Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows
Name:
2020_rautek_killingsurfaces_with_appendixes_hq.pdf
Size:
12.54Mb
Format:
PDF
Description:
Accepted manuscript
Name:
2020_rautek_killingsurfaces.mp4
Size:
227.2Mb
Format:
MPEG-4 video
Description:
Supplemental files
Name:
observer-relative-on-curved-manifolds-prerecorded-talk-vis2020_v03.mp4
Size:
369.5Mb
Format:
MPEG-4 video
Description:
Supplemental files
Type
ArticleAuthors
Rautek, PeterMlejnek, Matej
Beyer, Johanna
Troidl, Jakob
Pfister, Hanspeter
Theußl, Thomas
Hadwiger, Markus

KAUST Department
Visual Computing Center (VCC)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Core Labs
Computer Science Program
KAUST Grant Number
OSR-2015-CCF-2533-01Date
2020-10-13Online Publication Date
2020-10-13Print Publication Date
2021-02Permanent link to this record
http://hdl.handle.net/10754/665572
Metadata
Show full item recordAbstract
Computing and visualizing features in fluid flow often depends on the observer, or reference frame, relative to which the input velocity field is given. A desired property of feature detectors is therefore that they are objective, meaning independent of the input reference frame. However, the standard definition of objectivity is only given for Euclidean domains and cannot be applied in curved spaces. We build on methods from mathematical physics and Riemannian geometry to generalize objectivity to curved spaces, using the powerful notion of symmetry groups as the basis for definition. From this, we develop a general mathematical framework for the objective computation of observer fields for curved spaces, relative to which other computed measures become objective. An important property of our framework is that it works intrinsically in 2D, instead of in the 3D ambient space. This enables a direct generalization of the 2D computation via optimization of observer fields in flat space to curved domains, without having to perform optimization in 3D. We specifically develop the case of unsteady 2D geophysical flows given on spheres, such as the Earth. Our observer fields in curved spaces then enable objective feature computation as well as the visualization of the time evolution of scalar and vector fields, such that the automatically computed reference frames follow moving structures like vortices in a way that makes them appear to be steady.Citation
Rautek, P., Mlejnek, M., Beyer, J., Troidl, J., Pfister, H., Theussl, T., & Hadwiger, M. (2020). Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows. IEEE Transactions on Visualization and Computer Graphics, 1–1. doi:10.1109/tvcg.2020.3030454Sponsors
We thank Anna Fruhstück for the illustrations and for help with the figures and the video. Hurricane Isabel data courtesy of EU Copernicus project, path from National Hurricane Center/Wikipedia. This work was supported by King Abdullah University of Science and Technology (KAUST), and the KAUST Office of Sponsored Research (OSR) award OSR-2015-CCF-2533-01. This research used resources of the Core Labs of KAUST.Additional Links
https://ieeexplore.ieee.org/document/9222512/https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9222512
ae974a485f413a2113503eed53cd6c53
10.1109/TVCG.2020.3030454