Geometric Hermite interpolation with Tschirnhausen cubics
The authors consider the following Hermite interpolation problem: Given two distinct points in the plane, find a function that passes through these points and matches the (unit) tangent vectors there. The uniquely determined Tschirnhausen cubic that solves this Hermite problem is given explicitly. This solution is used to create a \(G^1\)-spline by pasting together segments of Tschirnhausen cubics. Moreover it is shown that if the Hermite data come from a sufficiently smooth function, then the approximation order of the Tschirnhausen cubic is four. The results are illustrated by a numerical example.
scientific article; zbMATH DE number 1043289