Computation of multi-degree B-splines
This work provides a practical tool for researchers and engineers using splines in geometric modeling and numerical analysis, but the contribution is incremental as it extends existing B-spline techniques.
The paper presents a method to construct basis functions for multi-degree splines, called MDB-splines, using an extraction operator that combines local B-splines of different degrees, enabling efficient evaluation and refinement.
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.