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http://dx.doi.org/10.4134/JKMS.j180433

C1 HERMITE INTERPOLATION WITH MPH CURVES USING PH-MPH TRANSITIVE MAPPINGS  

Kim, Gwangil (Department of Mathematics and RINS College of Natural Science GyeongSang National University)
Kong, Jae Hoon (Department of Mathematics GyeongSang National University)
Lee, Hyun Chol (Department of Mathematics GyeongSang National University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 805-823 More about this Journal
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;
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