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definition. signed distance bound [hart1996sphere, def. 2] [ag-000S]

A function \(f: \mathbb {R}^3 \rightarrow \mathbb {R}\) is a signed distance bound of its implicit surface \(f^{-1}(0)\) if and only if \[ |f(\boldsymbol {x})| \leq d\left (\boldsymbol {x}, f^{-1}(0)\right ) \] If equality holds, then \(f\) is a signed distance function.