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Approximate Implicitization of Space Curves and of Surfaces of Revolution

In: Geometric Modeling and Algebraic Geometry

Author

Listed:
  • Mohamed Shalaby

    (Johannes Kepler University, Institute of Applied Geometry)

  • Bert Jüttler

    (Johannes Kepler University, Institute of Applied Geometry)

Abstract

We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space curves, which are described as the intersection of two implicitly defined surfaces, we show how to generate an approximately orthogonalized implicit representation. In the case of surfaces of revolution, we address the problem of avoiding unwanted branches and singular points in the region of interest.

Suggested Citation

  • Mohamed Shalaby & Bert Jüttler, 2008. "Approximate Implicitization of Space Curves and of Surfaces of Revolution," Springer Books, in: Bert Jüttler & Ragni Piene (ed.), Geometric Modeling and Algebraic Geometry, chapter 12, pages 215-227, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-72185-7_12
    DOI: 10.1007/978-3-540-72185-7_12
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