Modeling and Visualizing Volumetric and Surface-on-Surface Data

An introduction and overview of methods for modeling and visualizing trivariate data is presented. One variable is identified as being dependent on three other, independent variables. Data of this type arises often in practical problems of science and engineering The modeling portion is concerned with finding a mathematical relationship which represents the data. Visualization is concerned with using Computer generated images to convey information so that the user can learn about the relationship. The discussion on modeling methods will concentrate on the two application areas of surface-on-surface and Volumetric data. Volumetric data Covers the case where the independent data values represent points in a three dimensional domain. The surface-on-surface case is where the independent data is restricted to lie on some surface such as the earth or the surface of an airplane wing. Mathematical models with volume or surface domains are developed, discussed and compared. Graphing and visualizing trivariate relationships is quite challenging. Extending methods which have proven to be successful in other situations is a starting point. Several resulting modifications and extensions for both the case of surface-on-surface and Volumetric data are presented, discussed and compared. This includes some interactive techniques, isosurface algorithms, volume rendering and hypersurface projection graphs. Some new interrogation methods are also presented.