Enhancing the Interactive Visualization of Procedurally Encoded Multifield Data with Ellipsoidal Basis Functions

Functional approximation of scattered data is a popular technique for compactly representing various types of datasets in computer graphics, including surface, volume, and vector datasets. Typically, sums of Gaussians or similar radial basis functions are used in the functional approximation and PC graphics hardware is used to quickly evaluate and render these datasets. Previously, researchers presented techniques for spatially-limited spherical Gaussian radial basis function encoding and visualization of volumetric scalar, vector, and multifield datasets. While truncated radially symmetric basis functions are quick to evaluate and simple for encoding optimization, they are not the most appropriate choice for data that is not radially symmetric and are especially problematic for representing linear, planar, and many non-spherical structures. Therefore, we have developed a volumetric approximation and visualization system using ellipsoidal Gaussian functions which provides greater compression, and visually more accurate encodings of volumetric scattered datasets. In this paper, we extend previous work to use ellipsoidal Gaussians as basis functions, create a rendering system to adapt these basis functions to graphics hardware rendering, and evaluate the encoding effectiveness and performance for both spherical Gaussians and ellipsoidal Gaussians.