User:Fgnievinski/Region (geometry)
From Wikipedia, the free encyclopedia
In geometry, a region is a "portion" – a connected open set – of Euclidean space En. This elementary geometry concept is generalized as the domain in real coordinate space and other topological spaces. One-dimensional space (1D), 2D, and 3D regions form curves, surfaces, and solid figures, respectively. The dimensionality of a bounded region equals that of its boundary plus 1.[1] The amount or extent of space are quantified by scalars such as length, area, and volume, respectively.[2] Special cases of flat regions in 1D and 2D are line segments and plane segments, respectively. Locus is a region satisfying a given condition. A convex region is defined such that an arbitrary line segment joining any two points is also contained in the region. A geometric region may be specified in terms of properties such as shape, scale, location, orientation, and reflection.[3] The concept is useful in computer graphics and geometric modeling,[4] such as in the computer representation of surfaces and in the solution of intersection problems. In physics, a region is a subset of physical space that is regular open, connected, and bounded (see also: closed regular set).[5]