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)


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).


Rational Curf Conic Section Quadric Surface Pythagorean Hodograph Focal Line 
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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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