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Optimal interpolation with spatial rational Pythagorean hodograph curves

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  • Schröcker, Hans-Peter
  • Šír, Zbyněk

Abstract

Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G1, C1, C2, C1/G2) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.

Suggested Citation

  • Schröcker, Hans-Peter & Šír, Zbyněk, 2023. "Optimal interpolation with spatial rational Pythagorean hodograph curves," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323003831
    DOI: 10.1016/j.amc.2023.128214
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    References listed on IDEAS

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    1. Knez, Marjeta & Pelosi, Francesca & Sampoli, Maria Lucia, 2022. "Construction of G2 planar Hermite interpolants with prescribed arc lengths," Applied Mathematics and Computation, Elsevier, vol. 426(C).
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