Fit rectangle around points

Question

I\'m trying to fit a rectangle around a set of 8 2D-Points, while trying to minimize the covered area.

Example:

The rectangle may be sc

Answer 1

They first thing that came to mind when I saw this problem was to use principal component analysis. I conjecture that the smallest rectangle is the one that satisfies two conditions: that the edges are parallel with the principal axes and that at least four points lie on the edges (bounded points). There should be an extension to n dimensions.