Polyhedral assembly partitioning with infinite translations or The importance of being exact

Abstract

Assembly partitioning with an infinite translation is the application of an infinite translation to partition an assembled product into two complementing subsets of parts, referred to as a subassemblies, each treated as a rigid body. We present an exact implementation of an efficient algorithm to obtain such a motion and subassemblies given an assembly of polyhedra in ℝ3. We do not assume general position. Namely, we handle degenerate input, and produce exact results. As often occurs, motions that partition a given assembly or subassembly might be isolated in the infinite space of motions. Any perturbation of the input or of intermediate results, caused by, for example, imprecision, might result with dismissal of valid partitioning-motions. In the extreme case, where there is only a finite number of valid partitioning-motions, no motion may be found, even though such exists. The implementation is based on software components that have been developed and introduced only recently. They paved the way to a complete, efficient, and concise implementation. Additional information is available at http://acg.cs.tau.ac.il/projects/internal-projects/ assembly-partitioning/project-page. © 2009 Springer-Verlag.