An Improved C1 rational Bernstein–Bézier triangular patch for scattered data interpolation

Scattered data interpolation is important in sciences, engineering, and medical-based problems. The degree smoothness attained is either $C^1$ or $C^2$. However, based on our simulations, we found that, Hussain and Hussain (2011) scheme is not producing $C^1$ everywhere. Motivated by this, in this study we will propose an improve sufficient condition for the $C^1$ on each adjacent triangle. Our scheme is guaranteed to produce $C^1$ everywhere. To support our claim, we have implemented both schemes and perform some numerical comparison including error measurement. From the results, our proposed scheme is producing $C^1$ interpolating surface while the interpolating surface produced by Hussain and Hussain (2011) is not $C^1$ everywhere. Furthermore, our proposed scheme give smaller error compared with Hussain and Hussain (2011) scheme. All numerical and graphical results are presented by using MATLAB programming.