Blended Hermite interpolants Original Research Article

In (Röschel, l997) B-spline technique was used for blending of Lagrange interpolants. In this paper we generalize this idea replacing Lagrange by Hermite interpolants. The generated subspline b(t) interpolates the Hermite input data consisting of parameter values ti and corresponding derivatives ai,j, j=0,…,αi−1, and is called blended Hermite interpolant (BHI). It has local control, is connected in affinely invariant way with the input and consists of integral (polynomial) segments of degree 2·k−1, where k−1⩾max{αi}−1 denotes the degree of the B-spline basis functions used for the blending. This method automatically generates one of the possible interpolating subsplines of class Ck−1 with the advantage that no additional input data is necessary.