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Self-Intersection Problems and Approximate Implicitization

In: Computational Methods for Algebraic Spline Surfaces

Author

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  • Jan B. Thomassen

    (University of Oslo, Centre of Mathematics for Applications
    SINTEF Applied Mathematics)

Abstract

We discuss how approximate implicit representations of parametric curves and surfaces may be used in algorithms for finding self-intersections. We first recall how approximate implicitization can be formulated as a linear algebra problem, which may be solved by an SVD. We then sketch a self-intersection algorithm, and discuss two important problems we are faced with in implementing this algorithm: What algebraic degree to choose for the approximate implicit representation, and — for surfaces — how to find self-intersection curves, as opposed to just points.

Suggested Citation

  • Jan B. Thomassen, 2005. "Self-Intersection Problems and Approximate Implicitization," Springer Books, in: Computational Methods for Algebraic Spline Surfaces, pages 155-170, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27157-4_11
    DOI: 10.1007/3-540-27157-0_11
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