Visualizing and modeling scattered multivariate data

Visualizing two types of scattered data-volumetric data sampled in a three-dimensional volume and surface-on-surface data sampled on a three-dimensional surface-is addressed. Since measurements are often sampled at discrete scattered locations, mathematical models that are defined over the entire domain and that interpolate or approximate the given scattered data are used. The modeling function can be evaluated over a grid, so that a conventional, off-the-shelf visualization tool that applies to data on a uniform grid can be used. Volumes, gradient, centroids, and other quantities can be computed from the model. Even though the two kinds of data and their problems look similar in their mathematical descriptions, they are solved by different methods, and the various solutions are visualized with methods that are quite different.<>