Cubic q-Bézier Triangular Patch for Scattered Data Interpolation and Its Algorithm

This paper presents an approach to scattered data interpolation using q-Bézier triangular patches via an efficient algorithm. While existing studies have formed q-Bézier triangular patches through convex combination, their application to scattered data interpolation has not been previously explored. Therefore, this study aims to extend the use of q-Bézier triangular patches to scattered data interpolation by achieving C1 continuity throughout the data points. We test the proposed scheme using both established data points and real-life engineering problems. We compared the performance of the proposed interpolation scheme with a well-known existing scheme by varying the q parameter. The comparison was based on visualization and error analysis. Numerical and graphical results were generated using MATLAB. The findings indicate that the proposed scheme outperforms the existing scheme, demonstrating a higher coefficient of determination (R2), smaller root mean square error (RMSE), and faster central processing unit (CPU) time. These results highlight the potential of the proposed q-Bézier triangular patches scheme for more accurate and reliable scattered data interpolation via the proposed algorithm.