Triangulation and CSG representation of polyhedra with arbitrary genus

Abstract

The main purpose behind decomposing an object into simpler components is to simplify a problem for complex objects into a number of subproblems dealing with simple objects. In particular, the problem of partitioning a three dimensional polyhedron into simpler parts arises in mesh generation for finite element methods, CAD/CAM applications, computer graphics, motion planning and solid modeling. Though several decomposition problems have been widely researched in two dimensions, very few results exist for their three dimensional counterparts. Two such problems, triangulation and CSG (Constructive Solid Geometry) tree partition of polyhedra are addressed in this paper.