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Computing the Topology of Three-Dimensional Algebraic Curves

In: Computational Methods for Algebraic Spline Surfaces

Author

Listed:
  • G. Gatellier

    (GALAAD, INRIA)

  • A. Labrouzy

    (GALAAD, INRIA)

  • B. Mourrain

    (GALAAD, INRIA)

  • J. P. Técourt

    (GALAAD, INRIA)

Abstract

In this paper, we present a new method for computing the topology of curves defined as the intersection of two implicit surfaces. The main ingredients are projection tools, based on resultant constructions and 0-dimensional polynomial system solvers. We describe a lifting method for points on the projection of the curve on a plane, even in the case of multiple preimages on the 3D curve. Reducing the problem to the comparison of coordinates of so-called critical points, we propose an approach which combines control and efficiency. An emphasis in this work is put on the experimental validation of this new method. Examples treated with the tools of the library axel1 (Algebraic Software-Components for gEometric modeLing) are showing the potential of such techniques.

Suggested Citation

  • G. Gatellier & A. Labrouzy & B. Mourrain & J. P. Técourt, 2005. "Computing the Topology of Three-Dimensional Algebraic Curves," Springer Books, in: Computational Methods for Algebraic Spline Surfaces, pages 27-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27157-4_3
    DOI: 10.1007/3-540-27157-0_3
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