A Time-Dependent Vector Field Topology Based on Streak Surfaces

Üffinger, Markus; Sadlo, Filip; Ertl, Thomas

doi:10.1109/tvcg.2012.131

Cited by 33 publications

(53 citation statements)

References 26 publications

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“…This colormap aids the identification of velocity magnitude values on 3D surfaces. Üffinger et al [101] apply a white to green sequential colormap to show hyperbolicity of path surfaces and a white to blue sequential colormap for the finite-time Lyapunov exponent (FTLE) representation. These colormaps are used for the comparison of the vector field attributes.…”

Section: Colormap Applicationsmentioning

confidence: 99%

“…By analyzing tasks associated with the colormaps, many applications utilize colormaps to carry out multiple tasks. They use multiple colormaps to cope with these tasks, 16 papers ([1], [2], [7], [14], [38], [39], [53], [54], [59], [63], [68], [69], [87], [98], [99], [101]) utilize more than one type of colormap for different data or tasks in their visualizations. Furthermore, many works, for example, [6], [8], [14], [37], [59], [69], require combined tasks to be performed with a single colormap.…”

Section: Colormap Applicationsmentioning

confidence: 99%

“…For the 18 papers with originally designed colormaps, colormaps from [13], [101] are similar to the ColorBrewer colormaps, whereas [6], [47], [59], [69] utilize luminance increasing multihue colormaps, and [26], [29], [37], [54], [97] design multihue colormaps with the issues of standard rainbow colormap in mind.…”

Section: Colormap Applicationsmentioning

confidence: 99%

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A Survey of Colormaps in Visualization

Zhou

Hansen

2016

IEEE Trans. Visual. Comput. Graphics

117

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Colormaps are a vital method for users to gain insights into data in a visualization. With a good choice of colormaps, users are able to acquire information in the data more effectively and efficiently. In this survey, we attempt to provide readers with a comprehensive review of colormap generation techniques and provide readers a taxonomy which is helpful for finding appropriate techniques to use for their data and applications. Specifically, we first briefly introduce the basics of color spaces including color appearance models. In the core of our paper, we survey colormap generation techniques, including the latest advances in the field by grouping these techniques into four classes: procedural methods, user-study based methods, rule-based methods, and data-driven methods; we also include a section on methods that are beyond pure data comprehension purposes. We then classify colormapping techniques into a taxonomy for readers to quickly identify the appropriate techniques they might use. Furthermore, a representative set of visualization techniques that explicitly discuss the use of colormaps is reviewed and classified based on the nature of the data in these applications. Our paper is also intended to be a reference of colormap choices for readers when they are faced with similar data and/or tasks.

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Section: Colormap Applicationsmentioning

confidence: 99%

Section: Colormap Applicationsmentioning

confidence: 99%

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A Survey of Colormaps in Visualization

Zhou

Hansen

2016

IEEE Trans. Visual. Comput. Graphics

117

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“…A repelling LCS is a material structure that repels all particles, whereas an attracting LCS attracts them [Hal01]. A number of variants to LCS calculation have been proposed in the literature, including localized FTLE [KPH * 09], a method based on streak surfaces [ÜSE13] and time line cell tracking [KER * 14]. Haller [Hal01] has demonstrated that LCS can be extracted as ridges of the finite-time Lyapunov exponent (FTLE) field.…”

Section: Inertial Particles In Visualizationmentioning

confidence: 99%

Finite‐Time Mass Separation for Comparative Visualizations of Inertial Particles

Günther¹,

Theisel²

2015

Computer Graphics Forum

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dp : 20 µm 200 µm x y t t τ ε Arclength (r) τ 0 20 0 2.5 Figure 1: Mass separation of inertial particles in the DOUBLE GYRE. Left image: Mass (color-coded) that separates strongest during integration over time τ = 17. Center image: inertial particles of different mass are released at the cross in the left image.In space-time their trajectories assemble a surface, with the purple line being its frontline-a so-called massline. The green line is the particle trajectory with strongest separation (here, with diameter dp = 99 µm). Right image: plot of difference to reference particle, here the smallest inertial particle (diameter dp = 20 µm), which makes the temporal evolution of the separation apparent. AbstractThe visual analysis of flows with inertial particle trajectories is a challenging problem because time-dependent particle trajectories additionally depend on mass, which gives rise to an infinite number of possible trajectories passing through every point in space-time. This paper presents an approach to a comparative visualization of the inertial particles' separation behavior. For this, we define the Finite-Time Mass Separation (FTMS), a scalar field that measures at each point in the domain how quickly inertial particles separate that were released from the same location but with slightly different mass. Extracting and visualizing the mass that induces the largest separation provides a simplified view on the critical masses. By using complementary coordinated views, we additionally visualize corresponding inertial particle trajectories in space-time by integral curves and surfaces. For a quantitative analysis, we plot Euclidean and arc length-based distances to a reference particle over time, which allows to observe the temporal evolution of separation events. We demonstrate our approach on a number of analytic and one real-world unsteady 2D field.

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“…This concept has been extended to 3D unsteady attracting and repelling manifolds by Üffinger et al . [USE12].…”

Section: Related Workmentioning

confidence: 99%

Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Kühn

Engelke

Rössl

et al. 2013

Computer Graphics Forum

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Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite-time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations.

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A Time-Dependent Vector Field Topology Based on Streak Surfaces

Cited by 33 publications

References 26 publications

A Survey of Colormaps in Visualization

A Survey of Colormaps in Visualization

Finite‐Time Mass Separation for Comparative Visualizations of Inertial Particles

Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

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