On geometric interpolation by planar parametric polynomial curves

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