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

It has been shown that the minimum area rectangle of a set of points is collinear with one of the edges of the collection's convex hull polygon ["Determining the Minimum-Area Encasing Rectangle for an Arbitrary Closed Curve" [Freeman, Shapira 1975]

An O(nlogn) solution for this problem was published in "On the computation of minimum encasing rectangles and set diameters" [Allison, Noga, 1981]

A simple and elegant O(n) solution was published in "A Linear time algorithm for the minimum area rectangle enclosing a convex polygon" [Arnon, Gieselmann 1983] when the input is the convex hull (The complexity of constructing a convex hull is equal to the complexity of sorting the input points). The solution is based on the Rotating calipers method described in Shamos, 1978. An online demonstration is available here.