polygonet

Polygonet is a term encountered in discussions of computational geometry and computer graphics to denote a network of polygonal faces that together approximate a surface. The term emphasizes the interconnected, small-scale arrangement of polygons—typically triangles or quadrilaterals—that share edges and vertices to form a boundary or a volumetric boundary when paired with an appropriate topology. Although not a standard mathematical object, polygonets are commonly treated as polygon meshes or polyhedral meshes in software and research contexts.

In practice, a polygonet is represented by a data structure that captures the connectivity among its elements, often using an adjacency model such as half-edge, winged-edge, or a face-vertex graph. These representations support operations that modify the mesh while preserving or adjusting its topology, such as refinement, simplification, subdivision, or remeshing. Polygonets can be planar or non-planar and may be manifold (where each edge belongs to a limited number of faces) or non-manifold, depending on the intended application.

Construction methods for polygonets include surface sampling and triangulation techniques (for example, Delaunay or marching cubes algorithms), as well as subdivision schemes that progressively refine a coarse mesh into a smoother one. They are widely used in 3D modeling, computer graphics, simulation, and geographic information systems, where a discrete surface representation is required.

See also: polygon mesh, mesh topology, half-edge data structure, triangulation. Note: polygonet is an informal term with variable usage across communities.