Orthogonal Cubic B-spline Interpolation Method Based on Energy Method

A new orthogonal cubic B-spline base function is constructed for the interpolation of equidistant points using the orthogonal property of the exponential function group. A general formula to calculate the coefficients of the orthogonal B-spline interpolation base functions is expressed in explicit formulation. The orthogonal B-spline interpolation method can be solved by defining the additional nodes at both ends of interpolation region without giving derivative boundary conditions. The energy potential function for curve is used in interpolation method to obtain the end add-node value. The interpolation curve is smooth. The method decouples the interpolation coefficients and it can be solved by Fourier transform and easy to parallel computation.