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An explicit representation of a C 1 piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation.It is shown that the interpolation method can be applied to convex and/or monotonic sets of data and an error analysis of the interpolant is given. The scheme includes, as a special case, the monotonic rational quadratic interpolant considered by the authors in [1] and [5]. However, the requirement of convexity necessitates the generalization to the rational cubic form employed here.

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Explicit formulae are developed for determining the derivative parameters of a monotonic interpolation method of Gregory and Delbourgo (1982).