Comparing Methods of Interpolation for Scattered Volumetric Data

This report describes the methodology and some of the results of an empirical study devoted to comparing methods of interpolating scattered volumetric data. The data is represented by (x_i, y_i, z_i,; F_i), i = 1, …, N, where P_i = (x_i, y_i, z_i) represents the independent data variables, and F_i is the dependent data variable. No assumptions about the distribution of independent data sites is made except that the points are distinct. Several methods for constructing a function F such that F(P_i) = F_i, i = 1, …, N, are described and compared. The comparisons are based upon test functions, data sets, and an interactive program for visualizing and comparing the graphs of different models.