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Superquadrics
In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the Lamé curves ("Superellipses").
The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics.
Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids.〔Barr, A.H. (January 1981), ''Superquadrics and Angle-Preserving Transformations''. IEEE_CGA vol. 1 no. 1, pp. 11–23〕〔Barr, A.H. (1992), ''Rigid Physically Based Superquadrics''. Chapter III.8 of ''Graphics Gems III'', edited by D. Kirk, pp. 137–159〕 However, the (proper) supertoroids are not superquadrics as defined above; and, while some superquadrics are superellipsoids, neither family is contained in the other.
== Formulas ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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