C-1 HERMITE INTERPOLATION WITH MPH CURVES USING PH-MPH TRANSITIVE MAPPINGS

초록

We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in R-2,R-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 R-2,R-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.

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