Constraining interpolation curves to be in the given region is an important problem in curve design. A kind of weighted rational cubic spline interpolation is constructed by using the rational cubic spline with quadratic polynomial denominators and the rational cubic spline based on function values.Suffcient conditions for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves, and suffcient and necessary conditions for the interpolating curves to be above, below ...