This paper discusses the positivity preserving by using rational cubic Ball interpolant of the form cubic/quadratic with two parameters. The sufficient condition for the positivity is derived on one parameter meanwhile the other one is a free parameter to control the final shape of the interpolating curves. The degree smoothness achieved is C1. From numerical results, the rational cubic Ball spline with two parameters gives smooth interpolating positive curves as well as visually pleasing for computer graphics visualization. Furthermore the scheme is better than existing schemes i.e. its easiness to use and less computation. All numerical results are produced by using Mathematica. © 2016 Penerbit UTM Press. All rights reserved.