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.


Hull Clarification 


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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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