Toward Effective Visualization of Ultrascale TimeVarying Data HanWei

Toward Effective Visualization of Ultra-scale Time-Varying Data Han-Wei Shen Associate Professor The Ohio State University SC 05 Time-Varying Visualization Workshop

Applications • Large Scale Time-Dependent Simulations • Richtmyer-Meshkov Turbulent Simulation (LLNL) – 2048 x 1920 grid per time step (7. 7 GB) – Run 27, 000 time steps – Multi-terabytes output LLNL IBM ASCI system SC 05 Time-Varying Visualization Workshop

Applications • Oak Ridge Terascale Supernova Initiative (TSI) – 640 x 640 floats – > 1000 time steps – Total size > 1 TB • NASA’s turbo pump simulation – – ORNL TSI data Multi-zones Moving meshes 300+ time steps Total size > 100 GB NASA turbo pump SC 05 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 SC 05 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 SC 05 Time-Varying Visualization Workshop

Bricking and Multi-resolution • Bricking – subdivide the volume into mutiple blocks SC 05 Time-Varying Visualization Workshop

Bricking and Multi-resolution • Create a multi-resolution representation for each block SC 05 Time-Varying Visualization Workshop

Spatial Data Hierarchy • Combining octree with multi-res transform bricks SC 05 Time-Varying Visualization Workshop

Temporal Data Hierarchy? • Option 1 - Multiple Octrees t=0 t=1 SC 05 Time-Varying Visualization Workshop t=2…

Temporal Data Hierarchy? • Option 2: Treat time as another dimension – a single 4 D tree (16 tree) … SC 05 Time-Varying Visualization Workshop

Time-Space Partition (TSP) Tree (Two Level Hierarchical Subdivision) • First level: spatial subdivision bricks “Shallow” Complete Octree SC 05 Time-Varying Visualization Workshop

Time-Space Partition (TSP) Tree (Two Level Hierarchical Subdivision) • Second level: temporal subdivision [0, 3] [0, 1] T= 0 4 time steps SC 05 Time-Varying Visualization Workshop [2, 3] 1 2 3

Spatio-Temporal Data Encoding • Wavelet Transform (DWT) 3 D wavelet transform 1 D WT SC 05 Time-Varying Visualization Workshop

Spatio-Temporal Data Indexing • Time-Space Partitioning (TSP) Trees SC 05 Time-Varying Visualization Workshop

Tree Traversal and Rendering T=1 [0, 3] [0, 1] T= 0 SC 05 Time-Varying Visualization Workshop [2, 3] 1 2 3

Image Compositing Front-to-back SC 05 Time-Varying Visualization Workshop

Rendering Performance • The cached partial images can be re-used for the nodes that have high temporal coherence [0, 3] [0, 1] T= 0 3 [2, 3] 1 SC 05 Time-Varying Visualization Workshop 2

Time-Varying Volume Rendering Error = 0 E = 0. 05 (3. 4% image diff. ) 11. 2 speedup SC 05 Time-Varying Visualization Workshop

I/O Efficiency Shock wave: 1024 x 128 , 40 time steps Minimum brick size 32 x 32 Temporal error tolerance = 0. 02 Time Step 0 # Bricks Loaded 561 73 100 % 13. 0 % Percentage 10 20 30 75 72 13. 3 % SC 05 Time-Varying Visualization Workshop 12. 8%

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 SC 05 Time-Varying Visualization Workshop

Analyzing Time-varying Features • Animation might not be sufficient SC 05 Time-Varying Visualization Workshop

Strategy 1: Tracking individual components SC 05 Time-Varying Visualization Workshop

Strategy 2: High Dimensional Visualization • Chronovolumes SC 05 Time-Varying Visualization Workshop

Tracking Time-Varying Isosurface • Two main goals: – Identify correspondence ? – Detect important evolution events and critical time steps SC 05 Time-Varying Visualization Workshop

Evolutionary Events SC 05 Time-Varying Visualization Workshop

Tracking Correspondence • Wang and Silver’s assumption - Corresponding features in adjacent time steps overlap with each other SC 05 Time-Varying Visualization Workshop

Tracking Correspondence • A common assumption - Corresponding features in adjacent time steps overlap with each other t=0 t=1 SC 05 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. SC 05 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 (4 D) isosurfaces SC 05 Time-Varying Visualization Workshop

