Boolean operations of 2-manifolds through vertex neighborhood classification

A topologically complete set operations algorithm for planar polyhedral Z-manifold objects is described; that is, under the assumption that all numerical tests required can be correctly evaluated, the algorithm is capable of solving all “special cases." The central component of the algorithm is a module here called the vertex neighborhood classifier. By virtue of the classifier, the various special cases can be reduced into a collection of classification problems involving a pair of coincident vertices. The classifier works by means of decision rules that guarantee the topological consistency and regularity of the resulting polyhedron. If the result is not a 2-manifold, a relaxed polyhedron will be produced.