research-article

Algorithm 999: Computation of Multi-Degree B-Splines

Author:

Hendrik SpeleersAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 45, Issue 4

Article No.: 43, Pages 1 - 15

https://doi.org/10.1145/3321514

Published: 09 December 2019 Publication History

Abstract

Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines with similar properties to standard B-splines. These basis functions are called multi-degree B-splines (or MDB-splines). The construction relies on an extraction operator that represents all MDB-splines as linear combinations of local B-splines of different degrees. This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context of multi-degree splines. A MATLAB implementation is provided to illustrate the computation and use of MDB-splines.

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Software for Computation of Multi-Degree B-Splines

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References

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https://doi.org/10.1016/j.matcom.2024.05.011
Ma XShen W(2023)Generalized de Boor–Cox Formulas and Pyramids for Multi-Degree Spline Basis FunctionsMathematics10.3390/math1102036711:2(367)Online publication date: 10-Jan-2023
https://doi.org/10.3390/math11020367
Manni CSande ESpeleers H(2023)Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problemsComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2023.116314417(116314)Online publication date: Dec-2023
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Index Terms

Algorithm 999: Computation of Multi-Degree B-Splines
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 45, Issue 4

December 2019

207 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3375544

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Copyright © 2019 ACM.

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Association for Computing Machinery

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Publication History

Published: 09 December 2019

Accepted: 01 March 2019

Revised: 01 December 2018

Received: 01 January 2018

Published in TOMS Volume 45, Issue 4

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Ministero dellðIstruzione, dellðUniversità e della Ricerca
Università degli Studi di Roma Tor Vergata

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Cited By

Boushabi MEddargani SIbáñez MLamnii A(2024)Normalized B-spline-like representation for low-degree Hermite osculatory interpolation problemsMathematics and Computers in Simulation10.1016/j.matcom.2024.05.011225(98-110)Online publication date: Dec-2024
https://doi.org/10.1016/j.matcom.2024.05.011
Ma XShen W(2023)Generalized de Boor–Cox Formulas and Pyramids for Multi-Degree Spline Basis FunctionsMathematics10.3390/math1102036711:2(367)Online publication date: 10-Jan-2023
https://doi.org/10.3390/math11020367
Manni CSande ESpeleers H(2023)Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problemsComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2023.116314417(116314)Online publication date: Dec-2023
https://doi.org/10.1016/j.cma.2023.116314
Takacs TToshniwal D(2023) Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems Computer Methods in Applied Mechanics and Engineering10.1016/j.cma.2022.115640403(115640)Online publication date: Jan-2023
https://doi.org/10.1016/j.cma.2022.115640
Grošelj JSpeleers H(2023)Extraction and application of super-smooth cubic B-splines over triangulationsComputer Aided Geometric Design10.1016/j.cagd.2023.102194103(102194)Online publication date: Jul-2023
https://doi.org/10.1016/j.cagd.2023.102194
Xiao ZShen W(2023)An Efficient Algorithm for Degree Reduction of MD-SplinesAdvances in Computer Graphics10.1007/978-3-031-50078-7_1(3-14)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-50078-7_1
Speleers H(2022)Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-SplinesACM Transactions on Mathematical Software10.1145/347868648:1(1-31)Online publication date: 16-Feb-2022
https://dl.acm.org/doi/10.1145/3478686
Thomas DEngvall LSchmidt STew KScott M(2022)U-splines: Splines over unstructured meshesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2022.115515401(115515)Online publication date: Dec-2022
https://doi.org/10.1016/j.cma.2022.115515
Manni CSande ESpeleers H(2022)Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizationsComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2021.114260389(114260)Online publication date: Mar-2022
https://doi.org/10.1016/j.cma.2021.114260
Toshniwal D(2022)Quadratic splines on quad-tri meshes: Construction and an application to simulations on watertight reconstructions of trimmed surfacesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2021.114174388(114174)Online publication date: Jan-2022
https://doi.org/10.1016/j.cma.2021.114174
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