In geometry, a slab is a region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in higher dimensions.
Set definition A slab can also be defined as a set of points:
{ x ∈ R n ∣ α ≤ n ⋅ x ≤ β } , {\displaystyle \{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \},} where n {\displaystyle n} is the normal vector of the planes n ⋅ x = α {\displaystyle n\cdot x=\alpha } and n ⋅ x = β {\displaystyle n\cdot x=\beta } . Or, if the slab is centered around the origin:
{ x ∈ R n ∣ | n ⋅ x | ≤ θ / 2 } , {\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},} where θ = | α − β | {\displaystyle \theta =|\alpha -\beta |} is the thickness of the slab.
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