$C^1$ Hermite interpolation with MPH curves using PH-MPH transitive mappings
J. Korean Math. Soc. 2019 Vol. 56, No. 3, 805-823
https://doi.org/10.4134/JKMS.j180433
Published online May 1, 2019
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
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