Scattered Data Interpolation Using Rational Quartic Triangular Patches with Three Parameters

Abstract

This paper discusses the construction of scattered data interpolation scheme based on rational quartic triangular patches with C1 continuity. The C1 sufficient condition is derived on each adjacent triangle. We employ rational corrected scheme comprising three local schemes defined on each triangle. The final scheme is then being applied for scattered data interpolation. In this study, we tested the proposed scheme on regular and irregular scattered data. For regular data, we used 36, 65 and 100 data sets, while for irregular data, we used some real data sets. Besides that, we compared the performance between the proposed scheme with cubic Ball and cubic Bézier schemes. We measure the error analysis by calculating the Root Mean Square Error (RMSE), maximum error (Max error), coefficient of determination (R^{2}) and CPU time (in seconds). Based on the comparisons, our proposed scheme performs better than the other two existing schemes. Furthermore, for large scattered data sets, the proposed scheme requires less computation time than existing schemes. The free parameters in the description of the proposed scheme provide greater flexibility in controlling the quality of the final interpolating surface. This is very useful in the designing processes.