Читать книгу Computer Aided Design and Manufacturing - Zhuming Bi - Страница 38

Geometry relates to the properties and relations of basic geometric elements such as points, lines, surfaces, solids, and higher dimensional analogues.

Figure 2.2 shows an example of basic geometric elements of an object. An object is represented by its geometric elements such as points, edges, surfaces, and solids. In addition, basic geometric elements are at different levels of the topological tree of an object. As shown in Figure 2.2, points and nodes are at the lowest level, edges formed by points or nodes are at the second level, surfaces formed by the boundary edges are at the third level, and solids with a given volume formed by a set of watertight boundary surfaces are at the upper level.

Figure 2.2 Example of basic geometric elements. (a) Points, nodes, lines, edges, axes, and planes. (b) Patches, surfaces, and operations. (c) Volumes, features, solids, and operations.

Geometry includes the relations of these geometric elements. These relations can be spatial or topological. To represent spatial relations of geometric elements, some references have to be established, and common references can be points, axes, planes, and coordinate systems. To represent topological relations, one has to be familiar with some common logical operations such as union, subtraction, and intersection.