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

Abstract

Scattered data interpolation is important in sciences, engineering, and medical-based problems. The degree smoothness attained is either C1 or C2. However, based on our simulations, we found that, Hussain and Hussain (2011) scheme is not producing C1 everywhere. Motivated by this, in this study we will propose an improve sufficient condition for the C1 on each adjacent triangle. Our scheme is guaranteed to produce C1 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 C1 interpolating surface while the interpolating surface produced by Hussain and Hussain (2011) is not C1 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.

Keywords

• Rational Cubic Bézier
• Patches
• Scattered data interpolation
• Continuity
• Visualization
• Surface reconstruction