Читать книгу Computer Aided Design and Manufacturing - Zhuming Bi - Страница 68

In CSG, an object is constructed from solid primitives by composition operations. Eligible composition operations are the Boolean operations on sets, i.e. union (∪), intersection (∩), and difference (\), as well as associated geometric transformations of those sets.

For a pair of solid primitives with given postures, different composition operations lead to different outcomes of assembled objects. Figure 2.30 shows three different objects from the compositions of a rectangular cuboid and a cylinder primitive.

Figure 2.30 Differences of Boolean operations. (a) Two primitives at given positions. (b) A∪B. (c) A∩B. (d) A\B. (e) B\A.

Other than the Boolean operations among solid primitives, a coordinate transformation can be applied to individual primitives before a Boolean operation takes place. Common operations of coordinate transformation include translating, copying, rotating, mirroring, and scaling. Figure 2.31 shows some examples of these operations.

Figure 2.31 Common operations of coordinate transformation. (a) Translating. (b) Rotating. (c) Mirroring. (d) Scaling.