Visualizing Scientific Computations: A System based on Lattice-Structured Data and Display Models
W. L. Hibbard, Ph.D. Dissertation, Computer Sciences Department Technical Report 1226, University of Wisconsin - Madison, May 1995.

Abstract

In this thesis we develop a system that makes scientific computations visible and enables physical scientists to perform visual experiments with their computations. Our approach is unique in the way it integrates visualization with a scientific programming language. Data objects of any user-defined data type can be displayed, and can be displayed in any way that satisfies broad analytic conditions, without requiring graphics expertise from the user. Furthermore, the system is highly interactive.

In order to achieve generality in our architecture, we first analyze the nature of scientific data and displays, and the visualization mappings between them. Scientific data and displays are usually approximations to mathematical objects (i.e., variables, vectors and functions) and this provides a natural way to define a mathematical lattice structure on data models and display models. Lattice-structured models provide a basis for integrating certain forms of scientific metadata into the computational and display semantics of data, and also provide a rigorous interpretation of certain expressiveness conditions on the visualization mapping from data to displays. Visualization mappings satisfying these expressiveness conditions are lattice isomorphisms. Applied to the data types of a scientific programming language, this implies that visualization mappings from data aggregates to display aggregates can always be decomposed into mappings of data primitives to display primitives.

These results provide very flexible data and display models, and provide the basis for flexible and easy-to-use visualization of data objects occurring in scientific computations.