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Superellipse
Family of closed mathematical curves / From Wikipedia, the free encyclopedia
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 defined by an equation that allows for various shapes between a rectangle and an ellipse.
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In two dimentional Cartesian coordinate system, a superellipse is defined as the set of all points on the curve that satisfy the equation
where
and
are positive numbers referred to as semi-diameters or semi-axes of the superellipse, and
is a positive parameter that defines the shape. When
, the superellipse is an ordinary ellipse. For
, the shape is more rectangular with rounded corners, and for
, it is more pointed.[1] [2][3]
In the polar coordinate system, the superellipse equation is (the set of all points on the curve satisfy the equation):