  We study the relationship between the concept of a continuous ellipsoid
$\Theta$ cover of $\mathbb{R}^n$, which was introduced by Dahmen, Dekel, and
Petrushev, and the space of homogeneous type induced by $\Theta$. We
characterize the class of quasi-distances on $\mathbb{R}^n$ (up to equivalence)
which correspond to continuous ellipsoid covers. This places firmly continuous
ellipsoid covers as a subclass of spaces of homogeneous type on $\mathbb{R}^n$
satisfying quasi-convexity and $1$-Ahlfors-regularity.
