Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2019; 56(3): 805-823

Online first article November 21, 2018      Printed May 1, 2019

https://doi.org/10.4134/JKMS.j180433

Copyright © The Korean Mathematical Society.

$C^1$ Hermite interpolation with MPH curves using PH-MPH transitive mappings

Gwangil Kim, Jae Hoon Kong, Hyun Chol Lee

GyeongSang National University; GyeongSang National University; GyeongSang National University

Abstract

We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in $\mathbb R^{2,1}$, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve $C^1$ Hermite interpolation problems in $\mathbb R^{2,1}$, for an admissible $C^1$ Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.

Keywords: Minkowski Pythagorean-hodograph curve, PH-MPH transitive mapping, MPH-preserving mapping, $C^1$ Hermite data-set, $C^1$ Hermite interpolation

MSC numbers: Primary 65D17, 65D18, 68U05

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning(NRF-2017R1E1A1A03070952).

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