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C 1-Smoothing of Multipatch BEZIER Surfaces

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Geometric Modelling

Part of the book series: Computing Supplementum ((COMPUTING,volume 8))

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Abstract

Handling and modelling multipatch tensorproduct BEZIER surfaces often causes continuity problems. A method is described how to approximate a given surface in such a way that C 1-continuity at a crossing point of four surface patches can be obtained. The approximated surface uses still a BEZIER representation with the same orders as before. The idea is to choose the four BEZIER control points associated with the mixed derivatives to build a fourside on a tangent hyperbolic paraboloid. This fourside and along with it the hyperbolic paraboloid can easily be obtained by approximation, minimizing the sum of the four distance squares.

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References

  1. Boehm, W., Farin, G., Kahmann, J.: A survey of Curve and surface methods in CAGD. Computer Aided Geometric Design 1, 1–60 (1984).

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Author information

Authors and Affiliations

  1. Institut für CAD-Datenaustausch, Kastanienweg 2, D-W-6500, Mainz, Federal Republic of Germany

    W. Schwarz

Authors
  1. W. Schwarz
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Arizona State University, Tempe, USA

    G. Farin

  2. Lehrstuhl für Informatik I, Universität Würzburg, Federal Republic of Germany

    H. Noltemeier

  3. Fachbereich Informatik, Universität Kaiserslautern, Federal Republic of Germany

    H. Hagen

  4. Institut für Informatik, Universität Leipzig, Federal Republic of Germany

    W. Knödel

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© 1993 Springer-Verlag

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Schwarz, W. (1993). C 1-Smoothing of Multipatch BEZIER Surfaces. In: Farin, G., Noltemeier, H., Hagen, H., Knödel, W. (eds) Geometric Modelling. Computing Supplementum, vol 8. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6916-2_20

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  • DOI: https://doi.org/10.1007/978-3-7091-6916-2_20

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82399-6

  • Online ISBN: 978-3-7091-6916-2

  • eBook Packages: Springer Book Archive

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