Monotonicity-preserving C2 rational cubic spline for monotone data

摘要

Designers in industries need to generate splines which can interpolate the data points in such a way that they preserve the inherited shape characteristics (positivity, monotonicity, convexity) of data. Among the properties that the spline for curves and surfaces need to satisfy, smoothness and shape preservation of given data are mostly needed by all the designers. In this paper, a rational cubic function with three shape parameters has been developed. Data dependent sufficient constraints are derived for one of these shape parameters to preserve the inherited shape feature like monotonicity of data. Remaining two shape parameters are left free for designer to refine the shape of the monotone curve as desired. Numerical examples and interpolation error analysis show that the interpolant is not only C2, local, computationally economical and visually pleasant but also smooth. The error of rational cubic function is also calculated when the arbitrary function being interpolated is C3 in an interpolating interval. The order of approximation of interpolant is O(hi3).