Local point control of a new rational quartic interpolating spline

A new rational quartic interpolating spline based on function values is constructed. The rational quartic interpolating spline curves have simple and explicit representation with parameters. The monotonicity-preserving, C
²
continuity and boundedness of rational quartic interpolating spline curves are confirmed. Function value control and derivative value control of rational quartic interpolation spline are given respectively. The advantage of these control methods is that they can be applied to modifying the local shape of interpolating curve only by selecting suitable parameters according to the practical requirements.