Planning geometric constraint decomposition via optimal graph transformations

Abstract

A central issue in dealing with geometric constraint systems that arise in Computer Aided Design and Assembly is the generation of an optimal decomposition recombination plan that is the foundation of an efficient solution of the constraint system. For the first time, in this paper, we formalize, motivate and explain the optimal decomposition-recombination (DR) planning problem as a problem of finding a sequence of graph transformations Ti that maximizes an objective function subject to a certain criteria. We also give several performance measures phrased as graph transformation properties by which DR-planning algorithms can be analyzed and compared. Using these perfomance measures and formulation of the problem we develop a new DR-planner which represents a significant improvement over existing algorithms.