| Summary: | 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
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