Streaming Compressionof Triangle Meshes

Martin IsenburgUniversity of California

at Berkeley

Jack SnoeyinkUniversity of North Carolina

at Chapel Hill

Peter LindstromLawrence Livermore

National Labs

Compression

Compression• physical

– sleeping bags

– compressed air

JPG GIF

• digital– text, programs …

– images

– voice, music

– movies

– Efficient Rendering

– Progressive Transmission

– Maximum Compression

• Connectivity

• Geometry

• Properties

Mesh Compression

“Geometry Compression” [Deering, 95]

storage / network

main memory

Maximum Compression

Current Schemes

“Triangle Mesh Compression” [Touma & Gotsman ‘98]

“Cut-Border Machine” [Gumhold & Strasser ‘98]

“Edgebreaker” [Rossignac ‘99]

“Face Fixer” [Isenburg & Snoeyink ‘00]

“Degree Duality Coder” [Isenburg ‘02]

“Angle Analyzer” [Lee, Alliez & Desbrun ‘02]

“FreeLence” [Kälberer et al. ‘05]

“Out-of-Core Compression” [Isenburg & Gumhold ‘03]

Current Approach

Current Approach

Underlying Assumption• original ordering of vertices and

triangles is not important– no need to preserve it

– compressor is allowed to re-order

• impose “canonical” ordering– only encode connectivity graph

– re-order mesh based on some deterministic traversal

Original Orderings

rendering the first 20to 40 percent of thetriangle array

Connectivity TraversalEntire Mesh As Input

triangles

vertices beforecompression

starts

createdata structurefor queryingand markingconnectivity

getNext(h_edge);getInv(h_edge);getOrigin(h_edge);isBorder(h_edge);isEncoded(h_edge);markAsEncoded(h_edge);

inv flags

Auxiliary Data Structures

001

11

1

1

1

1

11

11

1

1

1

1

1

1

1

0

0

0

00

0 0

00

0

00

0

0

0

0

00

0

0

0

Large Meshes

3D scans isosurfaces

Large Meshes

3D scans isosurfaces

Limited Main Memory

“Compressing Large Polygonal Models” [Ho et al. ‘01]

• cut mesh into pieces, compress separately, stitch back together

“Out-of-core Compression of Gigantic Polygon Meshes”[Isenburg and Gumhold. ‘03]

• use an external memory structure

• impossible to construct / store data structures for mesh traversal

Out-of-Core Compression• OoC-Mesh

– on-disk clustering

– construct in advance

– cache LRU clusters

• OoC-Compressor– make few queries

Out-of-Core Compression• OoC-Mesh

– on-disk clustering

– construct in advance

– cache LRU clusters

• OoC-Compressor– make few queries

• Decompression– “streaming”

Streaming

Streaming• physical

– water in a pipe

– drip coffee

• digital– streaming formats

• audio

• video

• triangle meshes

Two Types of Streaming• progressive

• non-progressive

Non-Progressive Streaming• consume immediately

• potentially without end

• keep small buffer

• delete data if no longer needed

small window

Streaming Mesh Formats•

interleave introduce finalizev 1.32 0.12 0.23v 1.43 0.23 0.92v 0.91 0.15 0.62f 1 2 3done 2 v 0.72 0.34 0.35f 4 1 3done 1 v 0.72 1.03 0.35

⋮ ⋮ ⋮ ⋮

vertex # 2finalized

not used bysubsequent

triangles

vertex # 2introduced

not used byprecedingtriangles

active

“Streaming Meshes” [Isenburg and Lindstrom ‘05]

number of active vertices“width”

Outputting Streaming Meshes• isosurface

– 235 million vertices

– 469 million trianglesover

8 Gigabyte

• marching cubes– extract layer by layer

– output elements as extracted

– finalize vertices of previous layer

Richtmeyer-Meshkov instability simulation at LLNL

Streaming Simplification

“Stream Algorithm for … ” [Wu & Kobbelt ‘03]

“Large Mesh Simplification …” [Isenburg et al. ‘03]

Streaming Compression

Streaming Compression (1)• streaming API

bool open(FILE* file, int bits);

bool write_vertex(float* position);bool write_triangle(int* index, bool* finalize);

bool close();

• compare to standard APIbool compress(FILE* file, int bits,

int num_pos, float* positions, int num_tri, int* indices);

Streaming Compression (2)

