Algorithms and data structures for Cs-smooth RMB-splines of degree 2s + 1

The simple mesh refinement algorithm of Groiss et al. (2023) generates T-meshes admitting Reachable Minimally supported (RM) B-splines that possess the property of local linear independence and form a non-negative partition of unity. The construction was first presented for the bilinear case and has...

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Vydáno v:Computer aided geometric design Ročník 114
Hlavní autoři: Pan, Maodong, Zou, Ruijie, Jüttler, Bert
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2024
Témata:
Binary tree data structure
Evaluation of RMB-spline surfaces
Local refinement
RMB-splines
RMB-splines
Local refinement
Binary tree data structure
Evaluation of RMB-spline surfaces
ISSN:0167-8396
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Shrnutí:The simple mesh refinement algorithm of Groiss et al. (2023) generates T-meshes admitting Reachable Minimally supported (RM) B-splines that possess the property of local linear independence and form a non-negative partition of unity. The construction was first presented for the bilinear case and has later been extended to Cs-smooth splines of degree p=2s+1. The present paper is devoted to algorithms and data structures for RMB-splines. We prove that the memory consumption of the data structures for representing a T-mesh and the associated RMB-splines is linear with respect to the mesh size, and we describe the details of the underlying refinement algorithm. Moreover, we introduce a novel evaluation algorithm for RMB-spline surfaces, which is based solely on repeated convex combinations of the control points, thereby generalizing de Boor's algorithm for tensor-product splines. Numerical experiments are included to demonstrate the advantageous behavior of the proposed data structures and algorithms with respect to their efficiency. We observe that the total computational time (which includes also error estimation and spline coefficient computation) scales roughly linearly with the number of degrees of freedom for the meshes considered. •Efficient data structures are proposed to allow manipulating RMB-splines.•A practical refinement algorithm to construct RMB-splines is described.•Analysis of memory consumption of data structures is provided.•A novel algorithm for evaluating RMB-spline surfaces is also presented.
ISSN:0167-8396
DOI:10.1016/j.cagd.2024.102389