A curve interpolation scheme is developed using rational cubic Ball functions with cubic numerator and cubic denominator. The two parameters, in the description of the rational interpolant have been constrained to preserve the shape of the data. The positivity preserving properties of this rational interpolant to a given data set are shown. The degree of smoothness C1 is attained (first order of parametric continuity). The numerical results show that the proposed schemes work well to all data sets and are comparable to the existing method. © 2013 Pushpa Publishing House, Allahabad, India.