Higher Dimensional Vector Field Visualization: A Survey

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

3. Introduction What’s Vector Field Visualization? • A sub-branch of scientific visualization • 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 Visualization of flow around a car [Garth’08] Arrows showing the wind direction and magnitude [Turk’96]

4. Introduction What’s the motivation of this paper? • 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 • Focus on the most recent developments in higher dimensional flow visualization techniques • Highlighting both solved and unsolved problems

5. Dimensions Spatial dimension: • 2D (planar flow) • 2.5D (boundary flow, flow on surface) • 3D (real-world flow, volumetric flow) Temporal dimension: • Steady flow - one time step (or instantaneous or static flow) • Time-dependent flow - multiple time steps (or unsteady or transient, real-world)

6. Classification • 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 • 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 Hedgehog Vector field clustering

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

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 • Predecessor: 2D method of [Lar03] • Concept: a simple, fast, and general glyph placement for surfaces • Implementation: • Project vector field to image plane • Reconstruction & glyph placement are performed in image space

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

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

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

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

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 • Concept: efficient representation of smoke surfaces in 3D space • Implementation: • Semi-transparent streak surfaces • Coupling the opacity to area, shapes and curvatures • With a fixed topology and connectivity • Interactive exploration [vFWTS08]

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

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

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

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