Point control of rational interpolating curves using parameters

A rational cubic spline, a kind of smooth interpolator with cubic denominator, is constructed using function values and first derivatives of a function. In order to meet the needs of practical design, a new method of value control, inflection-point control and convexity control of the interpolation at a point is employed to control the shapes of curves. The advantage of this method is that it can be used to modify the local shape of an interpolating curve simply through the selection of suitable parameters, and numerical examples are presented to show the performance of the method. Also when the interpolated function f(t)f(t) is in C2[t0,tn]C2[t0,tn], the error estimate of this interpolation is obtained.