Quickhull

Quickhull is a method of computing the convex hull of a finite set of points in n-dimensional space.

[1] N-dimensional Quickhull was invented in 1996 by C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa.

[1] It was an extension of Jonathan Scott Greenfield's 1990 planar Quickhull algorithm, although the 1996 authors did not know of his methods.

[2] Instead, Barber et al. describe it as a deterministic variant of Clarkson and Shor's 1989 algorithm.

[1] The 2-dimensional algorithm can be broken down into the following steps:[2] The problem is more complex in the higher-dimensional case, as the hull is built from many facets; the data structure needs to account for that and record the line/plane/hyperplane (ridge) shared by neighboring facets too.

It includes a similar "maximum point" strategy for choosing the starting hull.

This animation depicts the quickhull algorithm in two dimensions.
Steps 1-2: Divide the points into two subsets.
Steps 3-5: Find a point with the maximum distance, ignore points inside the triangle, and recurse.
Step 6: Recurse until no more points are left.