A topology simplification method for 2D vector fields
Proceedings of the conference on Visualization '00
Detection and Visualization of Closed Streamlines in Planar Flows
IEEE Transactions on Visualization and Computer Graphics
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Higher Order Singularities in Piecewise Linear Vector Fields
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Investigating Swirl and Tumble Flow with a Comparison of Visualization Techniques
VIS '04 Proceedings of the conference on Visualization '04
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Efficient Morse Decompositions of Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Computing Robustness and Persistence for Images
IEEE Transactions on Visualization and Computer Graphics
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
Towards multifield scalar topology based on pareto optimality
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Numerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the input. This paper introduces a technique to compute topological features of user-prescribed stability with respect to perturbation of the input vector field. In order to make our approach simple and efficient, we develop our algorithms for the case of piecewise constant (PC) vector fields. Our approach is based on a super-transition graph, a common graph representation of all PC vector fields whose vector value in a mesh triangle is contained in a convex set of vectors associated with that triangle. The graph is used to compute a Morse decomposition that is coarse enough to be correct for all vector fields satisfying the constraint. Apart from computing stable Morse decompositions, our technique can also be used to estimate the stability of Morse sets with respect to perturbation of the vector field or to compute topological features of continuous vector fields using the PC framework.