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Higher Dimensional Vector Field Visualization: A Survey

Zhenmin Peng, Robert S. Laramee

Department of Computer ScienceSwansea University, Wales UK

Email: {cszp, r.s.laramee}@swansea.ac.uk

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Overview

IntroductionIntroduction DimensionsDimensions ClassificationClassification

• Direct Flow VisualizationDirect Flow Visualization• Vector-field ClusteringVector-field Clustering• Texture-based TechniquesTexture-based Techniques• Geometric TechniquesGeometric Techniques

ConclusionConclusion

Streamsurface visualization of smokes [MLZ09]Streamsurface visualization of smokes [MLZ09]

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IntroductionWhat’s Vector Field Visualization?What’s Vector Field Visualization? A sub-branch of scientific visualizationA sub-branch of scientific visualization

Depiction of magnitude + direction (as opposed to scalar field vis)Depiction of magnitude + direction (as opposed to scalar field vis)

Various applications in our daily life: automotive simulation, Various applications in our daily life: automotive simulation,

aerodynamics, turbo machinery, meteorology, oceanography, aerodynamics, turbo machinery, meteorology, oceanography,

medical visualizationmedical visualization

Visualization of flow around a car [Garth’08]Visualization of flow around a car [Garth’08]Arrows showing the wind Arrows showing the wind

direction and magnitude [Turk’96]direction and magnitude [Turk’96]

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Introduction

What’s the motivation of this paper?What’s the motivation of this paper? The challenge of 2D flow visualization is virtually solvedThe challenge of 2D flow visualization is virtually solved

Higher dimensional (2.5D & 3D) flow visualization is still facing Higher dimensional (2.5D & 3D) flow visualization is still facing

many challenges like: coping with large, time-dependent data many challenges like: coping with large, time-dependent data

sets, perceptual difficulties and so onsets, perceptual difficulties and so on

Focus on the most recent developments in higher dimensional Focus on the most recent developments in higher dimensional

flow visualization techniquesflow visualization techniques

Highlighting both solved and unsolved problemsHighlighting both solved and unsolved problems

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Dimensions

Spatial dimension:Spatial dimension: 2D (planar flow)2D (planar flow)

2.5D (boundary flow, flow on surface)2.5D (boundary flow, flow on surface)

3D (real-world flow, volumetric flow)3D (real-world flow, volumetric flow)

Temporal dimension:Temporal dimension: Steady flow - one time step (or instantaneous or static flow)Steady flow - one time step (or instantaneous or static flow)

Time-dependent flow - multiple time steps (or unsteady or Time-dependent flow - multiple time steps (or unsteady or

transient, real-world)transient, real-world)

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Classification Direct: Direct: overview of vector field, minimal overview of vector field, minimal

computation, e.g. glyphs, colour mappingcomputation, e.g. glyphs, colour mapping

Feature-based:Feature-based: provides suggestive provides suggestive

visualization by extracting subsets of data before visualization by extracting subsets of data before

visualization, e.g. vector field clusteringvisualization, e.g. vector field clustering

Texture-based:Texture-based: covers domain with a convolved covers domain with a convolved

texture, e.g., Spot Noise, LIC, ISA, IBFV(S)texture, e.g., Spot Noise, LIC, ISA, IBFV(S)

Geometric:Geometric: coherent representation, integration- coherent representation, integration-

based geometric techniques, e.g. streamlinesbased geometric techniques, e.g. streamlines

Vector field clusteringVector field clustering

Hedgehog Hedgehog

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Survey Overview

*Related previous work in 2D is indicated by sub-scripts*Related previous work in 2D is indicated by sub-scripts

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Direct Flow VisualizationVector Glyphs for Surfaces: A Fast and Simple Glyph PlacementVector Glyphs for Surfaces: A Fast and Simple Glyph PlacementAlgorithm for Adaptive Resolution MeshesAlgorithm for Adaptive Resolution Meshes ( (Peng and Laramee ‘08Peng and Laramee ‘08))

Dimensions:Dimensions: 2.5D, Steady 2.5D, Steady

Predecessor:Predecessor: 2D method of [Lar03] 2D method of [Lar03]

Concept:Concept: a simple, fast, and general a simple, fast, and general

glyph placement for surfacesglyph placement for surfaces

Implementation:Implementation:

Project vector field to image planeProject vector field to image plane

Reconstruction & glyph placement Reconstruction & glyph placement

are performed in image spaceare performed in image space

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Vector Field Clustering VisualizationSimplified Representation of Vector FieldsSimplified Representation of Vector Fields ( (Telea and van Wijk ‘99Telea and van Wijk ‘99))

Dimensions:Dimensions: 3D, Steady 3D, Steady

Concept:Concept: a hierarchical clustering a hierarchical clustering

based method which presents a based method which presents a

suggestive overview of vector fieldssuggestive overview of vector fields

Implementation:Implementation:

