On geometric interpolation by planar parametric polynomial curves

Jaklič, Gašper; Kozak, Jernej; Krajnc, Marjeta; Žagar, Emil

doi:10.1090/S0025-5718-07-01988-6

On geometric interpolation by planar parametric polynomial curves
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by Gašper Jaklič, Jernej Kozak, Marjeta Krajnc and Emil Žagar PDF

Math. Comp. 76 (2007), 1981-1993 Request permission

Abstract:

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 $\le n$ can interpolate $2 n$ given points in $\mathbb {R}^2$ is confirmed for $n \le 5$ under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order $2 n$ can be achieved as soon as the interpolating curve exists.

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