Abstract
As a first step toward a Constructive Solid Geometry for designing general polyhedra, this paper develops the set theory of the trihedron, loosely speaking any set combination of three planar half spaces (monohedra). The trihedron can be decomposed precisely into its primitive monohedra and its CSG-tree of union or intersection operations with no designer topological input other than the convexity or concavity of each edge, giving a human-computer interface simpler than those for existing right-hand rule boundary representation methods. The somewhat visual trigonometric concepts of classical solid geometry are formulated in terms of vectors and matrices appropriate for numerical computation. This reorganization may be useful not only for designers of CAD systems, but also for educators seeking to strengthen and modernize the geometric education of engineering students wonting to make full use of CAD/CAM technology.
Optimization of Constructive Solid Geometry Via a Tree-Based Multi-objective Genetic Algorithm