1. SC05 Time-Varying Visualization Workshop Toward Effective Visualization of Ultra-scale Time-Varying Data Han-Wei Shen Associate Professor The Ohio State University

2. SC05 Time-Varying Visualization Workshop Applications Large Scale Time- Dependent Simulations Richtmyer-Meshkov Turbulent Simulation (LLNL) –2048x2048x1920 grid per time step (7.7 GB) –Run 27,000 time steps –Multi-terabytes output LLNL IBM ASCI system

3. SC05 Time-Varying Visualization Workshop Applications Oak Ridge Terascale Supernova Initiative (TSI) –640x640x640 floats –> 1000 time steps –Total size > 1 TB NASAs turbo pump simulation – Multi-zones –Moving meshes –300+ time steps –Total size > 100GB ORNL TSI data NASA turbo pump

4. SC05 Time-Varying Visualization Workshop Research Goals and Challenges Interactive data exploration Quick overview, detail on demand Feature enhancement and tracking Display the invisible Understand the evolution of salient features over time Challenges managing, indexing, and processing of data

5. SC05 Time-Varying Visualization Workshop Research Focuses Multi-resolution data management schemes Acceleration Techniques –Efficient data indexing –Coherence exploitation –Effective data culling –Parallel and distributed processing Feature tracking and enhancement –Visual representation –Geometric tracking

6. SC05 Time-Varying Visualization Workshop Bricking and Multi-resolution Bricking – subdivide the volume into mutiple blocks

7. SC05 Time-Varying Visualization Workshop Bricking and Multi-resolution Create a multi-resolution representation for each block

8. SC05 Time-Varying Visualization Workshop Spatial Data Hierarchy Combining octree with multi-res transform bricks

9. SC05 Time-Varying Visualization Workshop Temporal Data Hierarchy? Option1 - Multiple Octrees t = 0 t = 1 t = 2 …

10. SC05 Time-Varying Visualization Workshop Temporal Data Hierarchy? Option 2: Treat time as another dimension – a single 4D tree (16 tree) …

11. SC05 Time-Varying Visualization Workshop First level: spatial subdivision Time-Space Partition (TSP) Tree (Two Level Hierarchical Subdivision) Shallow Complete Octree bricks

12. SC05 Time-Varying Visualization Workshop Second level: temporal subdivision Time-Space Partition (TSP) Tree (Two Level Hierarchical Subdivision) T= 0 1 2 3 [0,3] [0,1][2,3] 4 time steps

13. SC05 Time-Varying Visualization Workshop Spatio-Temporal Data Encoding Wavelet Transform (DWT) 3D wavelet transform 1D WT

14. SC05 Time-Varying Visualization Workshop Spatio-Temporal Data Indexing Time-Space Partitioning (TSP) Trees

15. SC05 Time-Varying Visualization Workshop Tree Traversal and Rendering T= 0 1 2 3 [0,3] [0,1][2,3] T = 1

16. SC05 Time-Varying Visualization Workshop Image Compositing Front-to-back

17. SC05 Time-Varying Visualization Workshop Rendering Performance The cached partial images can be re-used for the nodes that have high temporal coherence T= 0 1 2 3 [0,3] [0,1][2,3]

18. SC05 Time-Varying Visualization Workshop E = 0.05 (3.4% image diff.) Time-Varying Volume Rendering Error = 0 11.2 speedup

19. SC05 Time-Varying Visualization Workshop I/O Efficiency Shock wave: 1024 x 128 x 128, 40 time steps Minimum brick size 32 x 32 x 32 Temporal error tolerance = 0.02 Time Step # Bricks Loaded Percentage 0 102030 561737572 100 %13.0 %13.3 %12.8%

20. SC05 Time-Varying Visualization Workshop Time-Space Partition (TSP) Tree More cohesively integrate the temporal and spatial information into a single hierarchical data structure Exploit both temporal and spatial coherence - Octree becomes a special case of the TSP tree

21. SC05 Time-Varying Visualization Workshop Analyzing Time-varying Features Animation might not be sufficient

22. SC05 Time-Varying Visualization Workshop Strategy 1: Tracking individual components

23. SC05 Time-Varying Visualization Workshop Strategy 2: High Dimensional Visualization Chronovolumes

24. SC05 Time-Varying Visualization Workshop Tracking Time-Varying Isosurface Two main goals: –Identify correspondence –Detect important evolution events and critical time steps ?

25. SC05 Time-Varying Visualization Workshop Evolutionary Events

26. SC05 Time-Varying Visualization Workshop Tracking Correspondence Wang and Silvers assumption - Corresponding features in adjacent time steps overlap with each other

27. SC05 Time-Varying Visualization Workshop Tracking Correspondence A common assumption - Corresponding features in adjacent time steps overlap with each other t = 0 t = 1

28. SC05 Time-Varying Visualization Workshop Previous Approach Algorithm: 1.Extract the complete set of isosurfaces 2.Overlap test 1.Overlapping features are identified and the number of intersecting nodes is calculated. 3.Best matching test 1.Find the best match among features.

