Creating a convex hull

Materials Project Materials Project Website/Apps
1

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

2

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.