Given the implicit expression of an ellipsoid $$\mathcal{E} : \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ finding the parameterization $$\begin{cases}x=a\cos(\theta)\cos(\phi)\\y=b\sin(\theta)\cos(\phi)\\z=c\sin(\phi)\end{cases}$$ on the internet is quite easy, but what is the procedure to find a parameterization of any quadric (hyperbolic/elliptic hyperboloid/paraboloid)?
2026-04-07 19:36:24.1775590584
Parametric equation of an ellipsoid
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