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superellipsoid : ウィキペディア英語版
superellipsoid

In mathematics, a super-ellipsoid or superellipsoid is a solid whose horizontal sections are super-ellipses (Lamé curves) with the same exponent ''r'', and whose vertical sections through the center are super-ellipses with the same exponent ''t''.
Super-ellipsoids as computer graphics primitives were popularized by Alan H. Barr (who used the name "superquadrics" to refer to both superellipsoids and 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, while some super-ellipsoids are superquadrics, neither family is contained in the other.
Piet Hein's supereggs are special cases of super-ellipsoids.
==Formulas==


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