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Compression and remote inspection of 4D data sets Jarek Rossignac, Jack Snoeyink, and Peter Linstrom) Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003 Pentas, 1 Simulation results are huge Computed over a regular 4D grid

SLIDE 1

Pentas, 1 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Compression and remote inspection of 4D data sets

Jarek Rossignac, Jack Snoeyink, and Peter Linstrom)

SLIDE 2

Pentas, 2 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Simulation results are huge

Computed over a regular 4D grid

– 10004 (x,y,z,t) samples – Several attributes per sample (pressure, temp…): 5D terrain

Issues and proposed approaches

– Storage / transmission: Simplification, Compression, Progressive – Interactive visualization: 2D slice or level-set of hyper-surface in 5D – Decide what to inspect: Control terrain + level-of-interest + mark-up – Access only what is needed: Iso-surface tracking and updating

HPPC Storage Visualization Server Local Model Selection 3D Viewing

SLIDE 3

Pentas, 3 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Regular... or not?

(x,y,z) t P(x,y,z,t) (x,y,z) t P(x,y,z,t) pentatope in 5D

SLIDE 4

Pentas, 4 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

4D Delaunay computation and refinement

Ajith Mascarenhas and Jack Snoeyink (UNC)

SLIDE 5

Pentas, 5 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Iso-surfaces from pentatopes

Mesh of 5-simplices are 4d

surface in 5d:

– Pentatopes (4d) – Tetrahedra (3d) – Triangles (2d)

Slice away 2 dimens

to form isosurface:

– Faces (2d) – Edges (1d) – Vertices (0d)

SLIDE 6

Pentas, 6 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Yes, this is crazy…

Regular grid stores values only
mesh adds (x,y,z,t) & incidence
Allows local ref inement, so we try anyway…

28 244 7 51 2 15 Simp/vertex Words/vertex 4d: Pentatope 3d: Tetrahedron 2d: Triangle

SLIDE 7

Pentas, 7 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Incremental 4D Delaunay

As expected: Mesh requires large storage space

Can’t use simplification (full resolution mesh is too large)
Implemented insertion heuristic to build interpolating mesh

– Add points with greatest error to 4D Delaunay and retriangulate

SLIDE 8

Pentas, 8 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Severe aliasing for sections of low-

resoution penta-meshes

Iso-surface from the JetDataChunk

data-set at iso-value = 128, time = 12

Iso-surfaces at three stages of refinement

Results

vert ices: 16K 45K 72K pent at opes: 0.4M 1.0M 1.7M

SLIDE 9

Pentas, 9 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Tools for remote exploration

What tools can we provide to suggest when & where to look in large simulation data sets?

SLIDE 10

Pentas, 10 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Interactive visualization

Time dependent slices: 1000 videos in parallel
Translucent (volumetric) video
Move color coded section through space and time
Color-coded iso-surface: S(p,t)

SLIDE 11

Pentas, 11 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Safari on the (p,t) plane

Samples from pressure p = f (x, y, z, t).
Level sets defined by two parameters:

L(P, T) = { (x, y, z) : P = f (x, y, z, T) }

Partition the

data dimensions

– Viewing volume (x, y, z) – Control plane (p, t )

SLIDE 12

Pentas, 12 Jarek Rossignac, CoC & GVU & IRIS, Georgia Tech VIS 2003

Iso-surface compression

Out-of-core compression and simplification of iso-surfaces

and geometric models

Jack Snoyink,Martin Isenburg (UNC)
Based on segmentation

Part of a 6GB iso-surface that compresses to 640MB losslessly, & decompresses with a memory footprint of 9MB.

SLIDE 13

Lorenzo Predictor f or the out- of - core compression of 4D data sets

Peter Lindstrom Lawrence Livermore National Labs Lorenzo Ibarria Jarek Rossignac Andrzej Szymczak Georgia Tech

L. Ibarria, P. Lindstrom, J. Rossignac, A. Szymczak,

Out-of-core compression and decompression of large n-dimensional scalar fields, Eurographics 2003.

