High accurate rational approximation of parametric curves
The aim of this paper is to give a more precise definition of the notion of approximation order and then to prove that order eight can be attained by rational cubics instead of polynomial ones. This way a third order contact can be attained at both endpoints. It is shown that this rises the approximation order up to eight. A detailed analysis of the asymptotic behavior (as the segment's length tends to zero) is given. It leads to a purely geometric condition for the existence of that rational cubic approximant.
scientific article; zbMATH DE number 431240