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Using Line Congruences for Parameterizing Special Algebraic Surfaces

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Mathematics of Surfaces

Part of the book series: Lecture Notes in Computer Science ((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).

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Authors and Affiliations

  1. Dept. of Applied Geometry, Johannes Kepler University, Altenberger Str. 69, 4040, Linz

    Bert Jüttler & Katharina Rittenschober

Authors
  1. Bert Jüttler
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  2. Katharina Rittenschober
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, P.O. Box, LS2 9JT, Leeds, UK

    Michael J. Wilson

  2. School of Computer Science, Cardiff University, Wales, UK

    Ralph R. Martin

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Jüttler, B., Rittenschober, K. (2003). Using Line Congruences for Parameterizing Special Algebraic Surfaces. In: Wilson, M.J., Martin, R.R. (eds) Mathematics of Surfaces. Lecture Notes in Computer Science, vol 2768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39422-8_16

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  • DOI: https://doi.org/10.1007/978-3-540-39422-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20053-6

  • Online ISBN: 978-3-540-39422-8

  • eBook Packages: Springer Book Archive

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