3D Convex Hull's Volume

Question

I have the points of a 3D convex hull, I want to find out the volume of the convex hull. Anyone knows any methods to do so? It would be really nice to inform me about any C++ library that can do that for me.

Answer 1

For the volume, simply see wikipedia , under "Orientable polyhedra". You want the formula with volume = 1/3 * sum...

Answer 2

If your input is just a set of points, you will need the faces of the convex hull to apply the formula bellow. This is implemented in CGAL or qhull. Once, the convex hull is computed, you just have to enumerate all facets (this is easy in CGAL) and add their volume.