definition. implicit surface [hart1996sphere, sec. 1] [ag-000K]

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If an SDF \(f\) is a continuous mapping, the subset \(\Omega \) can be implicitly described as the locus of points \[ \Omega = \{ p : f(p) \le 0 \} \]

By continuety, \(f\) is zero on \(\partial \Omega \) which forms the implicit surface of \(f\).