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Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion
Yang Song1; Elaine Cohen1
1 School of Computing, University of Utah, Salt Lake City, UT, USA
The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 3-25.

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 (HB-Rep) 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 HB- and 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.

Published online:
DOI: 10.5802/smai-jcm.49
Classification: 65D17
Keywords: $h$-refinement, Trimmed model, Volume completion

Yang Song 1; Elaine Cohen 1

1 School of Computing, University of Utah, Salt Lake City, UT, USA
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yang Song; Elaine Cohen. Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion. The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 3-25. doi : 10.5802/smai-jcm.49. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.49/

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