This study considers the construction a new C1 rational cubic spline (cubic numerator and quadratic denominator) with three parameters. Some mathematical properties of this rational function will be investigated in details. In order to use the proposed rational cubic spline for positivity preserving interpolation and constrained data that lie above any arbitrary straight line, the automatic choice of one parameter will be developed through some mathematical derivation. On each sub-interval this idea gives extra two free parameters that very useful for the user to manipulate the shape of the curve while at the same time maintaining the shape preservations of the data. Numerical comparison with some existing schemes shows that, the proposed scheme is on par. Furthermore, for some data sets, the proposed scheme is better as well as produce more visually pleasing interpolating curve for scientific visualization. © 2018, © 2018 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.