Creating a convex hull

I find that pymatgen.analysis.phase_diagram can construct a convex hull of a system. But,I failed to catch on the Mathematical principle of the method by reading source program. So, do you have any literatures about how to construct a convex hull and how to define energy above hull (Especially in high dimension)? I have read the literatures that you given in the source program, but they only show the results without methods.

Sorry for bother you again!

hope for your reply!

Tao Zhang

The general formulation of the quickhull algorithm is here:

I think the wikipedia animation and explanation is far more intuitive to understand, although it’s focused on two dimensions. The higher dimensional case generally reflects the logic of the 2-D case, but with higher-dimension simplices and hyperplanes for finding the points maximally distant from the current set of hull points.