1. 1 Higher Dimensional Vector Field Visualization: A Survey Zhenmin Peng, Robert S. Laramee Department of Computer Science Swansea University, Wales UK Email: {cszp, r.s.laramee}@swansea.ac.uk

2. 2 Overview Introduction Introduction Dimensions Dimensions Classification Classification Direct Flow Visualization Direct Flow Visualization Vector-field Clustering Vector-field Clustering Texture-based Techniques Texture-based Techniques Geometric Techniques Geometric Techniques Conclusion Conclusion Streamsurface visualization of smokes [MLZ09]

3. 3 Introduction What’s Vector Field Visualization? A sub-branch of scientific visualization A 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, aerodynamics, turbo machinery, meteorology, oceanography, medical visualization Various applications in our daily life: automotive simulation, aerodynamics, turbo machinery, meteorology, oceanography, medical visualization Visualization of flow around a car [Garth’08] Visualization of flow around a car [Garth’08] Arrows showing the wind direction and magnitude [Turk’96]

4. 4 Introduction What’s the motivation of this paper? The challenge of 2D flow visualization is virtually solved The challenge of 2D flow visualization is virtually solved Higher dimensional (2.5D & 3D) flow visualization is still facing many challenges like: coping with large, time-dependent data sets, perceptual difficulties and so on Higher dimensional (2.5D & 3D) flow visualization is still facing many challenges like: coping with large, time-dependent data sets, perceptual difficulties and so on Focus on the most recent developments in higher dimensional flow visualization techniques Focus on the most recent developments in higher dimensional flow visualization techniques Highlighting both solved and unsolved problems Highlighting both solved and unsolved problems

5. 5 Dimensions 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: 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 transient, real-world) Time-dependent flow - multiple time steps (or unsteady or transient, real-world)

6. 6 Classification Direct: overview of vector field, minimal computation, e.g. glyphs, colour mapping Direct: overview of vector field, minimal computation, e.g. glyphs, colour mapping Feature-based: provides suggestive visualization by extracting subsets of data before visualization, e.g. vector field clustering Feature-based: provides suggestive visualization by extracting subsets of data before visualization, e.g. vector field clustering Texture-based: covers domain with a convolved texture, e.g., Spot Noise, LIC, ISA, IBFV(S) Texture-based: covers domain with a convolved texture, e.g., Spot Noise, LIC, ISA, IBFV(S) Geometric: coherent representation, integration-based geometric techniques, e.g. streamlines Geometric: coherent representation, integration-based geometric techniques, e.g. streamlines Vector field clustering Hedgehog

7. 7 Survey Overview *Related previous work in 2D is indicated by sub-scripts

8. 8 Direct Flow Visualization Vector Glyphs for Surfaces: A Fast and Simple Glyph Placement Algorithm for Adaptive Resolution Meshes ( Peng and Laramee ‘08 ) Dimensions: 2.5D, Steady Dimensions: 2.5D, Steady Predecessor: 2D method of [Lar03] Predecessor: 2D method of [Lar03] Concept: a simple, fast, and general glyph placement for surfaces Concept: a simple, fast, and general glyph placement for surfaces Implementation: Implementation: Project vector field to image plane Project vector field to image plane Reconstruction & glyph placement are performed in image space Reconstruction & glyph placement are performed in image space

9. 9 Vector Field Clustering Visualization Simplified Representation of Vector Fields ( Telea and van Wijk ‘99 ) Dimensions: 3D, Steady Dimensions: 3D, Steady Concept: a hierarchical clustering based method which presents a suggestive overview of vector fields Concept: a hierarchical clustering based method which presents a suggestive overview of vector fields Implementation: Implementation: Bottom-up fashion Bottom-up fashion Merger driven by similarity error metric Merger driven by similarity error metric Interaction Interaction Simplification of 3D flow [TvW99]

