wingededge

Winged-edge is a topological data structure used to represent polygonal meshes in computer graphics and computational geometry. It stores the mesh’s vertices, edges, and faces along with explicit relationships among them, enabling efficient navigation and editing of topology. In a winged-edge representation, an edge maintains knowledge of the two vertices it connects, the two faces on its sides, and the surrounding edges that bound those faces and meet at the edge’s endpoints. This redundancy supports fast traversal without repeatedly searching for adjacent elements.

Typically, an edge includes pointers to its origin and destination vertices, the left and right faces, and the four surrounding edges around its endpoints (the wings). With these references, one can traverse a mesh by walking around a face to enumerate its edges, or walk around a vertex to find all incident edges, and similarly move between adjacent faces and edges. The structure thus supports common topology operations such as edge insertion or deletion, face subdivision, edge flips, and mesh repairs while maintaining consistent connectivity.

Winged-edge is one of several topological representations for polygonal meshes, alongside alternatives such as half-edge and the DCEL (doubly connected edge list) or quad-edge structures. It is used in computer-aided design, 3D modeling, and mesh processing tools where robust, local adjacency information is important. While powerful, winged-edge implementations can be memory-intensive due to the number of pointers, and they can be more complex to implement for non-manifold or highly irregular meshes.