Editing Superellipse (section)

=== Higher dimensions ===
The generalizations of the superellipse in higher dimensions retain the fundamental mathematical structure of the superellipse while adapting it to different contexts and applications.<ref>{{Cite book |last1=Boult |first1=Terrance E. |last2=Gross |first2=Ari D. |chapter=Recovery of Superquadrics from 3-D Information |editor-first1=David P. |editor-first2=Ernest L. |editor-last1=Casasent |editor-last2=Hall |date=1988-02-19 |title=Intelligent Robots and Computer Vision VI |chapter-url=http://dx.doi.org/10.1117/12.942759 |series=SPIE Proceedings |volume=0848 |page=358 |publisher=SPIE |doi=10.1117/12.942759|bibcode=1988SPIE..848..358B }}</ref>

* A [[superellipsoid]] extends the superellipse into three dimensions, creating shapes that vary between ellipsoids and rectangular solids with rounded edges. The superellipsoid is defined as the set of all points <math>(x,y,z)</math> that satisfy the equation:<math display="block">\left|\frac{x}{a}\right|^n\!\! + \left|\frac{y}{b}\right|^n\! + \left|\frac{z}{c}\right|^n\! = 1,</math>where <math>a,b</math> and <math>c</math> are positive numbers referred to as the semi-axes of the superellipsoid, and <math>n</math> is a positive parameter that defines the shape.<ref name=":1" />
* A [[hyperellipsoid]] is the <math>d</math>-dimensional analogue of an [[ellipsoid]] (and by extension, a superellipsoid). It is defined as the set of all points <math>(x_1,x_2,\ldots, x_d)</math> that satisfy the equation:<math display="block">\left|\frac{x_1}{a_1}\right|^n\!\! + \left|\frac{x_2}{a_2}\right|^n\! +\ldots+ \left|\frac{x_d}{a_d}\right|^n\! = 1,</math>where <math>a_1,a_2,\ldots, a_d</math> are positive numbers referred to as the semi-axes of the hyperellipsoid, and <math>n</math> is a positive parameter that defines the shape.<ref name=":0">{{Cite journal |last1=Ni |first1=B. Y. |last2=Elishakoff |first2=I. |last3=Jiang |first3=C. |last4=Fu |first4=C. M. |last5=Han |first5=X. |date=2016-11-01 |title=Generalization of the super ellipsoid concept and its application in mechanics |url=https://www.sciencedirect.com/science/article/pii/S0307904X16303225 |journal=Applied Mathematical Modelling |volume=40 |issue=21 |pages=9427–9444 |doi=10.1016/j.apm.2016.06.011 |issn=0307-904X}}</ref>