$C^2$ Continuous Quartic Hermite Spline Curves with Shape Parameters (Communications in Mathematical Research, 2019)
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 thiswork. The interpolation error and estimator of the quartic Hermite spline curves aregiven. 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 localor global shape adjustment and $C^2$ continuity by the shape parameters when theinterpolation conditions are fixed.
Keywords: Hermite spline curve; interpolation curve; shape adjustment; $C^2$ continuous