Superellipse

A superellipse is a type of plane curve generalizing the ellipse. It is given by the points $$(x, y)$$ such that


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

where $$a,b > 0$$ control the scaling of the superellipse and $$n > 0$$ is a parameter controlling the shape. $$0 < n < 1$$ produces a concave star-like shape, $$n = 1$$ a rhombus, $$1 < n < 2$$ a bloated rhombus, $$n = 2$$ an ellipse, and $$n > 2$$ a somewhat rounded rectangle (sometimes called a sqircle if $$a = b$$), and as $$n \rightarrow \infty$$ a rectangle is approached.