QQ-Complex: Efficient non-manifold boundary representation with inclusion topology

The interpretation of auxiliary entities as boundary entities in previous non-manifold boundary (NMB) representations may change a model’s intended topology and increase the complexity of the corresponding data structure. In this paper, entities appearing in a modeling process are classified into boundary and non-boundary entities. Non-boundary entities are usually embedded into embedding-space entities. These embedding relationships are described by inclusion topology. To support inclusion topology, a new mathematical framework—quasi-cell-complex, as well as a topological data structure—QQ-Complex, are proposed. Quasi-cell-complex is an extension of cell-complex with inclusion topology supported. QQ-Complex is an NMB representation, in which a new topological entity—embedder is created for inclusion topology and zone/disk is adopted to capture the complete adjacencies around a vertex. Thus, QQ-Complex allows full adjacencies, incidence-ordering, and inclusion relationships to be derived, and the efficiency of most basic queries is several times faster than most state-of-the-art NMB representations, without increasing storage. Additionally, the benefits of inclusion topology for shape modeling and feature modeling are explored.

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► Inclusion topology is introduced for non-manifold BB-Reps for the first time.
► The quasi-cell-complex mathematical model is proposed to support inclusion topology.
► QQ-Complex is a new data structure to represent a valid quasi-cell-complex model.
► QQ-Complex allows full adjacency, ordering, and inclusion to be derived.
► QQ-Complex is two times faster than state-of-the-art non-manifold B-rep.