Assembling Polyhedra with Single Translations

摘要

The problem of partitioning an assembly of polyhedral objects into twosubassemblies that can be separated arises in assembly planning. We describe an algorithm to compute the set of all translations separating two polyhedra with n vertices in 0(n) steps and show that this is optimal. Given an assembly of k polyhedra with a total of n vertices, an extension of this algorithm identifies a valid translation and removable subassembly in 0(k2n4) steps if one exists. Based on the second algorithm a polynomial time method for finding a complete assembly sequence consisting of single translations is derived. An implementation incorporates several changes to achieve better average-case performance; experimental results obtained for composite objects consisting of isothetic polyhedra are described.