Positivity and monotonicity shape preserving using radial basis function

The objective of this paper is to investigate whether radial basis functions (RBF) can be used as an alternative to Bezier and Ball splines in preserving positivity and monotonicity of the data. For positivity shape preserving, multiquadric and Gaussian form of RBF are used in the analysis while for monotonicity, multiquadric quasi-interpolation is used. The analysis involved a free shape parameter, ε in preserving positivity and monotonicity for real data set. To preserve positivity, the selection of ε is based on the positivity constraint, s(x) > 0 and also a proposed upper bound value. The output from several real data sets are presented and the choice of ε varies depending on the data set. The interpolants are comparable with existing interpolation schemes using rational cubic Bezier and rational cubic Ball. For monotonicity shape preserving, the behaviour of the interpolants using different ε are investigated. From the examples, the resulted curves using multiquadric quasi-interpolation as the basis can only approximate the data.