Slab (geometry)

In geometry, a slab is a region between two parallel lines in the Euclidean plane,[1] or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in higher dimensions.[2]

## Set definition

A slab can also be defined as a set of points:[3] {x∈ℝn∣α≤n⋅x≤β}, where n is the normal vector of the planes n⋅x=α and n⋅x=β.

Or, if the slab is centered around the origin:[4] {x∈ℝn∣|n⋅x|≤θ/2}, where θ=|α−β| is the thickness of the slab.

## See also

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

## References

1. ↑ "2.2.2.1 The slab method". Computational Geometry: An Introduction. New York: Springer. 1985. pp. 45–48. doi:10.1007/978-1-4612-1098-6. ISBN 978-1-4612-7010-2.
2. ↑ Jacob, Goodman. "Handbook of Discrete and Computational Geometry" (in en). CRC Press LLC. http://www.csun.edu/~ctoth/Handbook/HDCG3.html. Retrieved 24 July 2022.
3. ↑ S., Boyd. "Convex Optimization" (in en). Cambridge University Press. https://web.stanford.edu/~boyd/cvxbook/. Retrieved 14 March 2022.
4. ↑ Jean-Luc, Marichal; Mossinghoff, Michael J. (2008). "Slices, slabs, and sections of the unit hypercube". Online Journal of Analytic Combinatorics 3 (1). https://hosted.math.rochester.edu/ojac/vol3/Marichal_2008.pdf.

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