Efficient Visualization of Scattered Energy Distribution Data by Using Cubic Timmer Triangular Patches

This chapter discusses the application of the new cubic Timmer triangular patches constructed by Ali et al. [1] to interpolate the irregularly scattered data with C1 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 C1 continuity is derived along the adjacent triangles. Two methods are used to calculate the cubic Timmer ordinates on each triangle. The convex combination between three local schemes Ti, i = 1, 2, 3 is used to produce the C1 surface everywhere. The proposed scheme will be tested to visualize three types of energy data sets with irregular shape properties. Numerical and graphical results are presented using MATLAB. Comparisons of the proposed scheme with some existing procedures such as cubic Ball and cubic Bezier triangular patches are also carried out. The resulting surface produced by cubic Timmer triangular patch is better than that produced using cubic Ball and cubic Bezier triangular patches with an overall coefficient of determination R2 value obtained to be larger than 0.8359.