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Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to each other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We demonstrate the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.

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Complex networks require effective tools and visualizations for their analysis and comparison. Clique communities have been recognized as a powerful concept for describing cohesive structures in networks. We propose an approach that extends the computation of clique communities by considering persistent homology, a topological paradigm originally introduced to characterize and compare the global structure of shapes. Our persistence-based algorithm is able to detect clique communities and to keep track of their evolution according to different edge weight thresholds. We use this information to define comparison metrics and a new centrality measure, both reflecting the relevance of the clique communities inherent to the network. Moreover, we propose an interactive visualization tool based on nested graphs that is capable of compactly representing the evolving relationships between communities for different thresholds and clique degrees. We demonstrate the effectiveness of our approach on various network types.

The Sky View Factor (SVF) is a dimension-reduced representation of urban form and one of the major variables in radiation models that estimate outdoor thermal comfort. Common ways of retrieving SVFs in urban environments include capturing fisheye photographs or creating a digital 3D city or elevation model of the environment. Such techniques have previously been limited due to a lack of imagery or lack of full scale detailed models of urban areas. We developed a web based tool that automatically generates synthetic hemispherical fisheye views from Google Earth at arbitrary spatial resolution and calculates the corresponding SVFs through equiangular projection. SVF results were validated using Google Maps Street View and compared to results from other SVF calculation tools. We generated 5-meter resolution SVF maps for two neighborhoods in Phoenix, Arizona to illustrate fine-scale variations of intra-urban horizon limitations due to urban form and vegetation. To demonstrate the utility of our synthetic fisheye approach for heat stress applications, we automated a radiation model to generate outdoor thermal comfort maps for Arizona State University's Tempe campus for a hot summer day using synthetic fisheye photos and on-site meteorological data. Model output was tested against mobile transect measurements of the six-directional radiant flux density. Based on the thermal comfort maps, we implemented a pedestrian routing algorithm that is optimized for distance and thermal comfort preferences. Our synthetic fisheye approach can help planners assess urban design and tree planting strategies to maximize thermal comfort outcomes and can support heat hazard mitigation in urban areas.

We describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph‐theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy‐to‐interpret, minimally‐cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real‐world examples.

Abstract.We present a methodology to analyze and visualize an ensemble of finite pointset method (FPM) simulations that model the viscous fingering process of salt solutions inside water. In course of the simulations the solutions form structures with increased salt concentration called viscous fingers. These structures are of primary interest to domain scientists as it is not clear when and where viscous fingers appear and how they evolve. To explore the aleatoric uncertainty embedded in the simulations we analyze an ensemble of simulation runs which differ due to stochastic effects. To detect and track the viscous fingers we derive a voxel volume for each simulation where fingers are identified as subvolumes that satisfy geometrical and topological constraints. Properties and the evolution of fingers are illustrated through tracking graphs that visualize when fingers form, dissolve, merge, and split. We provide multiple linked views to compare, browse, and analyze the ensemble in real-time.