$C^2$ Continuous Quartic Hermite Spline Curves with Shape Parameters

Abstract

In order to relieve the deficiency of the usual cubic Hermite spline curves, the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed. The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and $C^2$ continuity by the shape parameters when the interpolation conditions are fixed.