Using Bézier-Ball Function to Interpolate Positive Real Data and it's Application

Abstract

This paper proposes a function that can interpolate real data as well as preserving the nature of the data. A rational cubic Bézier function expressed in terms of Ball control points and weights is presented. Four shape parameters are proposed which provides more freedom to the user to control the shape of the data. Sufficient conditions needed to preserve its positivity are presented. The degree of smoothness attained achieved $C$1 continuity. Three different real data are used in the application which are real data of oxygen level in gas, real data of a conductance obtained from experiments and real data consists of the output of a pressurizer inside a Pressurized Water Reactor. The output measures the water level of the pressurizer when the inputs which are the temperature and heat loss are varied. The results show that the proposed method managed to produce smooth interpolants as well as preserving the positivity of the data.