Bottom-up fashion Bottom-up fashion

Merger driven by similarity error Merger driven by similarity error

metricmetric

InteractionInteraction

Simplification of 3D flow [TvW99] Simplification of 3D flow [TvW99]

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Texture-based VisualizationImage Space Based Visualization of Unsteady Flow on SurfacesImage Space Based Visualization of Unsteady Flow on Surfaces((Laramee et al. ‘03Laramee et al. ‘03))

Dimensions:Dimensions: 2.5D, Unsteady 2.5D, Unsteady Predecessor:Predecessor: IBFV (2D) [vW02] IBFV (2D) [vW02] Concept:Concept: dense and coherent dense and coherent

representations for unsteady flow on representations for unsteady flow on surfacessurfaces

Implementation:Implementation: Project vector field to image space Project vector field to image space Advection mesh is distorted Advection mesh is distorted

according to pathlinesaccording to pathlines Texture is distorted and attached Texture is distorted and attached

based on the distorted meshbased on the distorted mesh Blend noise in image spaceBlend noise in image space

Gas Engine Simulation [LJH03] Gas Engine Simulation [LJH03]

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Texture-based VisualizationHigh-Quality and Interactive Animations of 3D High-Quality and Interactive Animations of 3D Time-Varying Vector Fields Time-Varying Vector Fields ((Helgeland & Elboth Helgeland & Elboth ‘06‘06))

Dimensions:Dimensions: 3D, Unsteady 3D, Unsteady Predecessor:Predecessor: DLIC (2D) [Sun03] DLIC (2D) [Sun03] Concept:Concept: efficiently and interactively efficiently and interactively

visualize unsteady 3D flow in sparse visualize unsteady 3D flow in sparse fashionfashion

Implementation:Implementation: Particles are evenly distributed to Particles are evenly distributed to

obtain pathlinesobtain pathlines A novel particle advection strategy A novel particle advection strategy

maintains the coherent particle density maintains the coherent particle density at each time stepat each time step

3D texture generated for each time step3D texture generated for each time step interactioninteraction

visualization of the hurricane velocity field visualization of the hurricane velocity field [HE06] [HE06]

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Geometric-based VisualizationEvenly-Spaced Streamlines for Surfaces: An Image-Based ApproachEvenly-Spaced Streamlines for Surfaces: An Image-Based Approach((Spencer et al. '09Spencer et al. '09))

Dimensions:Dimensions: 2.5D, Steady 2.5D, Steady Predecessor:Predecessor: Jobard and Lefer’s 2D Jobard and Lefer’s 2D

method [JL97]method [JL97] Concept:Concept: general streamline general streamline

placement for surfacesplacement for surfaces Implementation:Implementation:

Project vector field to image Project vector field to image space space

Perform streamline integration Perform streamline integration in image spacein image space

InteractionsInteractionsVisualization of flow at the surface Visualization of flow at the surface

of a cooling jacket.[SLCZ09] of a cooling jacket.[SLCZ09]

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Geometric-based VisualizationSmoke Surfaces: An Interactive Flow Visualization TechniqueSmoke Surfaces: An Interactive Flow Visualization Technique

Inspired by Real-World Flow Experiments (Inspired by Real-World Flow Experiments (Von Funck et al. '08Von Funck et al. '08))

Dimensions:Dimensions: 3D, Unsteady 3D, Unsteady Concept:Concept: efficient representation of efficient representation of

smoke surfaces in 3D spacesmoke surfaces in 3D space Implementation:Implementation:

Semi-transparent streak surfaces Semi-transparent streak surfaces Coupling the opacity to area, Coupling the opacity to area,

shapes and curvaturesshapes and curvatures With a fixed topology and With a fixed topology and

connectivityconnectivity Interactive explorationInteractive exploration

[vFWTS08] [vFWTS08]

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Conclusion

Dimensions and classifications.Dimensions and classifications. Up-to-date overview of the vector field visualization in higher Up-to-date overview of the vector field visualization in higher

dimensions.dimensions. Highlighting both mature areas and immature areas in higher Highlighting both mature areas and immature areas in higher

dimensional flow visualization.dimensional flow visualization.

Future Work:Future Work: Time-dependent flow datasets Time-dependent flow datasets Visual complexity and occlusionVisual complexity and occlusion Automatic or semi-automatic selection and simplification Automatic or semi-automatic selection and simplification approaches for visualizationapproaches for visualization

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Classification

*Related previous work in 2D is indicated by sub-scripts*Related previous work in 2D is indicated by sub-scripts

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Acknowledgments

Thanks to:Thanks to:

TPCG 2009 TPCG 2009 EPSRCEPSRC Visual and Interactive ComputingVisual and Interactive Computing Edward GrundyEdward Grundy

Paper and related animations available at:Paper and related animations available at:

http://cs.swan.ac.uk/~cszp/http://cs.swan.ac.uk/~cszp/

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Thank you for your attention.Thank you for your attention.

Questions or Suggestions?Questions or Suggestions?