Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion

Abstract

With the increasing need for volumetric B-spline representations and the lack of methodologies for creating semi-structured volumetric B-spline representations from B-spline Boundary Representations (B-Rep), hybrid approaches combining semi-structured volumetric B-splines and unstructured Bézier tetrahedra have been introduced, including one that transforms a trimmed B-spline B-Rep first to an untrimmed Hybrid B-Rep (HBRep) and then to a Hybrid Volume Representation (HV-Rep). Generally, the effect of h-refinement has not been considered over B-spline hybrid representations. Standard refinement approches to tensor product B-splines and subdivision of Bézier triangles and tetrahedra must be adapted to this representation. In this paper, we analyze possible types of h-refinement of the HV-Rep. The revised and trim basis functions for HBand HV-rep depend on a partition of knot intervals. Therefore, a naive h-refinement can change basis functions in unexpected ways. This paper analyzes the the effect of h-refinement in reducing error as well. Different h-refinement strategies are discussed. We demonstrate their differences and compare their respective consequential trade-offs. Recommendations are also made for different use cases. 2010 Mathematics Subject Classification. 65D17.