Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
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
Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles
SIAM Journal on Scientific Computing
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
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)
IEEE Transactions on Visualization and Computer Graphics
Texture-Based Visualization of Unsteady 3D Flow by Real-Time Advection and Volumetric Illumination
IEEE Transactions on Visualization and Computer Graphics
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications
IEEE Transactions on Visualization and Computer Graphics
Efficient Morse Decompositions of Vector Fields
IEEE Transactions on Visualization and Computer Graphics
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
Smoke Surfaces: An Interactive Flow Visualization Technique Inspired by Real-World Flow Experiments
IEEE Transactions on Visualization and Computer Graphics
Uncertain topology of 3D vector fields
PACIFICVIS '11 Proceedings of the 2011 IEEE Pacific Visualization Symposium
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
Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps
IEEE Transactions on Visualization and Computer Graphics
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We present an algorithm for computing nearly recurrent components, that represent areas of close to circulating or stagnant flow, for 3D piecewise constant (PC) vector fields defined on regular grids. Using a number of analytical and simulated data sets, we demonstrate that nearly recurrent components can provide interesting insight into the topological structure of 3D vector fields. Our approach is based on prior work on Morse decompositions for PC vector fields on surfaces and extends concepts previously developed with this goal in mind to the case of 3D vector fields defined on regular grids. Our contributions include a description of trajectories of 3D piecewise constant vector fields and an extension of the transition graph, a finite directed graph that represents all trajectories, to the 3D case. Nearly recurrent components are defined by strongly connected components of the transition graph. © 2012 Wiley Periodicals, Inc.