• when writing a triangle– look-up active vertices

– determine configuration

– compress triangle+ positions of new vertices

– remove finalized data structures

• when writing a vertex– insert in hash

Possible Configurations

start add

start1

fill

join end

written triangle

active elements

Compressing a Triangle– configuration

add

fill

– specify active vertex• log2(width) bits

• better: use cache

– specify other active vertices• use local edge lists

– position of new vertices• parallelogram prediction

– finalization flags

add

fill

Demo• compress triangles immediately

• use delay buffer

Greedy Local Reordering

Improving connectivity compression by reordering triangles in a delay buffer

0

2

4

6

8

10

12

14

16

18

non

e 25 5010

025

050

0 1

K 5

K

10K

50K

delay buffer size

bpv

lucy

(original)

(spectral)

(geometric)

(breadth)

(depth)

st. matthew

(original)

(spectral)

(geometric)

out-of-core

compressed 344 MB

pre-process 7 hours

4 hourscompress

main memory 384 MB

disk space 11.2 GB

streaming

---

28 min

---

12 MB

392 MB(coordinates uniformly quantized to 18 bits)

Example Processing Pipeline

P1P1 P2P2 P3P3

P1P1P2P2

P3P3

P1P1 P2P2 P3P3

• pipelined stream-processing

Pipelined Stream-Processing• conventional processing

P1P1 P2P2 P3P3

– super-linear speedup

– minimal end-to-end I/O delay

– optimal disk caching

Demo Pipeline

256

256

256

regular volume grid

smextract | smclean | smsimp | smcompress

P2P2 P3P3P1P1 P4P4

grid.raw mesh.smc

v 1.32 0.12 0.23v 1.43 0.23 0.92v 0.91 0.15 0.62f 1 2 3done 2 v 0.72 0.34 0.35f 4 1 3done 1 ⋮ ⋮ ⋮ ⋮

Conclusion

Current Schemes do not Scale

9 GB1 MB

Problems of Current Schemes

372 milliontriangles

(4 GB)

186 million vertices(2 GB)

dedicatedout-of-core

data structure(11 GB)

global reordering ofmesh duringcompression

entire mesh as input IO-inefficient for large data

Streaming Approach

bool open(FILE* file, int bits);

bool write_vertex(float* position);bool write_triangle(int* index, bool* finalize);

bool close();

out-of-core

compressed 344 MB

pre-process 7 hours

4 hourscompress

main memory 384 MB

disk space 11.2 GB

streaming

---

28 min

---

12 MB

392 MB(coordinates uniformly quantized to 18 bits)

Alternate Approaches•

– different re-ordering strategy• higher correlation

– deterministic growing strategy • let compressor choose & correct

– degree-based coding• need to relax “max delay” constraint

• geometry– local coordinate system, angles, …

• connectivity

Compressing Volume Meshesstandard streaming

torso

fighter

2.14 bpt 3.88 bptrate

time 7 min

115 MB

8 sec

3 MBmemory

1.81 bpt 3.56 bptrate

time 11 min

140 MB

12 sec

6 MBmemory

Current/Future Work• implement more stream modules

– streaming surface reconstruction

– streaming stripification

– streaming re-meshing

– streaming smoothing

– streaming segmentation

– streaming feature extraction

– streaming …

Acknowledgements• meshes

– Stanford University, Cyberware

• support– NSF grant 0429901

"Collaborative Research: Fundamentalsand Algorithms for Streaming Meshes."

– U.S. DOE / LLNL # W-7405-Eng-48

– Max Planck Institute für Informatik

Thank You

streaming compression API :http://www.cs.unc.edu/~isenburg/smc

Stream-Processing Modules• tasks that process mesh elements

one at a time– e.g. for each triangle t …

• tasks that only require access to local neighbors– e.g. for each triangle t of vertex v …

• tasks that are order independent– e.g. collapse edges shorter than

# triceratops.obj## 2832 vertices# 2834 polygons#v 3.661 0.002 -0.738v 3.719 0.347 -0.833v 3.977 0.311 -0.725v 4.077 0.139 -0.654 ⋮ ⋮ ⋮ ⋮ f 2806 2810 2815 2821f 2797 2801 2811 2805f 2789 2793 2802 2796f 2783 2794 2788 ⋮ ⋮ ⋮ ⋮

2832! permutations2832! • 2834! • 4

differentorderings

= 1.6E+18810possible

descriptions

2834

4 rotations 2834

2834! permutations

2806