Query-Driven Visualization Strategies for the Analysis and Visualization of Complex Datasets

There is an urgent need in scientific communities, driven by their ability to generate ever-larger, increasingly complex data, for scalable analysis methods that rapidly identify salient trends in scientific data. Query-Driven Visualization (QDV) methods are among the small subset of techniques that are able to address both large and highly complex datasets---e.g.\ multivariate, multitemporal, and multiresolution representations of scalar, vector, and function field data. This dissertation presents new methods that either directly extend the utility and accelerate the performance of QDV as a whole, or enable QDV's substantial and flexible analysis strengths to be applied to new areas of scientific research. The first part of this dissertation presents a new data-parallel strategy that accelerates the most fundamental task performed by QDV: the evaluation of user defined, ad~hoc queries. The second part of this dissertation extends QDV strategies to analyze and visualize time-varying adaptive mesh refinement (AMR) data. AMR techniques are used in many scientific communities to efficiently and accurately model complex, continuous physical phenomena. By extending QDV methods to address the dynamic spatiotemporal properties of time-varying AMR data, I provide scientists with a powerful tool for visually analyzing the data generated from these important simulations. The final part of this dissertation leverages statistical analysis methods to generate deeper insight into the regions that are selected by a user's query. In this effort I introduce two new methods that increase the utility of query-driven strategies. The first strategy uses correlation fields, created between pairs of variables, in conjunction with the cumulative distribution functions (CDF) of variables expressed in a user's query. This strategy identifies important variable interactions within query regions. The second strategy forms a statistical-based segmentation within the query-region to generate deeper insight into the ``statistical structure'' of a user's query. In this approach, segments indicate which variable contributes most to the underlying joint density distribution of the user's query. These segments, when used in conjunction with each variable's CDF, intuitively aid users in refining the constraints over the variables in their query