SLIDE 14

10/25/2003 Rossignac: Lorenzo

Focus on huge 4D scalar f ields

Input: P(x,y,z,t) sampled on regular 4D grid Quantized

to desired accuracy

Loss-less compression Trivial implementation Out-of-core codecs

(x,y,z) t P(x,y,z,t)

SLIDE 15

10/25/2003 Rossignac: Lorenzo

Scanline codecs

For t=0 to tmax do For z=0 to zmax do For y=0 to ymax do For x=0 to xmax do { Predict P(x,y,z,t) from visited neighbors Encode/decode the correction}

foot-print ˜ 1 slice

SLIDE 16

10/25/2003 Rossignac: Lorenzo

Lorenzo predict or

Predict P at corner of hypercube

from values at the other corners

– Set origin at opposite corner

2D: P(1,1)=P(1,0)+P(0,1)-P(0,0) 3D: P(1,1,1)= ? a–? b+c 4D: P(1,1,1,1)= ? n1–? n2+ ? n3–n4

– ni is reachable through i edges

– Exact predictor for cubics in 4D

SLIDE 17

10/25/2003 Rossignac: Lorenzo

Result s f or lossless compression

Small memory footprint Easy to implement Exactly reconstructs polynomials of degree n–1 Can outperform wavelets

SLIDE 18

10/25/2003 Rossignac: Lorenzo

How it all will come t oget her

Use Lorenzo predictor to compress data on server for

archival and posting

Use contour trees analysis in 4D on server to compute

imavge for (p,t) terrain

Use Safari on client to plan, conduct, record, annotate

exploration on the (p,t) terrain

Use seed-set on server to quickly extract iso-surface Use out-of-core compression/simplification to transmit

desired iso-surface

Use Lorenzo predictor decompression to download

Compression and remote inspection of 4D data sets

Jarek Rossignac, Jack Snoeyink, and Peter Linstrom)

Simulation results are huge

– 10004 (x,y,z,t) samples – Several attributes per sample (pressure, temp…): 5D terrain

– Storage / transmission: Simplification, Compression, Progressive – Interactive visualization: 2D slice or level-set of hyper-surface in 5D – Decide what to inspect: Control terrain + level-of-interest + mark-up – Access only what is needed: Iso-surface tracking and updating

HPPC Storage Visualization Server Local Model Selection 3D Viewing

Regular... or not?

(x,y,z) t P(x,y,z,t) (x,y,z) t P(x,y,z,t) pentatope in 5D

4D Delaunay computation and refinement

Ajith Mascarenhas and Jack Snoeyink (UNC)

Iso-surfaces from pentatopes

surface in 5d:

Slice away 2 dimens

to form isosurface:

– Faces (2d) – Edges (1d) – Vertices (0d)

Yes, this is crazy…

Incremental 4D Delaunay

Results

Tools for remote exploration

What tools can we provide to suggest when & where to look in large simulation data sets?

Interactive visualization

Safari on the (p,t) plane

L(P, T) = { (x, y, z) : P = f (x, y, z, T) }

data dimensions

– Viewing volume (x, y, z) – Control plane (p, t )

Iso-surface compression

and geometric models

Lorenzo Predictor f or the out- of - core compression of 4D data sets

Peter Lindstrom Lawrence Livermore National Labs Lorenzo Ibarria Jarek Rossignac Andrzej Szymczak Georgia Tech

Focus on huge 4D scalar f ields

Input: P(x,y,z,t) sampled on regular 4D grid Quantized

Loss-less compression Trivial implementation Out-of-core codecs

(x,y,z) t P(x,y,z,t)

Scanline codecs

For t=0 to tmax do For z=0 to zmax do For y=0 to ymax do For x=0 to xmax do { Predict P(x,y,z,t) from visited neighbors Encode/decode the correction}

foot-print ˜ 1 slice

Lorenzo predict or

from values at the other corners

– Set origin at opposite corner

– Exact predictor for cubics in 4D

Result s f or lossless compression

Small memory footprint Easy to implement Exactly reconstructs polynomials of degree n–1 Can outperform wavelets

How it all will come t oget her

archival and posting

imavge for (p,t) terrain

exploration on the (p,t) terrain

desired iso-surface

selected portions of the original 4D data for local exploration/analysis