Читать книгу Computer Aided Design and Manufacturing - Zhuming Bi - Страница 52

The information of solids must be stored in computers. Three popular methods to represent the data structure of solids are relational structure, hierarchical structure, and network structure.

A relational structure defines a set of lists for vertices, edges, and faces, and these lists are stored in term of arrays in a relational database. Taking an example of the pyramid in Figure 2.16, its rational structure includes the lists of vertices, edges, and faces shown in Table 2.2.

Figure 2.16 Relational structure of a pyramid object.

Table 2.2 Relational structure of pyramid object.

List of vertices	List of edges	List of faces
V1 (0.000, 0.000, 0.500) V2 (−0.500, −0.289, 0.000) V3 (0.500, −0.289, 0.000) V4 (−0.000, −0.577, 0.000)	E1 (V1, V2) E2 (V2, V3) E3 (V1, V3) E4 (V2, V4) E5 (V1, V4) E6 (V3, V4)	F1 (E1, E4, E5) F2 (E1, E2, E3) F3 (E3, E6, E5) F4 (E2, E6, E4)

A solid can also be represented by a hierarchical structure where geometric elements are organized by a tree‐like layer structure. For a pyramid object, the highest layer is the solid body, which is bounded by four faces, each face being bounded by three edges and each edge being defined by two vertices. The complete hierarchical structure of a pyramid object is shown in Figure 2.17.

Figure 2.17 Hierarchical structure of a pyramid object.

A hierarchical structure includes redundant information since the same geometric elements may have relations with multiple elements at high levels. Such redundancies can be eliminated by using a network data structure. As shown in Figure 2.18, a network data structure uses data pointers to represent the topological connections of geometric elements. The number of data pointers for a geometric element type can be varied based on the number of connections the element has with others.

Figure 2.18 Network structure of a pyramid object.