RATIONAL GENERALIZED BALL FUNCTIONS FOR CONVEX INTERPOLATING CURVES

A curve interpolation scheme based on the generalized Ball basis functions which has been developed by the authors uses piecewise rational quintic generalized Ball functions to visualize scientific data. In fact, this scheme uses a rational generalized Ball with quartic numerator and linear denominator, which involves shape parameters. In this paper, we discuss an interpolation problem for convex data. The two parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. We examine the convexity-preserving properties of this rational interpolant to a given data set. Based on the analysis, the degree of smoothness attained is C^1 . Some numerical results are presented.