Construction of vector field hierarchies

Heckel,; Weber, Gunther H.; Hamann,; Joy,

doi:10.1109/visual.1999.809863

Cited by 65 publications

(41 citation statements)

References 13 publications

(14 reference statements)

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“…A holistic overview in a coarser definition is exhibited along with clutter-free rendering. Heckel et al [6] introduced a top-down clustering method by splitting groups of voxels iteratively. This approach allows more than one level in the hierarchy to be visualized simultaneously.…”

Section: Related Workmentioning

confidence: 99%

A sketch-based interface for classifying and visualizing vector fields

Wei

Wang

et al. 2010

2010 IEEE Pacific Visualization Symposium (PacificVis)

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In flow visualization, field lines are often used to convey both global and local structure and movement of the flow. One challenge is to find and classify the representative field lines. Most existing solutions follow an automatic approach that generates field lines characterizing the flow and arranges these lines into a single picture. In our work, we advocate a user-centric approach to exploring 3D vector fields. Our method allows the user to sketch 2D curves for pattern matching in 2D and field lines clustering in 3D. Specifically, a 3D field line whose view-dependent 2D projection is most similar to the user drawing will be identified and utilized to extract all similar 3D field lines. Furthermore, we employ an automatic clustering method to generate field-line templates for the user to locate subfields of interest. This semi-automatic process leverages the user's knowledge about the flow field through intuitive user interaction, resulting in a promising alternative to existing flow visualization solutions. With our sketch-based interface, the user can effectively dissect the flow field and make more structured visualization for analysis or presentation.

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Section: Related Workmentioning

confidence: 99%

A sketch-based interface for classifying and visualizing vector fields

Wei

Wang

et al. 2010

2010 IEEE Pacific Visualization Symposium (PacificVis)

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“…Existing techniques can be classified into glyph and field-line based methods [29,16], dense texture methods [19,24], clustering-based methods [21,7,6], and topology-based methods [8,18]. Glyph or field-line visualization is particularly effective for the visualization of isolated regions in the vector field.…”

Section: Background and Related Workmentioning

confidence: 99%

Parallel hierarchical visualization of large time-varying 3D vector fields

Wang

2007

Proceedings of the 2007 ACM/IEEE Conference on Supercomputing

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We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a timeaccurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them.

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“…These methods build a hierarchical clustering tree and visualize the clusters with curved arrow icons. Heckel et al [Heckel et al 1999] place all data points in a single cluster, which is recursively split in a top-down manner. At each step, the cluster with the strongest discrepancy between streamlines generated by the original field and its approximation by the cluster is bisected by a plane, using principal component analysis.…”

Section: Introductionmentioning

confidence: 99%

Flow field clustering via algebraic multigrid

Griebel

Preußer

Rumpf

et al.

IEEE Visualization 2004

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We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite element technique. The entries of the corresponding stiffness matrix represent the anisotropically weighted couplings of adjacent nodes of the domain mesh. We use an algebraic multigrid algorithm to generate a hierarchy of fine to coarse descriptions for the above coupling data. This hierarchy comprises a set of coarse grid nodes, a multiscale of basis functions and their corresponding supports. We use these supports to obtain a multilevel decomposition of the flow structure. Standard streamline icons are used to visualize this decomposition at any user-selected level of detail. The method provides a single framework for vector field decomposition independent on the domain dimension or mesh type. Applications are shown in 2D, for flow fields on curved surfaces, and for 3D volumetric flow fields.

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Construction of vector field hierarchies

Cited by 65 publications

References 13 publications

A sketch-based interface for classifying and visualizing vector fields

A sketch-based interface for classifying and visualizing vector fields

Parallel hierarchical visualization of large time-varying 3D vector fields

Flow field clustering via algebraic multigrid

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