orregion

Orregion is an informal term used in geometry, GIS, and logic to denote the region produced by the boolean OR operation on two or more spatial regions. In set-theoretic terms, orregion(A,B) is A ∪ B, the union of A and B. For a collection of regions {A_i}, the orregion is ⋃_i A_i. This interpretation aligns with the idea of an “at least one condition true” region in logic and is a basic construct in computational geometry and map overlay analysis.

Key properties follow from basic set theory. A and B are both contained in orregion(A,B); the orregion depends on the union of the regions and satisfies μ(A ∪ B) = μ(A) + μ(B) − μ(A ∩ B) for measures such as area. Boundaries relate as ∂(A ∪ B) ⊆ ∂A ∪ ∂B ∪ (A ∩ B) in many common geometries, with more complex interactions possible for non-convex or highly curved regions.

Applications: In GIS, orregion is used to model areas that satisfy either criterion, such as lands designated for agriculture or conservation, or to perform overlays combining multiple feature layers. In computer graphics and computational geometry, it corresponds to overlay operations and region unions on polygonal meshes or raster data, often implemented via plane-sweep algorithms, boolean polygon operations, or bitmap unions.

Example: If A is a circle and B is another circle overlapping, orregion is the union shape formed by the two circles. Notes: the term is not standard across all mathematical texts; it serves as descriptive shorthand for the union of regions. Related concepts include union, disjunction, and overlay.