User:Fgnievinski/Region (geometry)



In geometry, a region is a "portion" – a connected open set – of Euclidean space $E^{n}$. 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. The amount or extent of space are quantified by scalars such as length, area, and volume, respectively. 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. The concept is useful in computer graphics and geometric modeling, 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).