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Advances in Computational Mathematics

, Volume 45, Issue 1, pp 75–98 | Cite as

Algebraic-Trigonometric Pythagorean-Hodograph space curves

  • Lucia RomaniEmail author
  • Francesca Montagner
Article

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.

Keywords

Space curve Pythagorean-Hodograph Algebraic-Trigonometric Bézier basis Arc length First-order Hermite interpolation 

Mathematics Subject Classification (2010)

65D17 65D05 41A30 41A05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly
  2. 2.Mariano Comense (CO)Italy

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