WELL-FORMED SYSTEMS OF POINT INCIDENCES FOR RESOLVING COLLECTIONS OF RIGID BODIES

Abstract

For tractability, many modern geometric constraint solvers recursively decompose an input geometric constraint system into standard collections of smaller, generically rigid subsystems or clusters. These are recursively solved and their solutions or realizations are recombined to give the solution or realization of the input constraint system. Even for generically wellconstrained systems in 3D, and even when the shared objects between clusters in the decomposition are restricted to be points, it is a significant hurdle to find a wellformed system of shared object incidences that recombines a cluster decomposition. By wellformed we mean that the recombination system generically preserves the classification of the original, undecomposed system as a well, under or overconstrained system. Here we motivate, formally state and give an efficient, greedy algorithm to find such a wellformed system for a general constraint system, when the shared objects in the cluster decomposition are restricted to be points. Our solution relies on an interesting new matroid structure underlying collections of rigid clusters with shared points.