A kind of rational cubic spline with parameters is constructed, which is the extension of the standard cubic spline. Selecting proper parameters, the given spline can more approximate the interpolated curve than the standard cubic spline. The shape of the interpolating curve can be adjusted by parameters locally, which is convenient for user to restrict the interpolating curves. How to constrain the interpolating curve to be in the given region is studied. The sufficient conditions for the interpolating curves to be above, below or between the given piecewise quadratic curves are derived. Two examples are given in this paper.

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