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Algebraic-Trigonometric Pythagorean-Hodograph space curves

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Abstract

We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition for this new class of curves, their quaternion representation is introduced and the fundamental properties are discussed. Then, as previously done with their quintic polynomial counterpart, a constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided. Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynomial PH curves.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via R. Cozzi 55, 20125, Milano, Italy

    Lucia Romani

  2. via S. Martino 93, 22066, Mariano Comense (CO), Italy

    Francesca Montagner

Authors
  1. Lucia Romani
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  2. Francesca Montagner
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Correspondence to Lucia Romani.

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Communicated by: Larry L. Schumaker

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Romani, L., Montagner, F. Algebraic-Trigonometric Pythagorean-Hodograph space curves. Adv Comput Math 45, 75–98 (2019). https://doi.org/10.1007/s10444-018-9606-8

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  • DOI: https://doi.org/10.1007/s10444-018-9606-8

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