Local shape control of the rational interpolation curves with quadratic denominator

Abstract

A rational cubic interpolating spline with quadratic denominator was constructed by Gregory and co-workers. This paper deals with the properties of the interpolation and local shape control of the interpolant curves. The methods of value control, convex control and inflection-point control of the interpolation at a point are developed. Some numerical examples are provided to illustrate these methods.

Keywords:

• rational spline
• constrained interpolation
• inflection-point control
• convex control
• value control

Acknowledgements

The support of the National Nature Science Foundation of China (No. 10771125) and of the Nature Science Foundation of Shandong Province of China (No. Y2007A20) are gratefully acknowledged.