On Planar Polynomial Geometric Interpolation

12/02/2020

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by   Jernej Kozak, et al.

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In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a certain discrete sense. This way the Höllig-Koch conjecture on the existence and the approximation order is confirmed in the planar case for parametric polynomial curves of any degree.