I need to generate a signed distance function field for an implicit surface embedded in $\mathbb{R}^3$:
\begin{equation} F(x, y, z) = 0 \end{equation}
for numerical purposes (so also an approximate method is accepted). Do I need to solve the Eikonal equation to obtain it?
For example, let's take an ellipsoid:
\begin{equation} \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} - 1 = 0 \end{equation}
Can I compute the SDF analitically?