# Hyper-Objective Vortices

@article{Guenther2020HyperObjectiveV, title={Hyper-Objective Vortices}, author={Tobias Guenther and Holger Theisel}, journal={IEEE Transactions on Visualization and Computer Graphics}, year={2020}, volume={26}, pages={1532-1547} }

Almost all properties of vector fields, including magnitude, direction, <inline-formula><tex-math notation="LaTeX">$\lambda _2$</tex-math><alternatives><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math><inline-graphic xlink:href="guenther-ieq1-2868760.gif"/></alternatives></inline-formula> and vorticity change under arbitrary movements of the observer. [...] Key Method Further, we present a generic approach that transforms almost any vortex measure into a hyper-objective one. We… Expand

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#### References

SHOWING 1-10 OF 53 REFERENCES

Generic objective vortices for flow visualization

- Computer Science, Mathematics
- ACM Trans. Graph.
- 2017

This paper proves that in the optimal frame, all local vortex extraction methods that are based on velocity and its derivatives become objective, and demonstrates the approach with objective counterparts to λ2, vorticity and Sujudi-Haimes. Expand

Acceleration feature points of unsteady shear flows

- Physics, Mathematics
- 2014

In this paper, we propose a novel framework to extract features such as vortex cores and saddle points in two-dimensional unsteady flows. This feature extraction strategy generalizes critical points… Expand

Opacity Optimization and Inertial Particles in Flow Visualization

- Physics
- 2016

Vector field visualization is a major discipline of scientific visualization that helps to push the frontiers of research in fluid mechanics, medicine, biology, astrophysics and many more. In… Expand

Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude

- Computer Science, Medicine
- IEEE Transactions on Visualization and Computer Graphics
- 2011

The interesting observation that vortex-like minima are enclosed by particularly pronounced ridges makes it possible to define boundaries of vortex regions in a parameter-free way, and a robust algorithm can be designed to extract such boundaries. Expand

The State of the Art in Vortex Extraction

- Physics, Computer Science
- Comput. Graph. Forum
- 2018

An overview over the advances that have been made in the analysis of vortices in the last 40 years is provided, providing sufficient background on differential vector field calculus, extraction techniques like critical point search and the parallel vectors operator, and the notion of reference frame invariance is introduced. Expand

On the identification of a vortex

- Physics
- 1995

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired… Expand

The Helmholtz-Hodge Decomposition—A Survey

- Computer Science, Medicine
- IEEE Transactions on Visualization and Computer Graphics
- 2013

The goal is to promote further research in the field by creating a common repository of techniques to compute the HHD as well as a large collection of example applications in a broad range of areas. Expand

Vortex and Strain Skeletons in Eulerian and Lagrangian Frames

- Computer Science, Medicine
- IEEE Transactions on Visualization and Computer Graphics
- 2007

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: They indicate… Expand

Introduction to Focus Issue: Objective Detection of Coherent Structures.

- Computer Science, Medicine
- Chaos
- 2015

Objectivity is a necessary condition for the reliability of any coherent structure method and narrows down the panoply of methods significantly to those that are at least consistent with their stated goal of detecting material (or Lagrangian) structures. Expand

Some perspectives on the dynamic history of a material element

- Mathematics
- 2008

Abstract Some kinematic concepts like MWCRPSH, extensional motion, and persistence of straining tensor are adapted to a dynamic framework. Then, a criterion based on the dynamics of a material is… Expand