Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines

  title={Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines},
  author={Hendrik Speleers},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  pages={1 - 31}
  • H. Speleers
  • Published 31 January 2021
  • Mathematics
  • ACM Transactions on Mathematical Software (TOMS)
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… 
2 Citations

C2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values

In this paper, a cubic Hermite spline interpolating scheme reproducing both linear polynomials and hyperbolic functions is considered. The interpolating scheme is mainly defined by means of integral…



Algorithm 999

  • H. Speleers
  • Computer Science
    ACM Transactions on Mathematical Software
  • 2019
This work describes a simple algorithmic construction of a set of basis functions for the space of multi-degree splines with similar properties to standard B-splines, and relies on an extraction operator that represents all MDB-spline as linear combinations of local B- splines of different degrees.

Tchebycheffian B-Splines Revisited: An Introductory Exposition

Tchebycheffian splines are smooth piecewise functions where the different pieces are drawn from extended Tchebycheff spaces. They are a natural generalization of polynomial splines and can be…

On multi-degree splines

A new approach to Tchebycheffian B-splines

Originally, Tchebycheean B-splines have been deened by generalized divided diierences. In this paper, we deene Tchebycheean B-splines by integration. Based upon this deenition, all basic algorithms…

Unified and extended form of three types of splines

The geometry of Tchebycheffian splines

  • H. Pottmann
  • Mathematics, Computer Science
    Comput. Aided Geom. Des.
  • 1993