls?

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.

[jixiong fei]

have you solve this problem？

Answer 1

[Matt J]

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)