Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Image-guided streamline placement
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A flow-guided streamline seeding strategy
Proceedings of the conference on Visualization '00
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
An Advanced Evenly-Spaced Streamline Placement Algorithm
IEEE Transactions on Visualization and Computer Graphics
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Computation of Localized Flow for Steady and Unsteady Vector Fields and Its Applications
IEEE Transactions on Visualization and Computer Graphics
Similarity-Guided Streamline Placement with Error Evaluation
IEEE Transactions on Visualization and Computer Graphics
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Efficient Morse Decompositions of Vector Fields
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
International Journal of Computer Vision
Topology-Aware Evenly Spaced Streamline Placement
IEEE Transactions on Visualization and Computer Graphics
An Information-Theoretic Framework for Flow Visualization
IEEE Transactions on Visualization and Computer Graphics
Morse Set Classification and Hierarchical Refinement Using Conley Index
IEEE Transactions on Visualization and Computer Graphics
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Visual reconstructability as a quality metric for flow visualization
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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Methods for vector field visualization strive to have a sparse representation of the field, while encoding all of its important features. Streamline visualization is one of the most popular such methods. Traditionally, a set of streamline methods have focused on capturing the salient features of the vector field such as sources, sinks, and vortices. However, not all features are created equal, and some features of the vector field are more important than others, which could simply be mere noise. It is this problem of characterizing feature importance through streamline visualization that we try to address in this paper. Specifically, a given 2D vector field can be decomposed into a rotation-free (gradient) component, divergence-free (curl) component and a harmonic component by the so-called Hodge decomposition. Features in the original vector field, in some sense, correspond to features in the first two components. Furthermore, the gradient and curl components are each induced by a scalar field. By analyzing these two corresponding scalar fields using topological methods (in particular the contour tree and the persistent homology), we develop a simple and novel algorithm whose streamline density tends to reflect the topological importance of the features in the input vector field. Such a feature-aware streamline sketch is more informative, yet still simple both visually and in terms of its generation. It enhances our understanding of the underlying vector field, which is demonstrated here by several experimental results.