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definition. point-to-set distance [hart1996sphere, def. 1] [ag-000R]

The point-to-set distance defines the distance from a point \(\boldsymbol {x} \in \mathbb {R}^3\) to a set \(A \subset \mathbb {R}^3\) as the distance from \(x\) to the closest point in \(A\), \[ d(\boldsymbol {x}, A)=\min _{y \in A}\lVert \boldsymbol {x}-\boldsymbol {y}\rVert \]