Topological modifications of hexahedral meshes via sheet operations: a theoretical study

Recently there has been a renewed interest in performing topological modifications on hexahedral meshes to enable clean up, mesh improvement, generation of more complex hexahedral topologies, and a deepened understanding of methods for producing hexahedral topologies in increasingly complex geometries. Additionally, generation of all-hexahedral topologies in arbitrary models remains an open-problem in the computational geometry community. In this paper we provide surveys of important research efforts in local hexahedral topology modification, and provide some formalization of many of these methods. We also provide some additional proofs giving credance to the community held notion that these topology modifications are feasible despite the historic difficulty in developing the methodologies for performing the modifications. Additionally, some formalization of modification operations will be provided for hexahedral sheet-based methods and a demonstration of how these operations are related to the atomic operations proposed by Tautges et al.