Positivity-preserving interpolation of positive data by rational cubics

This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C 1 piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.