What is "superellipse"

n. (context algebra geometry English) a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x =

1. cos^2/rt, y =

2. cos^2/rt

A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape.

In the Cartesian coordinate system, the set of all points (x, y) on the curve satisfy the equation

$$\left|\frac{x}{a}\right|^n\! + \left|\frac{y}{b}\right|^n\! = 1,$$

where n, a and b are positive numbers, and the vertical bars around a number indicate the absolute value of the number.