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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]

where is the normal vector of the planes and .

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

where is the thickness of the slab.

See also


  1. ^ Preparata, Franco P.; Shamos, Michael Ian (1985). " The slab method". Computational Geometry: An Introduction. New York: Springer. pp. 45–48. doi: 10.1007/978-1-4612-1098-6. ISBN  978-1-4612-7010-2. S2CID  206656565.
  2. ^ Jacob, Goodman. "Handbook of Discrete and Computational Geometry". CRC Press LLC. Retrieved 24 July 2022.
  3. ^ S., Boyd. "Convex Optimization". Cambridge University Press. Retrieved 14 March 2022.
  4. ^ Jean-Luc, Marichal; Mossinghoff, Michael J. (2008). "Slices, slabs, and sections of the unit hypercube" (PDF). Online Journal of Analytic Combinatorics. 3 (1). arXiv: math/0607715.