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In the paper the problem of geometric interpolation of planar data by parametric polynomial curves is revisited. The conjecture that a paramet- ric polynomial curve of degreen can interpolate 2n given points in R2 is conflrmed for n • 5 under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the op- timal order 2n can be achieved as soon as the interpolating curve exists.

On geometric interpolation by planar parametric polynomial curves