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.

Keywords: $h$-refinement, Trimmed model, Volume completion

Yang Song ^{1};
Elaine Cohen ^{1}

@article{SMAI-JCM_2019__S5__3_0, author = {Yang Song and Elaine Cohen}, title = {Refinement for a {Hybrid} {Boundary} {Representation} and its {Hybrid} {Volume} {Completion}}, journal = {The SMAI Journal of computational mathematics}, pages = {3--25}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {S5}, year = {2019}, doi = {10.5802/smai-jcm.49}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.49/} }

TY - JOUR AU - Yang Song AU - Elaine Cohen TI - Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion JO - The SMAI Journal of computational mathematics PY - 2019 SP - 3 EP - 25 VL - S5 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.49/ DO - 10.5802/smai-jcm.49 LA - en ID - SMAI-JCM_2019__S5__3_0 ER -

%0 Journal Article %A Yang Song %A Elaine Cohen %T Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion %J The SMAI Journal of computational mathematics %D 2019 %P 3-25 %V S5 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.49/ %R 10.5802/smai-jcm.49 %G en %F SMAI-JCM_2019__S5__3_0

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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