2 D Example • 2 D time-varying isocontours T=2 T=1 T=0 SC 05 Time-Varying Visualization Workshop

2 D Example • Extract 3 D isosurface and then slice back T=2 T=1 T=0 SC 05 Time-Varying Visualization Workshop

2 D Example • Extract 3 D isosurface and then slice back T=2 T=1 T=0 SC 05 Time-Varying Visualization Workshop

4 D Isosurface • 3 D time-varying = 4 D • Extract “isosurfaces” from 4 D hypercubes • Use 4 D maching cubes table (Bhaniramka’ 02) (x, y, z, t) • Slice the tetrahedra to get the surface at the desired time step SC 05 Time-Varying Visualization Workshop

Algorithm To track an isosurface component: • User chooses a local component at t • Propagate 4 D “isosurface” from the seed • Slice the 4 D isosurface at t+1 • Continue to t+2 if desired SC 05 Time-Varying Visualization Workshop

Detect critical time steps for isosurface tracking • A 4 D isocontour component is a tetrahedral mesh embedded in four dimensional space. We can treat the 4 D mesh as a normal 3 D 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 Local maximum Saddle Regular vertex Creation Dissipation Amalgamation/Bifurcation Continuation SC 05 Time-Varying Visualization Workshop

Color the components SC 05 Time-Varying Visualization Workshop

Color the components SC 05 Time-Varying Visualization Workshop

Critical Time Steps SC 05 Time-Varying Visualization Workshop

Chronovolumes • A Direct Rendering Technique for Visualizing Time-Varying Data (Jonathan Woodring and Han-Wei Shen 2003) SC 05 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 SC 05 Time-Varying Visualization Workshop

Early Work Chronophtography (Marey, 1830 -1904) Nude descending a staircase – Duchamp, 1912 SC 05 Time-Varying Visualization Workshop

Chronovolumes • 4 D rendering idea • Integration through time – Integration functions SC 05 Time-Varying Visualization Workshop

4 D Rendering • Direct visualization of 4 D data • Project the 4 D data into a visualizable lower dimensional space (2 D images) 2 D -> 1 D 3 D -> 2 D SC 05 Time-Varying Visualization Workshop

4 D Rendering • 4 D to 2 D projection? • Need to preserve the relationships between different objects in (3 D) space and also reveal their relationship in time SC 05 Time-Varying Visualization Workshop

Integration Through Time 1. 4 D to 3 D projection (chronovolume) 2. Regular volume rendering to visualize chronovolumes T t t+1 t+2 t+3 t+4 … SC 05 Time-Varying Visualization Workshop chronovolume

Integration Function • Vc = F (Vt, 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+4 … t+3 t t+1 t+2 SC 05 Time-Varying Visualization Workshop T

Alpha Compositing • Commonly used in 3 D volume rendering D C 0 t D C = c(s(x(t)) e - a(s(x(t’)))dt’ 0 0 2 D Image SC 05 Time-Varying Visualization Workshop dt

Alpha Compositing (2) • Adopt the model to time integration T … t+4 T C = c(s(x(t)) e t - a(s(x(t’)))dt’ 0 dt 0 t+3 t+2 t t+1 post-classified (color) volume SC 05 Time-Varying Visualization Workshop

Transfer Function • Color and opacity function t T C = c(s(x(t)) e - a(s(x(t’)))dt’ 0 dt 0 • Modulate by time stamp and data Alpha function example: a 0. 2 3 8 t * a 0. 7 6 SC 05 Time-Varying Visualization Workshop v

Alpha Compositing Example 10 time steps 3 time steps SC 05 Time-Varying Visualization Workshop

Additive Colors • Show features overlap T … t+4 T ~ C = c(s(x(t)) dt 0 t+3 t+2 t t+1 SC 05 Time-Varying Visualization Workshop

Additive Color Example Alpha Compositing Additive Color SC 05 Time-Varying Visualization Workshop

Additive Color Example Alpha Compositing Additive Colors SC 05 Time-Varying Visualization Workshop

Additive Color Example Alpha Compositing Additive Colors SC 05 Time-Varying Visualization Workshop

Min/Max Intensity • Detect the ‘hot spot’ T … F(V i) = t such that V t > Vi for any i < t+4 t+3 t+2 t t+1 • Show which time step has the highest (lowest) value, and also what that value is. SC 05 Time-Varying Visualization Workshop

Maximum Intensity Example Additive Colors Maximum Intensity SC 05 Time-Varying Visualization Workshop

Maximum Intensity Examples Alpha Compositing Maximum Intensity SC 05 Time-Varying Visualization Workshop