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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, e in preserving positivity and monotonicity for real data set. To preserve positivity, the selection of e 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 e 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 e are investigated. From the examples, the resulted curves using multiquadric quasi-interpolation as the basis can only approximate the data. [ABSTRACT FROM AUTHOR]

In this paper, the method of finding the line constrained between two quadratic Bezier curves and also finding the line constrained between a quadratic Bezier curve and a circle is presented. The application of the line constrained can be used in the construction of railway tracks between any obstacle or rolling a ball to the other side of a wall in a way that it just touches the wall. The method used is by using equal root properties of a quadratic equation in order to find one point where the line touches the curve. The work examples involved different curve orientations and different circle positions. Mathematica software is used to compute the solutions for the line constrained and present the solutions graphically. By using the method proposed, the number of intersection points obtained is used to determine the number of lines constrained between two curves and between a curve and a circle. The conclusion on whether all lines are acceptable to be considered as the line constrained are depending on the application of the line. [ABSTRACT FROM AUTHOR]