Faceadjacent

Faceadjacent is a term used in geometry and computer graphics to describe a relationship between polygonal faces of a mesh. Two faces are faceadjacent if they share a common boundary edge. In a typical manifold surface, each edge is incident to exactly two faces, and those faces are faceadjacent across that edge. The term is often written as face-adjacent or face adjacency, and it is sometimes contrasted with vertex-adjacent (sharing only a vertex) or non-adjacent faces.

In data structures for meshes, such as half-edge, winged-edge, or the DCEL representation, each face has information about the faces that lie across its edges. This adjacency information enables efficient traversal of a mesh’s 2D neighborhood, connectivity queries, region growing, and a variety of mesh processing operations including smoothing, remeshing, and collision detection. Face adjacency underpins algorithms that rely on local neighborhood topology, such as normal computation, visibility testing, and topological analysis.

Notes and variations: some texts use edge-adjacent to describe faces that share an edge and are therefore adjacent, while others reserve edge-adjacency for the relationship mediated by the shared edge, focusing on the boundary itself. In practice, faceadjacency is a core concept in mesh topology and is central to understanding how a surface is stitched together from polygonal faces.

See also: dual graph, half-edge data structure, winged-edge, DCEL, polygon mesh, manifold.