El elipsoide general está definido por:
\[ x = a \sin\theta \cos\phi, \quad y = b \sin\theta \sin\phi, \quad z = c \cos\theta \]Los vectores tangentes son:
\[ \partial_\theta \vec{r} = \begin{bmatrix} a \cos\theta \cos\phi \\ b \cos\theta \sin\phi \\ -c \sin\theta \end{bmatrix}, \quad \partial_\phi \vec{r} = \begin{bmatrix} -a \sin\theta \sin\phi \\ b \sin\theta \cos\phi \\ 0 \end{bmatrix} \]