A Survey of Topology‐based Methods in Visualization

Heine, Christian; Leitte, Heike; Hlawitschka, Mario; Iuricich, Federico; Floriani, Leila De; Scheuermann, Gerik; Hagen, Hans; Garth, Christoph

doi:10.1111/cgf.12933

Cited by 130 publications

(94 citation statements)

References 229 publications

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“…Previous work has demonstrated that tracking graphs are ideally suited to visualize the evolution and relation of components over time [HLH*16]. Several methods have been proposed to identify and track components of time‐varying scalar fields.…”

Section: Related Workmentioning

confidence: 99%

Nested Tracking Graphs

Lukasczyk

Weber

Maciejewski

et al. 2017

Computer Graphics Forum

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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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Section: Related Workmentioning

confidence: 99%

Nested Tracking Graphs

Lukasczyk

Weber

Maciejewski

et al. 2017

Computer Graphics Forum

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“…There exists a huge body of work that demonstrates that tracking graphs are ideally suited to visualize the evolution and relation of components over time [9]. To utilize these methods we first compute a volumetric representation of the point clouds via an adaptation of Shepard's kernel method [13] for three-dimensional domains.…”

Section: Related Workmentioning

confidence: 99%

Viscous Fingering: A Topological Visual Analytic Approach

Lukasczyk

Aldrich

Steptoe

et al. 2017

AMM

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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.

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“…More information on the extraction and tracking of feature is compiled in [PVH*03]. More recent reports summarize the efforts in topology‐based [HLH*16, LHZP07] and specifically unsteady topology‐based [PPF*11] flow visualization.…”

Section: Introductionmentioning

confidence: 99%

“…We refer to Heine et al . [HLH*16], Scheuermann and Tricoche [ST05] and Weinkauf [Wei08] for a comprehensive introduction into topology‐based methods.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The State of the Art in Vortex Extraction

Günther

Theisel

2018

Computer Graphics Forum

105

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Vortices are commonly understood as rotating motions in fluid flows. The analysis of vortices plays an important role in numerous scientific applications, such as in engineering, meteorology, oceanology, medicine and many more. The successful analysis consists of three steps: vortex definition, extraction and visualization. All three have a long history, and the early themes and topics from the 1970s survived to this day, namely, the identification of vortex cores, their extent and the choice of suitable reference frames. This paper provides an overview over the advances that have been made in the last 40 years. We provide sufficient background on differential vector field calculus, extraction techniques like critical point search and the parallel vectors operator, and we introduce the notion of reference frame invariance. We explain the most important region‐based and line‐based methods, integration‐based and geometry‐based approaches, recent objective techniques, the selection of reference frames by means of flow decompositions, as well as a recent local optimization‐based technique. We point out relationships between the various approaches, classify the literature and identify open problems and challenges for future work.

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A Survey of Topology‐based Methods in Visualization

Cited by 130 publications

References 229 publications

Nested Tracking Graphs

Nested Tracking Graphs

Viscous Fingering: A Topological Visual Analytic Approach

The State of the Art in Vortex Extraction

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