A class of quintic Hermite interpolation curve and the free parameters selection

Abstract

The classical C² quintic Hermite interpolation curve not only needs the positions and derivatives but also needs the second-order derivatives as input. For most applications, one has to estimate the second-order derivatives in advance. In addition, the classical C² quintic Hermite interpolation curve is unique once the input data are fixed, the shape of the curve will not be modified when the interpolation is poor. In this paper, a class of C² quintic Hermite interpolation curve with free parameters that only needs the points and tangent vectors as input is presented. Due to the self-contained free parameters, the shapes of the proposed interpolation curve can be controlled. Moreover, the free parameters can be chosen reasonably so that the interpolation curve can meet some certain geometric requirements. Some numerical experiments show the feasibility of the proposed methods.