Convexity control of a bivariate rational interpolating spline surfaces

A bivariate rational interpolation surface based on function values has been constructed in the authors’ earlier works. This paper deals with the convexity control of interpolating surfaces. The sufficient and necessary conditions for interpolating surfaces to be convex are derived. The convexity of the interpolating surface can be changed locally by selecting suitable parameters under the condition that the interpolation data are not changed. Examples are given to show how the parameters can be chosen and the shapes of the surfaces changed.