Point control of the interpolating curve with a rational cubic spline

A rational cubic spline, a kind of smoothness interpolation with quadratic denominator, is constructed using the values of a function only. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of curves. The method of value control, inflection-point control and convexity control of the interpolation at a point is also developed. The advantage of this new control method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters simply.