A Robust Parity Test for Extracting Parallel Vectors in 3D

Ju, Tao; Cheng, Minxin; Wang, Xu; Duan, Ye

doi:10.1109/tvcg.2014.2346412

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…A parity test method was proposed in [2] to eliminate ambiguities when multiple pairs of PV points exist on the faces of a cell. Ambiguity cases produced by the Peikert-Roth method can be used as the input, and the parity test samples u and v on the boundary of the faces and uses Poincare-Hopf and Gauss-Bonnett theorems to determine the parity.…”

Section: Other Methodsmentioning

confidence: 99%

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Exact Analytical Parallel Vectors

Guo,

Peterka

2021

Preprint

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This paper demonstrates that parallel vector curves are piecewise cubic rational curves in 3D piecewise linear vector fields. Parallel vector curves-loci of points where two vector fields are parallelhave been widely used to extract features including ridges, valleys, and vortex core lines in scientific data. We define the term generalized and underdetermined eigensystem in the form of Ax + a = λ (Bx + b) in order to derive the piecewise rational representation of 3D parallel vector curves. We discuss how singularities of the rationals lead to different types of intersections with tetrahedral cells.

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Section: Other Methodsmentioning

confidence: 99%

“…We consider λ in the extended real domain R = R ∪ {∞}. This is reasonable because normally (when P(λ ) and Q(λ ) have nonzero 2 We omit the very long expansion for space. cubic coefficients) the limits of P(λ )/Q(λ ) at positive and negative infinities exist and are equal:…”

Section: Solution Intervals Of Each Cubic Rational Inequalitymentioning

confidence: 99%

Exact Analytical Parallel Vectors

Guo,

Peterka

2021

Preprint

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“…Works that go beyond direct application of the PV operator include the one by Ju et al [JCWD14], who derive a parity test for the number of PV solutions, and, most closely related to our work, the coplanar vectors operator, defined by Weinkauf and Theisel [WSTH07] for the extraction of vortex core lines in time‐dependent flow. Similar to their previous work [TSW*05], which derives a feature flow field formulation for representing the surfaces that a vortex core line sweeps over time, they also operate in space‐time there.…”

Section: Related Workmentioning

confidence: 96%

The Dependent Vectors Operator

Hofmann

Sadlo

2019

Computer Graphics Forum

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In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four‐dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic technique to extract and filter the solution manifolds. We exemplify our approach for vortex cores, bifurcations, and ridges as well as valleys in higher dimensions.

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“…For cell‐based extractions, Ju et al . [JCWD14] recently proposed a robust parity test to determine the number of PV points per cell face. When it comes to vortices, we are usually only interested in PV curves that exist in areas, where eigenvalues of the Jacobian are complex, i.e.…”

Section: Introductionmentioning

confidence: 99%

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 Robust Parity Test for Extracting Parallel Vectors in 3D

Cited by 7 publications

References 18 publications

Exact Analytical Parallel Vectors

Exact Analytical Parallel Vectors

The Dependent Vectors Operator

The State of the Art in Vortex Extraction

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