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Design of \(C^2\) algebraic-trigonometric pythagorean hodograph splines with shape parameters

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Abstract

In this paper, we construct \(C^2\) Algebraic-Trigonometric Pythagorean Hodograph (ATPH) splines by solving a non-linear system of equations in complex variables. We compare these splines, which depend on several shape parameters, with their polynomial PH counterpart as well as with the well-known \(C^2\) cubic B-splines. We finally present criteria for choosing the free shape parameters based on the minimization of certain fairness functionals.

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Acknowledgements

We acknowledge financial support by ECOS Nord through Grant no. C13M01. M. Paluszny and M. Lentini were also supported by the project COLCIENCIAS 712.

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Authors and Affiliations

  1. UNIV Lille Nord de France, UVHC, LAMAV, Fédération de Recherche (research federation) No. 2956, 59313, Valenciennes, France

    C. González

  2. Escuela de Matemáticas, Universidad Nacional de Colombia, sede Medellín, Calle 59A No. 63-20, Medellín, Colombia

    G. Albrecht, M. Paluszny & M. Lentini

Authors
  1. C. González
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  2. G. Albrecht
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  3. M. Paluszny
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  4. M. Lentini
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Correspondence to C. González.

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Communicated by Armin Iske.

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González, C., Albrecht, G., Paluszny, M. et al. Design of \(C^2\) algebraic-trigonometric pythagorean hodograph splines with shape parameters. Comp. Appl. Math. 37, 1472–1495 (2018). https://doi.org/10.1007/s40314-016-0404-y

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