10. 10 Texture-based Visualization Image Space Based Visualization of Unsteady Flow on Surfaces ( Laramee et al. ‘03 ) Dimensions: 2.5D, Unsteady Dimensions: 2.5D, Unsteady Predecessor: IBFV (2D) [vW02] Predecessor: IBFV (2D) [vW02] Concept: dense and coherent representations for unsteady flow on surfaces Concept: dense and coherent representations for unsteady flow on surfaces Implementation: Implementation: Project vector field to image space Project vector field to image space Advection mesh is distorted according to pathlines Advection mesh is distorted according to pathlines Texture is distorted and attached based on the distorted mesh Texture is distorted and attached based on the distorted mesh Blend noise in image space Blend noise in image space Gas Engine Simulation [LJH03]

11. 11 Texture-based Visualization High-Quality and Interactive Animations of 3D Time-Varying Vector Fields ( Helgeland & Elboth ‘06 ) Dimensions: 3D, Unsteady Dimensions: 3D, Unsteady Predecessor: DLIC (2D) [Sun03] Predecessor: DLIC (2D) [Sun03] Concept: efficiently and interactively visualize unsteady 3D flow in sparse fashion Concept: efficiently and interactively visualize unsteady 3D flow in sparse fashion Implementation: Implementation: Particles are evenly distributed to obtain pathlines Particles are evenly distributed to obtain pathlines A novel particle advection strategy maintains the coherent particle density at each time step A novel particle advection strategy maintains the coherent particle density at each time step 3D texture generated for each time step 3D texture generated for each time step interaction interaction visualization of the hurricane velocity field [HE06]

12. 12 Geometric-based Visualization Evenly-Spaced Streamlines for Surfaces: An Image-Based Approach ( Spencer et al. '09 ) Dimensions: 2.5D, Steady Dimensions: 2.5D, Steady Predecessor: Jobard and Lefer’s 2D method [JL97] Predecessor: Jobard and Lefer’s 2D method [JL97] Concept: general streamline placement for surfaces Concept: general streamline placement for surfaces Implementation: Implementation: Project vector field to image space Project vector field to image space Perform streamline integration in image space Perform streamline integration in image space Interactions Interactions Visualization of flow at the surface of a cooling jacket.[SLCZ09]

13. 13 Geometric-based Visualization Smoke Surfaces: An Interactive Flow Visualization Technique Inspired by Real-World Flow Experiments ( Von Funck et al. '08 ) Dimensions: 3D, Unsteady Dimensions: 3D, Unsteady Concept: efficient representation of smoke surfaces in 3D space Concept: efficient representation of smoke surfaces in 3D space Implementation: Implementation: Semi-transparent streak surfaces Semi-transparent streak surfaces Coupling the opacity to area, shapes and curvatures Coupling the opacity to area, shapes and curvatures With a fixed topology and connectivity With a fixed topology and connectivity Interactive exploration Interactive exploration [vFWTS08]

14. 14 Conclusion Dimensions and classifications. Dimensions and classifications. Up-to-date overview of the vector field visualization in higher dimensions. Up-to-date overview of the vector field visualization in higher dimensions. Highlighting both mature areas and immature areas in higher dimensional flow visualization. Highlighting both mature areas and immature areas in higher dimensional flow visualization. Future Work: Time-dependent flow datasets Time-dependent flow datasets Visual complexity and occlusion Visual complexity and occlusion Automatic or semi-automatic selection and simplification approaches for visualization Automatic or semi-automatic selection and simplification approaches for visualization

15. 15 Classification *Related previous work in 2D is indicated by sub-scripts

16. 16 Acknowledgments Thanks to: TPCG 2009 TPCG 2009 EPSRC EPSRC Visual and Interactive Computing Visual and Interactive Computing Edward Grundy Edward Grundy Paper and related animations available at: http://cs.swan.ac.uk/~cszp/

17. 17 Thank you for your attention. Questions or Suggestions?