29. SC05 Time-Varying Visualization Workshop Challenges Exhaust search is expensive Solution: A local tracking –The user selects a local feature of interest and start tracking –Extract high dimensional (4D) isosurfaces

30. SC05 Time-Varying Visualization Workshop 2D Example 2D time-varying isocontours T = 0 T = 1 T = 2

31. SC05 Time-Varying Visualization Workshop 2D Example Extract 3D isosurface and then slice back T = 0 T = 1 T = 2

32. SC05 Time-Varying Visualization Workshop 2D Example Extract 3D isosurface and then slice back T = 0 T = 1 T = 2

33. SC05 Time-Varying Visualization Workshop 4D Isosurface 3D time-varying = 4D Extract isosurfaces from 4D hypercubes Use 4D maching cubes table (Bhaniramka02) Slice the tetrahedra to get the surface at the desired time step (x,y,z,t)

34. SC05 Time-Varying Visualization Workshop Algorithm To track an isosurface component: User chooses a local component at t Propagate 4D isosurface from the seed Slice the 4D isosurface at t+1 Continue to t+2 if desired

35. SC05 Time-Varying Visualization Workshop Detect critical time steps for isosurface tracking A 4D isocontour component is a tetrahedral mesh embedded in four dimensional space. We can treat the 4D mesh as a normal 3D mesh, with the time values as the scalar values defined over the tetrahedron vertices. The critical points of this mesh indicate when and where the topology of the isosurface will change. –Local minimum Creation –Local maximum Dissipation –Saddle Amalgamation/Bifurcation –Regular vertex Continuation

36. SC05 Time-Varying Visualization Workshop Color the components

37. SC05 Time-Varying Visualization Workshop Color the components

38. SC05 Time-Varying Visualization Workshop Critical Time Steps

39. SC05 Time-Varying Visualization Workshop Chronovolumes A Direct Rendering Technique for Visualizing Time-Varying Data (Jonathan Woodring and Han-Wei Shen 2003)

40. SC05 Time-Varying Visualization Workshop Main Idea Render data at different time steps to a single image –Establish correspondences between features –Compare shapes and sizes of features in time –Reason about the positions of the features –Reveal temporal trend

41. SC05 Time-Varying Visualization Workshop Early Work Chronophtography (Marey, 1830-1904) Nude descending a staircase – Duchamp, 1912

42. SC05 Time-Varying Visualization Workshop Chronovolumes 4D rendering idea Integration through time –Integration functions

43. SC05 Time-Varying Visualization Workshop 4D Rendering Direct visualization of 4D data Project the 4D data into a visualizable lower dimensional space (2D images) 2D -> 1D3D -> 2D

44. SC05 Time-Varying Visualization Workshop 4D Rendering 4D to 2D projection? Need to preserve the relationships between different objects in (3D) space and also reveal their relationship in time

45. SC05 Time-Varying Visualization Workshop Integration Through Time 1.4D to 3D projection (chronovolume) 2.Regular volume rendering to visualize chronovolumes t t+1 t+2 t+3 t+4 … T chronovolume

46. SC05 Time-Varying Visualization Workshop Integration Function Vc = F (V t, V t+1, V t+2, V t+3, …, V t+n- 1) No so called correct integration – the design of F depends on the visualization need t t+1 t+2 t+3 t+4 … T ???

47. SC05 Time-Varying Visualization Workshop Alpha Compositing Commonly used in 3D volume rendering C = c(s(x(t)) e dt - a(s(x(t)))dt 0 D 0 t C 0 D 2D Image

48. SC05 Time-Varying Visualization Workshop Alpha Compositing (2) Adopt the model to time integration t t+1 t+2 t+3 t+4 … T C = c(s(x(t)) e dt - a(s(x(t)))dt 0 T 0 t post-classified (color) volume

49. SC05 Time-Varying Visualization Workshop Transfer Function Color and opacity function Modulate by time stamp and data C = c(s(x(t)) e dt - a(s(x(t)))dt 0 T 0 t t v * Alpha function example: 3 8 0.20.7 6

50. SC05 Time-Varying Visualization Workshop Alpha Compositing Example 10 time steps 3 time steps

51. SC05 Time-Varying Visualization Workshop Additive Colors Show how features overlap t t+1 t+2 t+3 t+4 … T C = c(s(x(t)) dt 0 T ~

52. SC05 Time-Varying Visualization Workshop Additive Color Example Alpha Compositing Additive Color

53. SC05 Time-Varying Visualization Workshop Additive Color Example Alpha Compositing Additive Colors

54. SC05 Time-Varying Visualization Workshop Additive Color Example Alpha Compositing Additive Colors

55. SC05 Time-Varying Visualization Workshop Min/Max Intensity Detect the hot spot t t+1 t+2 t+3 t+4 … T F(V i ) = such that V > V i for any i < Show which time step has the highest (lowest) value, and also what that value is.

56. SC05 Time-Varying Visualization Workshop Maximum Intensity Example Additive Colors Maximum Intensity

57. SC05 Time-Varying Visualization Workshop Maximum Intensity Examples Alpha Compositing Maximum Intensity