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) :
^Barr (1981). "Superquadrics and Angle-Preserving Transformations". IEEE Computer Graphics and Applications. 1 (1): 11–23. doi:10.1109/MCG.1981.1673799. ISSN 1558-1756. S2CID 9389947.
^Liu, Weixiao; Wu, Yuwei; Ruan, Sipu; Chirikjian, Gregory S. (2022). "Robust and Accurate Superquadric Recovery: A Probabilistic Approach". 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 2666–2675. arXiv:2111.14517. doi:10.1109/CVPR52688.2022.00270. ISBN 978-1-6654-6946-3. S2CID 244715106.
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