Matchmaker: manifold BReps for non-manifold r-sets

Many modeling techniques produce non-manifold solids. A non-manifold model N may be approximated by a manifold model M that is infinitely close to N in the geometric sense. M may be derived by replicating and bending the non-manifold edges of N (this produces an edge-manifold model) and then by replicating the remaining non-manifold vertices and moving them slightly apart. Although inconsistent, the connectivity of M and the geometry of N may be combined in a pseudo-manifold representation of N, which exhibits space and performance advantages for many popular applications, especially when N is a triangulated polyhedron. The Matchmaker algorithm introduced here matches pairs of adjacent faces of N and produces an edge-manifold topology with 5 to IO times fewer non-manifold vertices than N.