Vortex identification—applications in aerodynamics: a case study
VIS '97 Proceedings of the 8th conference on Visualization '97
Extracting iso-valued features in 4-dimensional scalar fields
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Vortex tracking in scale-space
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Computing singularities of 3D vector fields with Geometric Algebra
Proceedings of the conference on Visualization '02
Tracking and Visualizing Turbulent 3D Features
IEEE Transactions on Visualization and Computer Graphics
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Topological Segmentation in Three-Dimensional Vector Fields
IEEE Transactions on Visualization and Computer Graphics
The Feature Tree: Visualizing Feature Tracking in Distributed AMR Datasets
PVG '03 Proceedings of the 2003 IEEE Symposium on Parallel and Large-Data Visualization and Graphics
Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Surface techniques for vortex visualization
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices
IEEE Transactions on Visualization and Computer Graphics
Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation
Computer Graphics Forum
A Quantized Boundary Representation of 2D Flows
Computer Graphics Forum
Galilean invariant extraction and iconic representation of vortex core lines
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
Visualization methods for vortex rings and vortex breakdown bubbles
EUROVIS'07 Proceedings of the 9th Joint Eurographics / IEEE VGTC conference on Visualization
Interactive visual exploration of unsteady 3D flows
EUROVIS'07 Proceedings of the 9th Joint Eurographics / IEEE VGTC conference on Visualization
Path line oriented topology for periodic 2D time-dependent vector fields
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Toward a lagrangian vector field topology
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Topology-based visualization of transformation pathways in complex chemical systems
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Geometry-preserving topological landscapes
Proceedings of the Workshop at SIGGRAPH Asia
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In this paper, we present an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincaré index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose. We examine structures that exhibit topological variations with time and describe some of the insight gained with our method. Examples are given that show a correlation in the evolution of physical quantities that play a role in vortex breakdown.