Algorithms for Space Mapping Method on Spline Spaces over Modified Hierarchical T-Meshes

Jingjing Liu, Li Zhang () and Weihong Zhang
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Jingjing Liu: School of Mathematics and Statistics, Hefei Normal University, Heifei 230601, China
Li Zhang: School of Mathematics, Hefei University of Technology, Heifei 230000, China
Weihong Zhang: School of Mathematics and Statistics, Hefei Normal University, Heifei 230601, China

Mathematics, 2022, vol. 10, issue 20, 1-26

Abstract: The space-mapping method provides a novel method for dimension formulae explanation and basis construction for the spline space over hierarchical T-meshes. By the space-mapping method, we provide a unique basis construction framework that incorporates basis modification of the spline space over modified hierarchical T-meshes. The subdivision rules on the modified hierarchical T-meshes are given to prevent the redundant edges that exist on hierarchical T-meshes. In the basis construction framework, we describe the spline-modification mechanism over the modified hierarchical T-mesh when the cells of the corresponding crossing vertex relationship graph (CVR graph) are adjusted. We provide the framework’s algorithms for basis construction and modification. Moreover, we discuss the application of the splines that are constructed by the framework to surface reconstruction with adaptive refinement. In comparison to splines over hierarchical T-meshes, the modified hierarchical T-meshes have fewer cells subdivided when achieving similar accuracy.

Keywords: modified hierarchical T-meshes; space mapping method; subdivision rules; basis modification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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