The superellipsoid is a generalization of the ellipsoid by allowing different exponents of the variables in the algebraic representation.
It is similarly a generalization of the superellipse
to three dimensions.
The version called the superquadratic ellipsoid is defined by the equation
where
and
are the east-west and north-south exponents, respectively. This superellipsoid can
be rendered in POVRay® with the command
superellipsoid{ <e, n> }
The generalization
of the surface considered by Gray (1997) may also be called a superellipsoid. Some special cases of this surface are summarized in the following table.
and 
are the east-west and north-south exponents, respectively. This superellipsoid can
be rendered in POVRay® with the command
, 
