A blending interpolator with value control and minimal strain energy

A weighted blending rational interpolator, a kind of smooth interpolator, is constructed using the rational cubic spline with linear denominator and the standard Hermite interpolator. In order to meet the needs of practical design, a new method of value control is employed to control the shape of curves, and the optimal solution for the value control equation with minimal strain energy is derived. The advantage of the method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters and weight coefficients simply. Also when the weight coefficient is in [0,1], the error estimation formula of this interpolator is obtained.