The NURBS Book pp 141-228 | Cite as

Fundamental Geometric Algorithms

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


In this chapter we present five tools which are fundamental in the implementation of B-spline curves and surfaces; these are knot insertion, knot refinement, knot removal, degree elevation, and degree reduction. We devote a section to each topic, and the layout of each section is roughly:
  • a statement of the problem (for curves);

  • a list of applications;

  • clarification of the problem and solution approaches (curves);

  • a list of references where more rigorous derivations and proofs can be found;

  • the solution formulas (curves);

  • worked examples (curves);

  • computer algorithms;

  • examples of applications;

  • the solution for surfaces, and outlines of the surface algorithms.


Control Point Spline Curve Degree Reduction NURBS Curve Bezier Curve 
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.


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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

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