Superellipse
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.
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) :