geometrycell

Geometrycell is a concept in computational geometry and related fields referring to a basic unit of space that carries both geometric shape and topological connectivity. In practice, a geometrycell is a bounded region of Euclidean space, usually polygonal in two dimensions and polyhedral in higher dimensions, whose boundary is defined by a finite set of facets, edges and vertices. Each geometrycell is associated with metadata such as a representative point (centroid), volume or area, and an adjacency graph describing neighboring cells.

In 2D, geometrycells appear naturally in space-partitioning constructions such as Voronoi diagrams, where each cell consists of all points closer to a given site than to any other. In 3D, geometrycells take the form of convex or nonconvex polyhedra that partition space according to a chosen criteria. Geometrycells are central to mesh generation, geographic information systems, and collision detection, where they allow efficient queries by spatial locality.

Common operations on geometrycells include testing whether a point lies inside the cell, computing intersections or unions with other cells, and performing subdivision or merging as the underlying partition changes. Data structures used to represent geometrycells include half-edge, quad-edge, or other boundary-representation schemes that support fast traversal of the cell's boundary and its neighbors.

Although not a formal standard term, geometrycell serves as a generic descriptor for any cellular unit in a space-partitioning scheme. See also Voronoi cell, Delaunay triangulation, and spatial index.