Rational generalised ball functions for convex interpolating curves - Samsul Ariffin Abdul Karim,; Abd Rahni Mt Piah, (Penerbit ukm, 2009)

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A curve interpolation scheme based on the generalised Ball basis functions which has been developed by the authors uses piecewise rational quintic generalised Ball functions to visualise scientific data. In fact, this scheme uses a rational generalised 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 C1. Some numerical results are presented