First, let me preface by saying I've done a few searches both on here and on Google, and have not been able to find anything that suits my purposes, at least as far as I am aware. My maths have gotten a bit rusty over the years.

Now then, I would like to find the minimum bounding box/rectangle given a set of points on a 2-dimensional plane, one that is properly rotated to be the smallest. At the moment, the only thought process that has come to mind is to compute 180 different bounding boxes and find the one with the lowest area, but this seems to be the opposite of ideal.

Any help is greatly appreciated and please excuse if it is something obvious/simple/etc.

Thanks!