On a Generalization of Cubic Spline Interpolation

Abstract—Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arbitrary two nodes or second derivatives of arbitrary two node are given. At last, these calculation methods are illustrated through examples. Index Terms—cubic spline function, boundary, clamped spline, first derivative, second derivative I.