Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines

Weinkauf, Tino; Theisel, Holger; Sorkine, Olga

doi:10.1007/978-3-642-23175-9_11

Cited by 11 publications

(13 citation statements)

References 13 publications

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“…By close inspection, one also observes additional features in the |∇Φ| field that do not correspond to an LCS, that is, those cusp-like curves near the two vortices as highlighted by the arrow in Figure 7(b). They are essentially the cusp-like seeding curve discussed in [27]. This cusp-like behavior in pathlines is caused by the abrupt change in the pathline direction (i.e., almost angle of π between the previous and current directions), which is in turn caused by the intersection of the pathlines with the paths of singularities.…”

Section: Visualization Of φ and |∇φ|mentioning

confidence: 91%

Flow Visualization Based on A Derived Rotation Field

Zhang

Chen

Laramee

et al. 2016

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We identify and investigate the Φ field -a derived flow attribute field whose value at a given spatial location is determined by the integral curve initiated at the point. Specifically, we integrate the angle difference between the velocity vectors at two consecutive points along the integral curve to get the Φ field value. Important properties of the Φ field and its gradient magnitude |∇Φ| field are studied. In particular, we show that the patterns in the derived Φ field are generally aligned with the flow direction based on an inequality property. In addition, we compare the Φ field with some other attribute fields and discuss its relation with a number of flow features, such as LCS and cusp-like seeding structures. Furthermore, we introduce a unified framework for the computation of the Φ field and its gradient field, ∇Φ, and employ the Φ field and |∇Φ| field to a number of flow visualization and exploration tasks, including integral curve filtering, seeds generation and flow domain segmentation. We show that these tasks can be conducted more efficiently based on the information encoded in the Φ field.

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Section: Visualization Of φ and |∇φ|mentioning

confidence: 91%

Flow Visualization Based on A Derived Rotation Field

Zhang

Chen

Laramee

et al. 2016

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“…Indeed, close to a critical point, a streakline might intersect itself for a long time interval; see [27] for an example of self-intersecting streaklines near a critical point of type center. Lemma 3.4.…”

Section: Characteristic Curves Of a Flowmentioning

confidence: 99%

On Donating Regions: Lagrangian Flux through a Fixed Curve

Zhang¹

2013

SIAM Rev.

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Lagrangian flux through a fixed curve segment naturally gives rise to the notion of a donating region, a compact point set in which each particle will pass through the curve and contribute to the flux. A precise geometric determination of the donating region has not been available until now. The author proposes an explicit, constructive, and analytical definition of the donating region based on two characteristic curves of the flow field, viz. streaklines and timelines. It is also shown that, within a time interval of finite size, each particle in the proposed donating region has a net effect of going across the fixed curve once. The presented analysis might be potentially useful for flow topology studies, Lagrangian flux calculation, and explicit interface tracking.

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“…Günther et al [GRT13] present a general method for sets of lines—including pathlines—which adapts the opacity to avoid the occlusion of important features. Pathline selection can also be achieved with the methods by Weinkauf et al [WTS12], Salzbrunn et al [SGSM08], and Falk et al [FSf*10].…”

Section: Related Workmentioning

confidence: 99%

“…Comparison to pathline selection. Figure (a) was generated with the method by Weinkauf et al [WTS12], which tries to select and display only pathlines that do not intersect with others. (b) Pathline glyphs do not require any selection algorithm and can densely cover the domain.…”

Section: Comparisons and Examplesmentioning

confidence: 99%

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Pathline glyphs

Hlawatsch

Sadlo

Jang

et al. 2014

Computer Graphics Forum

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a) (b) (c) Figure 1: Multi-scale visualization of unsteady flow with pathline glyphs. (a) Emergent patterns visible on the overview scale correspond to structures in the flow and provide the basis for detailed exploration, but individual pathline glyphs cannot be perceived. (b) On an intermediate scale, patterns remain present, but the shapes of the glyphs become visible. (c) A close-up facilitates detailed analysis of time-dependent transport: particles started in the left area later move downward (blue), while particles from the right area stay in the whirl. AbstractVisualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well-established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph-based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time-dependent flow behavior. Zooming-in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context-preserving zoom lens and interactive pathline-based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.

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Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines

Cited by 11 publications

References 13 publications

Flow Visualization Based on A Derived Rotation Field

Flow Visualization Based on A Derived Rotation Field

On Donating Regions: Lagrangian Flux through a Fixed Curve

Pathline glyphs

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