N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS 论文

摘要

The scope of this work is Geometric Modeling. We study the representation and the construction of subdivisions of quasi-manifolds, using a topology-based approach. Quasi-manifolds are here defined as a subset of pseudo-manifolds, which are well-known objects in Algebraic Topology. N-dimensional generalized maps (resp. n-dimensional maps) are combinatorial models defined for representing the topology of subdivisions of orientable or non-orientable quasi-manifolds with or without boundaries (resp. orientable quasi-manifolds without boundaries). In this paper, we define the models, main related notions and properties as cells, boundaries, duality, orientability, Euler characteristic. Basic operations are proposed for handling the models. We also show the correspondence between the combinatorial models and combinatorial cellular quasi-manifolds, here defined as combinatorial simplicial quasi-manifolds to which a structure into cells is added. This correspondence establishes that the models are rigorous and unambiguous ones. Moreover, the definitions of the models and the related notions and operations are quite simple, and they can be easily implemented and used in geometric modellers.