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This paper presents efficient methods for supporting robust Boolean operations on pairs of polyhedral manifolds. A new spatial hashing technique is proposed for detecting intersections of pairs of polygon faces quickly and robustly. Robust predicates are used to compute the exact topology of the resulting polyhedron. Degenerate intersections are identified explicitly but handled in the topological routines. Geometric positions of new vertices are then approximated using finite-precision computations. Although vertex locations are rounded off, the exact connectivity graph is kept. The faces of the rounded-off triangulated final model thus could intersect each other and have the potential for an invalid embedding.