# How to calculate volume of 3d convex hull?

Convex hull is defined by a set of planes (point on plane, plane normal). I also know the plane intersections points which form polygons on each face.

How to calculate volume of convex hull?

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This is a difficult problem. See Algorithm for finding the volume of a convex polytope – bobobobo Aug 21 '13 at 11:28

## 2 Answers

Since you have the plane intersections too, It is equivalent to the volume of a polyhedron. (the fact that yours is convex doesn't matter).

http://en.wikipedia.org/wiki/Polyhedron#Volume

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Find a point $O$ within the hull. Then add up the volumes of the cones made by $O$ and each face. Volume of each cone is $\frac{1}{3}\times \text{(height)}\times \text{(area of face)}$

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