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I have a library (quickhull in C++) that I am using to create a hull from a set of points. I am able to see the vertices of the hull but not the facets. I would like to compute the volume of the hull. What is the best way to do this?

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  • $\begingroup$ See mathoverflow.net/questions/979/… . I believe qhull has approximate volume computation in 3D. $\endgroup$
    – icurays1
    Jun 15, 2016 at 22:25
  • $\begingroup$ I don't want to use qhull - it's not possible to easily integrate it into my code (written in C++). I am using this library: github.com/akuukka/quickhull $\endgroup$ Jun 15, 2016 at 22:42
  • $\begingroup$ There is a C++ interface to qhull, check the website. At any rate, my point is that there isn't a good, explicit way to do this unless you have the faces, which if you did you could compute face areas and add up cone volumes (see here). If you only have the point cloud, triangulating it is definitely possible but fairly slow. Approximate methods to compute volumes of convex hulls are mostly Monte Carlo based (i.e. random), and I believe this is what qhull uses. $\endgroup$
    – icurays1
    Jun 16, 2016 at 5:28
  • $\begingroup$ Ok. Thanks. I will see if i can get the faces of the hull. $\endgroup$ Jun 17, 2016 at 7:32
  • $\begingroup$ Calculate inner point of convex hull (simple mean of vertices). Then summarize all the volumes for all simplices constructed from inner point + facet of convex hull. $\endgroup$ Nov 4, 2016 at 17:45

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