Modeling and manipulating cell complexes in two, three and higher dimensions

Abstract

© 2012, Springer Science+Business Media Dordrecht. Cell complexes have been used in geometric and solid modeling as a discretization of the boundary of 3D shapes. Also, operators for manipulating 3D shapes have been proposed. Here, we review first the work on data structures for encoding cell complexes in two, three and arbitrary dimensions, and we develop a taxonomy for such data structures. We review and analyze basic modeling operators for manipulating complexes representing both manifold and non-manifold shapes. These operators either preserve the topology of the cell complex, or they modify it in a controlled way. We conclude with a discussion of some open issues and directions for future research.