How to calculate the volume of a convex figure given by points?

Question

Mathematics

There is a set of points in space forming a convex figure. What are the methods for finding its volume? Perhaps there are some ready-made implementations (libraries), I would be very grateful for tips.
They know about the method of tetrahedra - any figure is divided into tetrahedra, after each we find the volume. But firstly, the complexity is O(n^4), and secondly, the existing implementation fails on complex figures, I can’t catch the error for 2 days already.

Answer 1

If you do not need high accuracy or you need a beautiful solution, you can use the Monte Carlo method. To do this, you need to know whether the point is inside the shape or not. Here is the first link about it But about Monte Carlo
There is another way - numerical integration. If you know how easy it is to get a projection of a cut of a figure anywhere on a plane, then there is nothing complicated here either.