Fast and stable evaluation of box-splines via the BB-form

DOI10.1007/s11075-008-9231-6zbMath1162.65005OpenAlexW2007587494MaRDI QIDQ1014371

Jörg Peters, Minho Kim

Publication date: 27 April 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9231-6

zbMATH Keywords

algorithmnumerical examplesexact evaluationrational coefficientsface-centered cubic latticebox-splineSplineBernstein-Bézier-formray-tracing package

Mathematics Subject Classification ID

Numerical computation using splines (65D07)

Related Items (14)

High-quality topological structure extraction of volumetric data on \(C^2\)-continuous framework ⋮ Characterization of bivariate hierarchical quartic box splines on a three-directional grid ⋮ A closed PP form of box splines via Green's function decomposition ⋮ Volumetric data modeling and analysis based on seven-directional box spline ⋮ A practical Box Spline compendium ⋮ Near-best \(C^2\) quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains ⋮ Analytic evaluation of the FCC Voronoi-splines ⋮ Numerical integration based on trivariate \(C ^{2}\) quartic spline quasi-interpolants ⋮ Quasi-interpolation operators based on the trivariate seven-direction \(C^2\) quartic box spline ⋮ Fast and stable evaluation of splines and their derivatives generated by the seven-direction quartic box-spline ⋮ Symmetric box-splines on root lattices ⋮ On the construction of trivariate near-best quasi-interpolants based on \(C^2\) quartic splines on type-6 tetrahedral partitions ⋮ Completeness characterization of type-I box splines ⋮ Inner products of box splines and their derivatives

Uses Software

• Matlab
• MDDS
• na11
• na2
• PovRay

Cites Work

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• The mixed directional difference-summation algorithm for generating the Bézier net of a trivariate four-direction box-spline
• Algorithms for cardinal interpolation using box splines and radial basis functions
• Fortran subroutines for B-nets of box splines on three- and four- directional meshes
• Algorithms for generating B-nets and graphically displaying spline surfaces on three- and four-directional meshes
• A note on optimal unimodular lattices
• Box splines
• On the evaluation of box splines
• Stable evaluation of box-splines
• Stationary subdivision
• On Lattices Admitting Unique Lagrange Interpolations
• On a Class of Finite Elements Generated by Lagrange Interpolation

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