Quantifying uncertainty is an increasingly important topic across many domains. The uncertainties present in data come with many diverse representations having originated from a wide variety of disciplines. Communicating these uncertainties is a task often left to visualization without clear connection between the quantification and visualization. In this paper, we first identify frequently occurring types of uncertainty. Second, we connect those uncertainty representations to ones commonly used in visualization. We then look at various approaches to visualizing this uncertainty by partitioning the work based on the dimensionality of the data and the dimensionality of the uncertainty. We also discuss noteworthy exceptions to our taxonomy along with future research directions for the uncertainty visualization community.

Abstract-Interactive visualization of architecture provides a way to quickly visualize existing or novel buildings and structures. Such applications require both fast rendering and an effortless input regimen for creating and changing architecture using high-level editing operations that automatically fill in the necessary details. Procedural modeling and synthesis is a powerful paradigm that yields high data-amplification and can be coupled with fast rendering techniques to quickly generate plausible details of a scene without much or any user interaction. Previously, forward generating procedural methods have been proposed where a procedure is explicitly created to generate a particular content. In this article, we present our work in inverse procedural modeling of buildings and describe how to use an extracted repertoire of building grammars to facilitate the visualization and quick modification of architectural structures and buildings. We demonstrate an interactive application where the user draws simple building blocks and using our system can automatically complete the building "in the style of" other buildings using view-dependent texture mapping or nonphotorealistic rendering techniques. Our system supports an arbitrary number of building grammars created from user subdivided building models and captured photographs. Using only edit, copy and paste metaphors, entire building styles can be altered and transferred from one building to another in a few operations, enhancing the ability to modify an existing architectural structure or to visualize a novel building in the style of others.

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Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features.