B-Spline Basis Functions

  • Les Piegl
  • Wayne Tiller
Part of the Monographs in Visual Communications book series (VISUALCOMM)


Curves consisting of just one polynomial or rational segment are often inadequate. Their shortcomings are:
  • a high degree is required in order to satisfy a large number of constraints; e.g., (n − 1)-degree is needed to pass a polynomial Bézier curve through n data points. However, high degree curves are inefficient to process and are numerically unstable;

  • a high degree is required to accurately fit some complex shapes;

  • single-segment curves (surfaces) are not well-suited to interactive shape design; although Bézier curves can be shaped by means of their control points (and weights), the control is not sufficiently local.


Basis Function Control Point Bezier Curve Piecewise Polynomial Function Polynomial Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Les Piegl
    • 1
  • Wayne Tiller
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of South FloridaTampaUSA
  2. 2.GeomWare, Inc.TylerUSA

Personalised recommendations