Hyper-Objective Vortices

Günther T, Theisel H (2020)

Publication Type: Journal article

Publication year: 2020

Journal

IEEE Transactions on Visualization and Computer Graphics Institute of Electrical and Electronics Engineers (IEEE)

Book Volume: 26

Pages Range: 1532-1547

Article Number: 8454764

Journal Issue: 3

DOI: 10.1109/TVCG.2018.2868760

Abstract

Almost all properties of vector fields, including magnitude, direction, λ2 and vorticity change under arbitrary movements of the observer. This is undesirable since measurements of physical properties should ideally not depend on the way the (virtual) measurement device moves. There are some properties that are invariant under certain types of reference frame transformations: Galilean invariance (invariance under equal-speed translation) and objectivity (invariance under any smooth rotation and translation of the reference frame). In this paper, we introduce even harder conditions than objectivity: we demand invariance under any smooth similarity transformation (rotation, translation and uniform scale) as well as invariance under any smooth affine transformation of the reference frame. We show that these new hyper-objective measures allow the extraction of vortices that change their volume or deform. Further, we present a generic approach that transforms almost any vortex measure into a hyper-objective one. We apply our methods to vortex extraction in 2D and 3D vector fields, and analyze the numerical robustness, extraction time and the minimization residuals for the Galilean invariant, objective, and the two new hyper-objective approaches.

Authors with CRIS profile

Tobias Günther

Involved external institutions

Otto-von-Guericke-Universität Magdeburg DE Germany (DE) Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich CH Switzerland (CH)

How to cite

APA:

Günther, T., & Theisel, H. (2020). Hyper-Objective Vortices. IEEE Transactions on Visualization and Computer Graphics, 26(3), 1532-1547. https://dx.doi.org/10.1109/TVCG.2018.2868760

MLA:

Günther, Tobias, and Holger Theisel. "Hyper-Objective Vortices." IEEE Transactions on Visualization and Computer Graphics 26.3 (2020): 1532-1547.

BibTeX: Download