Hyper ellipses (also called super ellipses) are a more generalized form of the familiar ellipse. An ellipse is a conic section, described by the equation:

when centered at the origin.

A hyper ellipse, centered at the origin is described by the equation:

where k and m can assume any real value. The shape converges to a rectangle is dimensions: a X b, as k and m become large. For k and m < 2, the shape morphs into a 4 point star. See below.