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Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning

Author

Listed:
  • Kinga Kruppa

    (Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary)

  • Roland Kunkli

    (Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary)

  • Miklós Hoffmann

    (Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary
    Institute of Mathematics and Informatics, Eszterházy Károly University, 3300 Eger, Hungary)

Abstract

Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the R 2 , 1 Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in R 2 , 1 that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently.

Suggested Citation

  • Kinga Kruppa & Roland Kunkli & Miklós Hoffmann, 2021. "Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning," Mathematics, MDPI, vol. 9(8), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:843-:d:534928
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    References listed on IDEAS

    as
    1. Li, Shi & Chen, Guang & Wang, Yigang, 2019. "An improved rational cubic clipping method for computing real roots of a polynomial," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 207-213.
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