Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Computing contour trees in all dimensions
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Continuous topology simplification of planar vector fields
Proceedings of the conference on Visualization '01
Visualizing Nonlinear Vector Field Topology
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
Trekking in the Alps Without Freezing or Getting Tired
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Stability of Critical Points with Interval Persistence
Discrete & Computational Geometry
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Quantifying Transversality by Measuring the Robustness of Intersections
Foundations of Computational Mathematics
Fast Combinatorial Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields
IEEE Transactions on Visualization and Computer Graphics
Visual 4D MRI blood flow analysis with line predicates
PACIFICVIS '12 Proceedings of the 2012 IEEE Pacific Visualization Symposium
Efficient Computation of Combinatorial Feature Flow Fields
IEEE Transactions on Visualization and Computer Graphics
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Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features.