User:Fgnievinski/Region (geometry)
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]
See also
[edit]- Computational geometry
- Facet (geometry)
- Geometric primitive
- Neighbourhood (mathematics)
- Image region
- Interval (mathematics)
- Jordan curve theorem
- Point (geometry)
- Riemann mapping theorem
- Simple polygon
- Support (mathematics)
- Surface patch
- Ball regions
- Spherical regions
References
[edit]- ^ Deshko, Y. (2022). Special Relativity: For Inquiring Minds. Undergraduate Lecture Notes in Physics. Springer International Publishing. ISBN 978-3-030-91142-3. Retrieved 2023-03-12.
- ^ Stein, S.K. (2016). Calculus in the First Three Dimensions. Dover Books on Mathematics. Dover Publications. p. 583. ISBN 978-0-486-80114-8. Retrieved 2022-01-03.
In mathematics, the terms length, area, and volume always refer to numbers. To name geometric objects or regions, we use terms such as plane set, surface, and solid. Throughout the text we assume that the curves we deal with have length, that the surfaces have area, and that the solids have volume.
- ^ Kendall, D.G. (1984). "Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces". Bulletin of the London Mathematical Society. 16 (2): 81–121. doi:10.1112/blms/16.2.81.
- ^ Agoston, M.K. (2005). Computer Graphics and Geometric Modelling. Computer Graphics and Geometric Modeling. Springer. ISBN 978-1-85233-818-3. Retrieved 2022-01-11.
- ^ Coecke, B. (2010). New Structures for Physics. Lecture Notes in Physics. Springer. p. 766. ISBN 978-3-642-12820-2. Retrieved 2022-01-12.