Out-of-CoreCompression for Gigantic Polygon Meshes

Martin Isenburg Stefan Gumhold

University of North Carolina WSI/GRIS

at Chapel Hill Universität Tübingen

Gigantic Meshes

3D scans CAD models isosurfaces

Gigantic Meshes

3D scans CAD models isosurfaces

Gigantic Meshes

3D scans CAD models isosurfaces

St. Matthew Statue

slows down:• transmission• storage• loading• processing

over 6 Gigabyte

186 million vertices372 million triangles

cut into 12

pieces

Mesh Compression

• many efficient schemes, but ...– mesh has to fit into memory– 2/4 GB limit on common PCs

“Geometry Compression” [Deering ‘95]

• active research area since ‘95

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

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

Mesh De-Compression

• but decompress on desktop PC– single pass – small memory foot-print

• use 64-bit super computer

• eliminates number of schemes“Topological Surgery” [Taubin & Rossignac ‘98]

“Edgebreaker” [Rossignac ‘99]

“Face Fixer” [Isenburg & Snoeyink ‘00]

Contributions

Contributions• Compressor

– minimal access

Contributions• Compressor

– minimal access

• Out-of-Core Mesh– transparent– caching clusters

Contributions• Compressor

– minimal access

• Out-of-Core Mesh– transparent– caching clusters

• Compact Format– small footprint– streaming

Overview

• Related Work

• Out-of-Core Mesh

• Compression Scheme

• Processing Sequences

• Conclusion

• Current Work

Related Work

• Main Out-of-Core Techniques 1. Mesh Cutting 2. Batch Processing 3. Online Processing

Related Work• Large Mesh Processing

– Simplification– Visualization ( Multi-Resolution)– Compression

1. Mesh Cutting• cut mesh into smaller pieces• process each piece separately• give special treatment to cuts• stitch result back together

Compression[Ho et al. 01]

[Hoppe 97]

[Bernadini et al. 99]SimplificationVisualization

• cut / compress pieces / stitch

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

• artificial discontinuities– special treatment for cuts– compression rates 25 % lower

• multi-pass decompression– each separately, then stitch – decompression 100 times slower

2. Batch Processing• work on “polygon soup”• process mesh in increments of

single triangles• make no use of connectivity

Simplification[Lindstrom 00]

[Lindstrom 03] Visualization+ external sorting

3. Online Processing• reorganize mesh data into an

external memory structure• allow “random” mesh access• full connectivity available

[this paper] Compression

[Cignoni et al. 03] Simplification

Cignoni et al.

• motivation: enable use of high quality simplification– use edge-collapse– simplify in one piece– just like “in-core”

figure courtesy of Paolo Cignoni

“Octree-based External Memory Mesh” [Cignoni et al. ‘03]

• clusters do not storeexplicit connectivity

Out-of-Core Mesh

struct HalfEdge { Index origin; Index inv; Index next;};

• half-edge based

Out-of-Core Mesh (1)

next

invorigin

• spatial clustering– stored on disk– cached clusters

Out-of-Core Mesh (2)

struct IndexPair {int ci : 15;int li : 17;

};

• cluster index + local index– hide clustering– try to fit in 32 bits

mesh.getNext(edge);mesh.getInv(edge);mesh.getOrigin(edge);mesh.isBorder(edge);mesh.isEncoded(edge);

mesh.setIsEncoded(edge);

mesh.getPosition(vertex);mesh.isManifold(vertex);

"isEncoded"

