Visualizing the Energy of Scattered Data by Using Cubic Timmer Triangular Patches

Abstract

This paper discusses the application of the new cubic Timmer triangular patches constructed by Ali et al. [1] to interpolate the irregularly scattered data with C 1 continuity. In order to apply the cubic Timmer triangular patches for scattered data interpolation, the data is first triangulated by using the Delaunay algorithm, and then the sufficient condition for C 1 continuity is derived along the adjacent triangles. Two methods will be used to calculate the cubic Timmer ordinates on each triangle. The convex combination between three local schemes Ti , i = 1,2,3 will be used to produce the C 1 surface everywhere. The proposed scheme will be tested to visualize one energy data set with irregular shape properties. Numerical and graphical results are presented by using MATLAB. Comparisons between the proposed scheme and existing schemes such as cubic Ball and cubic Bézier triangular patches are also carried out. The results indicate that the surface produced by cubic Timmer triangular patch is better than surface produced using cubic Ball and cubic Bezier triangular patches with overall coefficient of determination R2 value obtained to be larger than 0.9234.