Data interpolation is essential in geometric modelling and computer graphics (CG) specially to model some complex shapes or surfaces. There is a need for the industry of geometric modelling to make changes in the shapes of the curves/surfaces without relying on new data. To achieve this, we proposed a new rational quartic spline (RQS) scheme with three free parameters. We derive the convergence analysis based on Peano-Kernel theorem. Furthermore, the proposed scheme used for shape control and error analysis by manipulating the values of the free parameters. We have calculated the absolute error, Root Mean Square Error (RMSE) and higher coefficient of determination (R2) as error measurement. It observed that the proposed scheme gives higher accuracy in term of smaller error as compared to some existing schemes. This showed that the data interpolation using new RQS scheme with three parameters gives better results as compared to existing quartic polynomial. Furthermore, an application in signal processing shows that the proposed RQS is highly accurate to increase the discrete-time signal sampling. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.