Slab (geometry)

A slab can also be defined as a set of points:[3]

$${\displaystyle \{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \},}$$

where ${\displaystyle n}$ is the normal vector of the planes ${\displaystyle n\cdot x=\alpha }$ and ${\displaystyle n\cdot x=\beta }$.

Or, if the slab is centered around the origin:[4]

$${\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},}$$

where ${\displaystyle \theta =|\alpha -\beta |}$ is the thickness of the slab.

• Bounding slab
• Convex polytope
• Half-plane
• Hyperplane
• Prismatoid
• Slab decomposition
• Spherical shell