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Using Line Congruences for Parameterizing Special Algebraic Surfaces

  • Bert Jüttler
  • Katharina Rittenschober
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

Surfaces in line space are called line congruences. We consider several special line congruences forming a fibration of the three–dimensional space. These line congruences correspond to certain special algebraic surfaces. Using rational mappings associated with the line congruences, it is possible to generate rational curves and surfaces on them. This approach is demonstrated for quadric surfaces, cubic ruled surfaces, and for Veronese surfaces and their images in three–dimensional space (quadratic triangular Bézier surfaces).

Keywords

Rational Curf Conic Section Quadric Surface Pythagorean Hodograph Focal Line 
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 2003

Authors and Affiliations

  • Bert Jüttler
    • 1
  • Katharina Rittenschober
    • 1
  1. 1.Dept. of Applied GeometryJohannes Kepler UniversityLinz

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