Given finite points on a plane, how to calculate the Newton polygon, i.e. the lower bound of its convex hull?

The convex hull can be obtained by ConvexHull command from ComputationalGeometry package, but I don't know how to get its lower bound easily. Besides that, theoretically the Newton polygon does not depend on the full structure of convex hull, so maybe there is a more effective way to do that?

P.S. There is a method DEplot_polygon in DETools that can "generate the plot of the Newton polygon of a linear differential operator at a point“, but I not sure how it can be used to calculate the Newton polygon for general cases.