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Fairness Criteria for Algebraic Curves

In: Geometric Modelling

Author

Listed:
  • Pavel Chalmovianský

    (Johannes Kepler University, Special Research Programme SFB F013)

  • Bert Jüttler

    (Johannes Kepler University, Institute of Applied Geometry)

Abstract

We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we take certain feasibility criteria for the algebraic curve segment into account. We describe a computational technique for the variational design of algebraic curves, using an SQP (sequential quadratic programming) — type method for constrained optimization. As demonstrated in this paper, the powerful techniques of variational design can be used not only for parametric representations, but also for curves in implicit form.

Suggested Citation

  • Pavel Chalmovianský & Bert Jüttler, 2004. "Fairness Criteria for Algebraic Curves," Springer Books, in: Stefanie Hahmann & Guido Brunnett & Gerald Farin & Ron Goldman (ed.), Geometric Modelling, pages 41-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0587-0_4
    DOI: 10.1007/978-3-7091-0587-0_4
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