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On G1 and G2 Hermite interpolation by spatial Algebraic-Trigonometric Pythagorean Hodograph curves with polynomial parametric speed

Author

Listed:
  • Bay, Thierry
  • Cattiaux-Huillard, Isabelle
  • Romani, Lucia
  • Saini, Laura

Abstract

In this paper we focus on the class of Algebraic-Trigonometric Pythagorean Hodograph curves (ATPH for short) that is characterized by a purely polynomial parametric speed. Within such a class of ATPH curves, we first construct interpolants to spatial G1 Hermite data equipped with curvature values. With respect to the solutions proposed in [24], the G1 Hermite ATPH interpolants we here propose are characterized by C0- and C1-continuous curvature plots. Secondly, we investigate the existence of ATPH interpolants to spatial G2 Hermite data and show that solutions exist under some restrictions on the Hermite input data.

Suggested Citation

  • Bay, Thierry & Cattiaux-Huillard, Isabelle & Romani, Lucia & Saini, Laura, 2023. "On G1 and G2 Hermite interpolation by spatial Algebraic-Trigonometric Pythagorean Hodograph curves with polynomial parametric speed," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004095
    DOI: 10.1016/j.amc.2023.128240
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    Keywords

    Algebraic-Trigonometric curves; Pythagorean Hodograph; Polynomial parametric speed; G1 and G2 Hermite interpolation;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services

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