Algorithm 999 swMATH ID: 36032 Software Authors: Speleers, Hendrik Description: Algorithm 999: Computation of multi-degree B-splines. 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. Homepage: https://dl.acm.org/doi/10.1145/3321514 Keywords: B-splines; extraction operator; MDB-splines; multi-degree splines Related Software: mctoolbox; Algorithm 1020; GitHub; Macaulay2; Matlab Cited in: 10 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 999: Computation of multi-degree B-splines. Zbl 1486.65019Speleers, Hendrik 2019 all top 5 Cited by 9 Authors 6 Speleers, Hendrik 4 Hughes, Thomas J. R. 4 Manni, Carla 4 Toshniwal, Deepesh 2 Beccari, Carolina Vittoria 2 Casciola, Giulio 2 Hiemstra, René R. 2 Sande, Espen 1 Mourrain, Bernard all top 5 Cited in 7 Serials 2 Computer Methods in Applied Mechanics and Engineering 2 ACM Transactions on Mathematical Software 2 Journal of Computational and Applied Mathematics 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Computer Aided Geometric Design 1 Advances in Computational Mathematics all top 5 Cited in 6 Fields 10 Numerical analysis (65-XX) 6 Approximations and expansions (41-XX) 2 Computer science (68-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year