Algorithm 1020

swMATH ID: 41905
Software Authors: Speleers, Hendrik
Description: Algorithm 1020: computation of multi-degree Tchebycheffian B-splines. Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab. The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.
Homepage: https://dl.acm.org/doi/10.1145/3478686
Keywords: Tchebycheffian splines; multi-degree splines; B-splines; extraction operator; constant-coefficient linear differential operators
Related Software: Algorithm 999
Cited in: 1 Publication

Cited by 1 Author

1 Speleers, Hendrik

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