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.