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.
Speleers, H. (2019). Algorithm 999: Computation of multi-degree B-splines. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 45(4), 1-15 [10.1145/3321514].
Algorithm 999: Computation of multi-degree B-splines
Speleers H.
2019-12-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
