A curve interpolation scheme based on generalized Ball basis functions to visualize scientific data has been developed. The scheme uses piecewise rational quartic Said-Ball functions with linear denominator. The parameter, in the description of the rational interpolant, has been constrained to preserve the shape of the data. We examine the positivity-preserving properties of this rational interpolant to a given data set. The degree of smoothness attained is. Numerical results show that the proposed scheme works well for all tested data sets. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.