definition. implicit surface [winchenbach2024lipschitz, sec. 1] [ag-000X]

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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 \[ f(\boldsymbol {p})\begin {cases} \le 0 & \text { if } \boldsymbol {p} \in \Omega \\ > 0 & \text { if } \boldsymbol {p} \notin \Omega \end {cases} \]