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Family of closed mathematical curves / From Wikipedia, the free encyclopedia

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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.

Examples of superellipses for

In the Cartesian coordinate system, the set of all points on the curve satisfy the equation

where and are positive numbers, and the vertical bars around a number indicate the absolute value of the number. The 3-dimensional generalization is called superellipsoid (some literatures also name it superquadrics).[1][2]

In the Polar coordinate system, the superellipse equation is (the set of all points on the curve satisfy the equation) :