Developing a Mathematical Method for Controlling the Generation of Cubic Spline Curve based on Fixed Data Points, Variable Guide Points and Weighting Factors

Abstract

The cubic spline interpolation method is used to design the developed curve. The method enables the designer to change the shape of the curve to the desired one without changing the original data points. That done by changing the value of the parameter ti depending on defined guide points and weighting factors that assigned secretly by the designer, so that not easily recreate the same design by anyone else even he knows the original data points that used to design the curve. These curves can be used in many fields such as banknote design, secure printed documents, the design of cars and airplanes structures, and Ornament.This paper modifies a mathematical technique to design complex curves, which are not easy to recreate. The results of this research had compared with other related methods since the improved models of this research is used the negative values of the guide to compute the parametric rather than using the only positive ones; the efficiency of the modified technique had proved by several comparative examples.

Keywords

• cubic spline
• negative parametric
• weighting factor
• area parameterization