• functionality– read only– except for

flag per edge

Constructiongeometry passes compute bounding box create clustering sort vertices into clusters

connectivity passes sort edges into clusters match inverse half-edges link border edges mark non-manifold vertices

clusteringinput

computingconnectivity

Clustering Input

9

2 6

54

9

1 6 8 6

7 7 7

1 8 9 7

3

8 7 7

3 7

7

9

6

7 7 7 27

48777

8 8 9 7 7

26 589

compute bounding box

create clustering– counter grid– nearest

neighbors– graph

partitioning

sort vertices into clusters

Clustering Input

9

2 6

54

9

1 6 8 6

7 7 7

1 8 9 7

3

8 7 7

3 7

7

9

6

7 7 7 27

48777

8 8 9 7 7

26 589

compute bounding box

create clustering– counter grid– nearest

neighbors– graph

partitioning

sort vertices into clusters

Clustering Input

compute bounding box

create clustering– counter grid– nearest

neighbors– graph

partitioning

sort vertices into clusters

Computing Connectivity

sort edges into clusters

match inverse half-edges– border edges– non-manifold

edges are cut

link borders non-manifold

verticesnext

next

inv

inv

Example Timings

build 7 hours35 min19 min

4 hours14 min49 mincompression

cache misses 2.11.311.0

96 MBin-core limit 192 MB 384 MB

871 MBon-disk size 1.7 GB 11.2 GB

128 MB

2.1

5 min

Compression Scheme

Popular Schemes“Topological Surgery” [Taubin & Rossignac ‘98]

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

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

“Edgebreaker” [Rossignac ‘99]

“Face Fixer” [Isenburg & Snoeyink ‘00]

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

“Dual Graph Approach” [Li & Kuo ‘98]

“Spectral Compression” [Karni & Gotsman ‘00]

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

Triangle Mesh Compression

Data Structure

prev next

across

origin edge

already encoded

not yet encoded

struct BoundaryEdge { BoundaryEdge* prev; BoundaryEdge* next; Index edge; Index origin_idx; int origin[3]; int across[3]; int slots; bool border;};

Holes

Non-Manifold Vertices

Parallelogram Prediction

Quantization• precision of 32-bit float?• largest exponent least precise

- 4.095 190.974

0 1286432

x - axis

1684

23 bit ofprecision

23 bit ofprecision

23 bit ofprecision

Samples per Millimeter16 bit 18 bit 20 bit 22 bit 24 bit

97 388 15532.7 m

327 1311 20 cm

5 22 86195 m

Results

508 MBoriginal 1 GB 6.7 GB

compressed 344 MB61 MB37 MB

174 sec27 sec15 secload-time

foot-print 9.4 MB2.8 MB1.5 MB

double eagle

power plant

Results

1.8 GB

285 MB

original

28 MB

180 MB

compressed

63 sec

9 sec

load-time

1 MB

1 MB

foot-print

Processing Sequences

• polygon soup– efficient processing– no connectivity

• external memory mesh– seamless connectivity– slow to build & use

Mesh Formats• indexed meshes

– bad for large data sets2 GB

4 GB

Processing Sequences

seamless connectivity during fixed traversal

Large Mesh Simplification

output boundary

input boundary

bufferedregion

processed region

unprocessed region

“Large Mesh Simplification using Processing Sequences”[Isenburg, Lindstrom, Gumhold, Snoeyink Visualization ‘03]

original method

using processing sequences

Conclusion

Summary• Compressor

– minimal access

• Compact Format– small footprint– streaming

• Out-of-Core Mesh– transparent– caching clusters

Issues• length of compression boundary

– possible – but we use only local heuristics– may require too many clusters– causes thrashing

O( n ) [Bar-Yehuda & Gotsman ‘96]

• external memory mesh– expensive to build & use– avoid using it ?

Current Work

Small Footprint Streaming• vertices & triangles interleaved

streaming

small memory footprint

• concept: “Streaming Meshes”

• knowledge when vertex is nolonger needed

Streaming Meshes• interleave vertices & triangles• “finalize” vertices

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 ⋮ ⋮ ⋮ ⋮

verticesfinalized

(not used bysubsequenttriangles)

Streaming Compression

applicationindexedmesh

out-of-coremesh

compressedstreaming

mesh

streamingmesh

compressedstreaming

mesh

some kindof

processing

compressedstreaming

mesh

Thank You.

gigantic thanks to

Stanford’s Digital Michelangelo projectWalkthru group at UNC

Newport News ShipbuildingLLNL