sc05 time-varying visualization workshop toward effective visualization of ultra-scale time-varying...

SC05 Time-Varying Visualization Workshop

Toward Effective Visualization of Ultra-scale Time-Varying

Han-Wei Shen Associate Professor

The Ohio State University

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

Applications • Oak Ridge Terascale

Supernova Initiative (TSI)– 640x640x640 floats– > 1000 time steps– Total size > 1 TB

• NASA’s turbo pump simulation – Multi-zones – Moving meshes – 300+ time steps – Total size > 100GB

ORNL TSI data

NASA turbo pump

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

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

Bricking and Multi-resolution• Bricking – subdivide the volume into

mutiple blocks

Bricking and Multi-resolution• Create a multi-resolution representation

for each block

Spatial Data Hierarchy

• Combining octree with multi-res transform

bricks

Temporal Data Hierarchy?

• Option1 - Multiple Octrees

t = 0 t = 1 t = 2 …

Temporal Data Hierarchy?

• Option 2: Treat time as another dimension – a single 4D tree (16 tree)

• First level: spatial subdivision

Time-Space Partition (TSP) Tree(Two Level Hierarchical Subdivision)

“Shallow” Complete Octree

bricks

• Second level: temporal subdivision

Time-Space Partition (TSP) Tree(Two Level Hierarchical Subdivision)

T= 0 1 2 3

[0,1] [2,3]

4 time steps

Spatio-Temporal Data Encoding

• Wavelet Transform (DWT)

3D wavelet transform

Spatio-Temporal Data Indexing• Time-Space Partitioning (TSP) Trees

Tree Traversal and Rendering

T= 0 1 2 3

[0,1] [2,3]

Image Compositing

Front-to-back

Rendering Performance

• The cached partial images can be re-used for the nodes that have high temporal coherence

T= 0 1 2 3

[0,1] [2,3]

E = 0.05 (3.4% image diff.)

Time-Varying Volume Rendering

Error = 0

11.2 speedup

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 10 20 30

561 73 75 72

100 % 13.0 % 13.3 % 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

Analyzing Time-varying Features

• Animation might not be sufficient

Strategy 1: Tracking individual components

Strategy 2: High Dimensional Visualization

• Chronovolumes

Tracking Time-Varying Isosurface

• Two main goals:– Identify correspondence

– Detect important evolution events and critical time steps

Evolutionary Events

Tracking Correspondence

• Wang and Silver’s assumption - Corresponding features in adjacent time steps overlap with each other

Tracking Correspondence

• A common assumption - Corresponding features in adjacent time steps overlap with each other

t = 0t = 1

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 test1. Find the best match among features.

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

2D Example

• 2D time-varying isocontours

2D Example

• Extract 3D isosurface and then slice back

2D Example

• Extract 3D isosurface and then slice back

4D Isosurface

• 3D time-varying = 4D • Extract “isosurfaces” from 4D hypercubes• Use 4D maching cubes table (Bhaniramka’02)

• Slice the tetrahedra to get the surface at the desired time step

(x,y,z,t)

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

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

Color the components

Critical Time Steps

Chronovolumes

• A Direct Rendering Technique for Visualizing Time-Varying Data

(Jonathan Woodring and Han-Wei Shen 2003)

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

Early Work

Chronophtography (Marey, 1830-1904)

Nude descending a staircase – Duchamp, 1912

Chronovolumes

• 4D rendering idea

• Integration through time– Integration functions

4D Rendering • Direct visualization of 4D data

• Project the 4D data into a visualizable lower dimensional space (2D images)

2D -> 1D 3D -> 2D

4D Rendering

• 4D to 2D projection?

• Need to preserve the relationships between different objects in (3D) space and also reveal their relationship in time

Integration Through Time

1. 4D to 3D projection (chronovolume)

2. Regular volume rendering to visualize chronovolumes

t+2 t+3t+4 …

T 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+2 t+3t+4 …

Alpha Compositing

• Commonly used in 3D volume rendering

C = c(s(x(t)) e dt - a(s(x(t’)))dt’

2D Image

Alpha Compositing (2)

• Adopt the model to time integration

t+2t+3

post-classified (color) volume

Transfer Function

• Color and opacity function

• Modulate by time stamp and data

Alpha function example:

0.2 0.7

Alpha Compositing Example

10 time steps 3 time steps

Additive Colors

• Show how features overlap

t+2t+3

C = c(s(x(t)) dt 0

Additive Color Example

Alpha Compositing Additive Color

Alpha Compositing Additive Colors

Min/Max Intensity

• Detect the ‘hot spot’

t+2t+3

T F(V i) = such that V > Vi for any i<

• Show which time step has the highest(lowest) value, and also what that value is.

Maximum Intensity Example

Additive Colors Maximum Intensity

Maximum Intensity Examples

Alpha Compositing Maximum Intensity

sc05 time-varying visualization workshop toward effective visualization of ultra-scale time-varying...

time challenges

tree slide

processing of data slide

time steps total size

speedup slide

block slide

time steps minimum brick

d wt slide

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