Scattered Data Interpolation Using Cubic Trigonometric Bézier Triangular Patch

Abstract

This paper discusses scattered data interpolation using cubic trigonometric Bezier triangular patches with C1 continuity everywhere. We derive the C1 condition on each adjacent triangle. On each triangular patch, we employ convex combination method between three local schemes. The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets. We tested the proposed scheme with 36,65, and 100 data points for some well-known test functions. The scheme is also applied to interpolate the data for the electric potential. We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell-Sabin (PS) and Clough-Tocher (CT) by measuring the maximum error, root mean square error (RMSE) and coefficient of determination (R2). From the results obtained, our proposed method is competent with cubic Bezier, cubic Ball, PS and CT triangles splitting schemes to interpolate scattered data surface. This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.