Abstract.A smooth curve interpolation scheme for positive data is developed. Conditions have been incorporated into this scheme to preserve the shape of the data lying above a line. This scheme uses rational cubic Ball representation. Conditions are derived for preserving positivity and C 1 continuity. The outputs from a number of numerical experiments are presented.

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A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness isC1. The outputs from a number of numerical experiments are presented.

Abstract.A problem of monotonicity preserving interpolation is discussed in this presentation. If a given set of data is monotonic, we want the interpolant to also be monotonic. A rational interpolation scheme is developed. This scheme utilizes piecewise rational cubic Ball functions with four shape parameters in its description. Sufficient conditions to preserve the shape inherent in the data are derived. Three parameters will be allowed for a designer to further refine or control the shape of the curve, if desired. The arithmetic mean algorithm is used to approximate the first derivative at each data point. The degree of smoothness is C 1 . A number of numerical examples are presented.