Visualization and analysis techniques play a key role in the discovery of relevant features in ensemble data. Trends, in the form of persisting commonalities or differences in time-varying ensemble datasets, constitute one of the most expressive feature types in ensemble analysis. We develop a flow-graph representation as the core of a system designed for the visual analysis of trends in time-varying ensembles. In our interactive analysis framework, this graph is linked to a representation of ensemble parameter-space and the ensemble itself. This facilitates a detailed examination of trends and their correlations to properties of input-space. We demonstrate the utility of the proposed trends analysis framework in several benchmark data sets, highlighting its capability to support goal-driven design of time-varying simulations.

Numerical ensemble forecasting is a powerful tool that drives many risk analysis efforts and decision making tasks. These ensembles are composed of individual simulations that each uniquely model a possible outcome for a common event of interest: e.g., the direction and force of a hurricane, or the path of travel and mortality rate of a pandemic. This paper presents a new visual strategy to help quantify and characterize a numerical ensemble's predictive uncertainty: i.e., the ability for ensemble constituents to accurately and consistently predict an event of interest based on ground truth observations. Our strategy employs a Bayesian framework to first construct a statistical aggregate from the ensemble. We extend the information obtained from the aggregate with a visualization strategy that characterizes predictive uncertainty at two levels: at a global level, which assesses the ensemble as a whole, as well as a local level, which examines each of the ensemble's constituents. Through this approach, modelers are able to better assess the predictive strengths and weaknesses of the ensemble as a whole, as well as individual models. We apply our method to two datasets to demonstrate its broad applicability.

Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space. While this approach helps address conceptual and parametric uncertainties, the ensemble datasets produced by this technique present a special challenge to visualization researchers as the ensemble dataset records a distribution of possible values for each location in the domain. Contemporary visualization approaches that rely solely on summary statistics (e.g., mean and variance) cannot convey the detailed information encoded in ensemble distributions that are paramount to ensemble analysis; summary statistics provide no information about modality classification and modality persistence. To address this problem, we propose a novel technique that classifies high-variance locations based on the modality of the distribution of ensemble predictions. Additionally, we develop a set of confidence metrics to inform the end-user of the quality of fit between the distribution at a given location and its assigned class. Finally, for the special application of evaluating the stability of bimodal regions, we develop local and regional metrics.

Despite nearly universal support for the IEEE 754 floating-point standard on modern general-purpose processors, a wide variety of more specialized processors do not provide hardware floating-point units and rely instead on integer-only pipelines. Ray tracing on these platforms thus requires an integer rendering process. Toward this end, we clarify the details of an existing fixed-point ray/triangle intersection method, provide an annotated implementation of that method in C++, introduce two refinements that lead to greater flexibility and improved accuracy, and highlight the issues necessary to implement common material models in an integer-only context. Finally, we provide the source code for a template-based integer/floating-point ray tracer to serve as a testbed for additional experimentation with integer ray tracing methods.