$C^1$ Hermite interpolation with MPH curves using PH-MPH transitive mappings
J. Korean Math. Soc.
Published online 2018 Nov 21
Gwangil Kim, Jae Hoon Kong, and Hyun Chol Lee
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 the junction method can obtain interpolants for
at least some inadmissible data-sets.
Keywords : Minkowski Pythagorean-hodograph curve, PH-MPH transitive mapping, MPH-preserving mapping, $C^1$ Hermite data-set, $C^1$ Hermite interpolation
MSC numbers : 65D17, 65D18, 68U05
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