I'm looking for an algorithm to do a best fit of an arbitrary rectangle to an unordered set of points. Specifically, I'm looking for a rectangle where the sum of the distances of the points to any one of the rectangle edges is minimised. I've found plenty of best fit line, circle and ellipse algorithms, but none for a rectangle. Ideally, I'd like something in C, C++ or Java, but not really that fussy on the language.

The input data will typically be comprised of most points lying on or close to the rectangle, with a few outliers. The distribution of data will be uneven, and unlikely to include all four corners.

c algorithm rectangles best-fit
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