This paper discusses the positivity and monotonicity preserving by using rational cubic Ball interpolant of the form cubic/quadratic with three parameters. The sufficient conditions for the positivity and monotonicity are derived with two parameters for controlling the final resulting interpolating curves (positive and monotone). The degree of smoothness attained is C1. Four data sets are chosen in order to test the capability of the proposed rational cubic Ball interpolation for positivity and monotonicity preserving. From all graphical results, rational cubic Ball with three parameters gives smooth interpolating curves and visually pleasing for scientific visualization. © 2015 Pushpa Publishing House.