Consider a general quadratic surface in implicit form:
\begin{equation} ax^2 + by^2 + cz^2 + 2exy + 2fyz + 2gxz + 2lx + 2my + 2nz + d = 0 \end{equation}
I can parametrise this in the form $f(x, y, z(x,y))$ but this involves solving a quadratic and is not pretty. Is there a better parametrisation that avoids the double solution $z_{+/-}$?