Winged-Edge Representation:

Possibly the oldest data structure for a b-rep is Baumgart's winged-edge data structure. This is quite different from that of a wire-frame model, as the winged- edge data structure uses edges to keep track almost everything. In what follows, we will assume there are no holes in each face and later extend it to cope with holes. Furthermore, we will assume edges and faces are line segments and polygons. Topologically, one may always stretch curvilinear edges and faces so that they become flat without changing the relationships among them.

 Figure

Figure illustrated a polyhedron along with vertices, edges & faces mentioned with upper cases, lower cases & digits, respectively. Let us take a look at edge a = XY. This edge contains two incident vertices X and Y, & two incident faces 1 and 2. Face is a polygon surrounded through edges. For instance, face 1 contain its edges a, c and b, and face 2 has its edges a, e and d. Note down that the ordering is clockwise viewed from outside of the solid. If the direction of the edge is from X to Y, faces 1 and 2 are upon the right and left side of edge a, respectively. In order to capture the ordering of edges correctly, we require four more pieces of information. Since edge a is traversed once while traversing face 1 and traversed a second time while traversing face 2, it is utilized twice in different directions. For instance, while traversing the edges of face 1, the predecessor & the successor of edge a are edge b and edge c, and while traversing the edges of face 2, the predecessor & successor of edge a are edge d and edge e. Note down that although there are four edges incident to vertex X, only three of them are utilized when finding faces incident to edge a.