Let \(\Omega \) be a subset of a topological space \(X\), and \(\partial \Omega \) be its boundary.
\(\partial \Omega \) as an implicit surface can be defined by a level set \(L_0(f)\)
where
\[
f(\boldsymbol {p})\begin {cases}
\le 0 & \text { if } \boldsymbol {p} \in \Omega \\
> 0 & \text { if } \boldsymbol {p} \notin \Omega
\end {cases}
\]