A method of shape control of curve design

Constraining an interpolating curve to be bounded in a given region is an important task in curve design. In (Qi Duan et al., 1999) the rational cubic spline with a linear denominator has been used to control the interpolating curves to be bounded in the given region, but it does not work in some cases. This paper deals with the weighted rational cubic spline with a linear denominator for this kind of constraint, the sufficient condition for controlling the interpolating curves to be bounded in the given region are derived. An example is given which shows that the constraint which cannot be done by the rational spline defined in (Qi Duan et al., 1999) could be achieved by the weighted rational spline.