Computer Aided Engineering Design

260 COMPUTER AIDED ENGINEERING DESIGN

parenthesis and polygonal faces denoted alphabetically. Consider edge (3) in Figure 8.17 (b) formed
by vertices 2 and 4. The edge has two associated faces A and B, and if the direction of the edge is
from vertex 2 to vertex 4, A is on the left and B on the right of the edge. When viewed from outside
the solid, the faces are traversed clockwise so that the normal to the faces using the right-handed rule
points into the solid. As shown in Figure 8.17(b), edge (3) is traversed twice in two different
directions, once while traversing A and the other while traversing B. On face A, edge (5) precedes
edge (3) while edge (1) succeeds it. Similarly on B, (2) is the preceding edge while (6) is the
succeeding edge. Note that the schemetic in Figure 8.17(b) is suggestive of the winged-edge with
edges (1), (2), (5) and (6) being the wings of (3) for which reason, the data structure is named so.
We can tabulate the above information for edge (3) as shown in the edge table. Likewise, similar
information can be tabulated for all the edges. We would note that the order of the two vertices
comprising the edge would determine the direction of the latter, which in turn would help decide the
faces on the left and right of the edge. In case the order of the vertices is changed, the entries in the
edge table would get altered accordingly.

Back face D

4

3

2

1

A

(6)

(3)

(4) (2)

(1)

(a) (b)

A

C

B B

(3)

(5) (6)

4

2

(1) (2)

(5)

Figure 8.17 Winged-edge data structure for a tetrahedron

In addition to the edge table, the data structure also requires a vertex table and a face table. Both
tables document the edges associated with the vertices and faces, respectively. Since more than one
edge may be associated with a vertex (or face), the following tables are not unique.

Edge table

Clockwise Clockwise

Edge Vertices Faces traverse on left face traverse on right face

Name Start End Left Right Preceding Suceeding Preceding Suceeding

edge edge edge edge

(3) 2 4 AB (5) (1) (2) (6)

(1) 1 2 AC (3) (5) (4) (2)

(2) 2 3 BC (6) (3) (1) (4)

(4) 1 3 DC (5) (6) (2) (1)

(5) 1 4 DA (6) (4) (1) (3)

(6) 3 4 BD (3) (2) (4) (5)