Locating closed streamlines in 3D vector fields
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Continuous topology simplification of planar vector fields
Proceedings of the conference on Visualization '01
Tools for Computing Tangent Curves for Linearly Varying Vector Fields over Tetrahedral Domains
IEEE Transactions on Visualization and Computer Graphics
Detection and Visualization of Closed Streamlines in Planar Flows
IEEE Transactions on Visualization and Computer Graphics
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Vorticity Based Flow Analysis and Visualization for Pelton Turbine Design Optimization
VIS '04 Proceedings of the conference on Visualization '04
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines
IEEE Transactions on Visualization and Computer Graphics
Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Robust Loop Detection for Interactively Placing Evenly Spaced Streamlines
Computing in Science and Engineering
Efficient Morse Decompositions of Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Introduction to discrete differential geometry: the geometry of plane curves
ACM SIGGRAPH ASIA 2008 courses
Algorithm for computer control of a digital plotter
IBM Systems Journal
Parallel algorithms for finding SCCs in implicitly given graphs
FMICS'06/PDMC'06 Proceedings of the 11th international workshop, FMICS 2006 and 5th international workshop, PDMC conference on Formal methods: Applications and technology
Computing and Visualization in Science
Fast Combinatorial Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
Robust Morse Decompositions of Piecewise Constant Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Morse Set Classification and Hierarchical Refinement Using Conley Index
IEEE Transactions on Visualization and Computer Graphics
Visualization of Vorticity and Vortices in Wall-Bounded Turbulent Flows
IEEE Transactions on Visualization and Computer Graphics
Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps
IEEE Transactions on Visualization and Computer Graphics
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Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations. © 2012 Wiley Periodicals, Inc.