VertexEdgeFace

Vertex-Edge-Face (VEF) is a data structure used to store and manipulate the topology of polygonal meshes by organizing information around the three primitive elements: vertices, edges, and faces. It is designed to support efficient traversal and editing of polyhedral surfaces in computer graphics, CAD, and computational geometry.

In a VEF representation the mesh is described by three interrelated collections. The vertex set stores geometric coordinates and a reference to an incident edge. The edge set stores the two endpoint vertices and references to the adjacent faces, commonly through an embedded representation such as half-edges. The face set stores a boundary loop, typically as a cyclic sequence of edges or half-edges. Some variants emphasize explicit half-edges to facilitate traversal around vertices and faces, enabling straightforward navigation of incidences and adjacencies.

Topological properties and constraints are characteristic of VEF. For a manifold surface, each edge is incident to at most two faces; boundaries are indicated by a single adjacent face or a null reference. Non-manifold situations may require the edge to be associated with multiple faces. The design aims to provide a compact yet flexible representation that supports common editing operations while maintaining clear incidence information.

Typical operations in a VEF framework include insertion and deletion of vertices, edges, and faces; querying incidences (for example, listing all edges incident to a vertex or all faces adjacent to an edge); and editing operations such as splitting or collapsing edges and adding or removing faces. These operations rely on consistent updates to the interconnected vertex, edge, and face records.

VEF is commonly compared to other topological mesh representations, such as the DCEL (doubly connected edge list) and winged-edge structures. It offers a balance between simplicity and traversability, at times trading some traversal efficiency for easier implementation and maintenance. See also: DCEL, winged-edge, half-edge data structures.