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Face FixerFace FixerCompressing Polygon MeshesCompressing Polygon Meshes
with Propertieswith Properties
Martin Isenburg Jack SnoeyinkMartin Isenburg Jack Snoeyink
University of North Carolina at Chapel HillUniversity of North Carolina at Chapel Hill
Polygon Models: Triceratops
356356 trianglestriangles22662266 quadranglesquadrangles
140140 pentagonspentagons6363 hexagonshexagons1010 heptagonsheptagons
77 octagonsoctagons22 undecagonsundecagons
Polygon Models: Others
Faces and Corners: Sandal
• Fewer polygonsFewer polygons less connectivity information less connectivity information
• Polygons tend to be planar & convexPolygons tend to be planar & convex better geometry prediction better geometry prediction
• Better triangle stripsBetter triangle strips
Do not triangulate!
Group Structures: Teapot & Cow
Group Structures: Others
Overview
• Do not triangulate!Do not triangulate!
• Connectivity Compression for Manifold Connectivity Compression for Manifold Polygon MeshesPolygon Meshes• Compact mesh representations
• Simple implementation
• Beyond Faces: Quadrilateral grids
• Capture Structures!Capture Structures!
Previous WorkPrevious Work
Previous Work
• Fast RenderingFast Rendering
• Progressive TransmissionProgressive Transmission
• Maximum CompressionMaximum Compression
Previous Work
• Fast RenderingFast Rendering
• Progressive Transmission
• Maximum Compression
graphics boardmain memory
Previous Work
• Fast RenderingFast Rendering
• Progressive Transmission
• Maximum Compression
• Triangle Strips [?]
• Generalized Triangle Mesh [Deering]
• Transparent Vertex Caching [Hoppe,nVIDIA]
Previous Work
• Fast Rendering
• Progressive TransmissionProgressive Transmission
• Maximum CompressionMaximum Compression
main memorystorage / network
Previous Work
• Fast Rendering
• Progressive TransmissionProgressive Transmission
• Maximum Compression
• Progressive Meshes [Hoppe]
• Progressive Forest Split [Taubin et]
• Compressed Progressive Meshes [Pajarola et]
• Progressive Geometry Compression [Khodakovsky et]
Previous Work
• Fast Rendering
• Progressive Transmission
• Maximum CompressionMaximum Compression
• Topological Surgery [Taubin, Rossignac]
• Triangle Mesh Compression [Costa, Gotsman]
• Edgebreaker [Rossignac, King et]
• Cut-border Machine [Gumhold, Strasser]
ver1 (x,y,z)ver2 (x,y,z)ver3 (x,y,z)
vern
Standard Mesh Representation
face1 1 2 3 4face2 3 4 3face3 5 2 1 3
facem
connectivity
n = 10,000 66 KB 60 KBn = 100,000 830 KB 600 KB
n = 1,000,000 10 MB 6 MB
geometry
ver1 (x,y,z)ver2 (x,y,z)ver3 (x,y,z)
vern
Standard Mesh Representation
face1 1 2 3 4face2 3 4 3face3 5 2 1 3
facem
nor1 (x,y,z)nor2 (x,y,z)nor3 (x,y,z)
nori
tex1 (u,v)tex2 (u,v)tex3 (u,v)
texk
col1 (r,g,b)col2 (r,g,b)col3 (r,g,b)
colj
Face FixerFace Fixer
Face Fixer
• encoding is a sequence of labels:encoding is a sequence of labels:• one label . . . . per face
• one label per hole
• one label per handle
• labels and fix it all together
• number of labels = number of edgesnumber of labels = number of edges
• reverse decodingreverse decoding
Face Fixer
F4 F5
R
F3
L S E
Hn
M
Encoding
Encoding
F4
Encoding
F4
F3
Encoding
F4
F3
R
Encoding
F4
F3F5
R
Encoding
F4
F3F5
R
F5
Encoding
F4
F3F5
R
F5
R
Encoding
F4
F3F5
R
F5
R R
Compressing
• Resulting label sequence:Resulting label sequence:
• non-uniform label frequencies
• correlation among subsequent labels
• Adaptive order-3 arithmetic codingAdaptive order-3 arithmetic coding• Compact probability tables
• Fast bit-operations
F4 F3 F5R F5 R F4. . . R RF4 R . . .
Decoding
R
Decoding
R
Decoding
F5
Decoding
F5
Decoding
R
Decoding
F3
Decoding
F4
Decoding
+2.0 +2.0
TG
2.2
2.4
Compression Results
Triceratops 2.1Galleon 2.6Cessna 2.8
Beethoven 2.9Shark 1.7Cupie 2.3
bitsvertexmodel
fragmented disks
half-diskdisk
Non-Manifold Meshes (1)
Non-Manifold Meshes (2)
cutcut
Beyond FacesBeyond Faces
Extension: Quadrilateral Grids
Encoding a Quad Grid
right
left
height
Encoding a Quad Grid
QG
Triceratops 1.9 -0.2Galleon 2.2 -0.4
Beethoven 2.6 -0.3Shark 1.4 -0.3Teapot 1.1 -0.6
Trumpet 0.6 -0.5
bitsvertexmodel
Compression with Quad Grids
diff
Extension: Repeated Patches
StructuresStructures
Extension: Structures
case D
case Bcase A
case C
Super Faces
connected by anedge
connected by avertex
Encoding a Super Face
Encoding a Super Face
Encoding a Super Face
SF
Encoding a Super Face
Encoding a Super Face
F4
Encoding a Super Face
F4
F3
Encoding a Super Face
F4
F3
R
Encoding a Super Face
F4
F3
R
F5
Encoding a Super Face
F4
F3
R
F5 R
Encoding a Super Face
F4
F3
R
F5 R
R
Encoding a Super Face
F4
F3
R
F5 R
RF3
Encoding a Super Face
F4
F3
R
F5 R
RF3
R
+0.1+0.1+0.2+0.1+0.0+0.1
Compression with Structures
bitsvertexmodel diff
Triceratops 2.4 +0.3Galleon 2.7 +0.1Cessna 3.5 +0.7
Beethoven 3.0 +0.1Shark 2.0 +0.3Cupie 2.3 +0.1
SummarySummary
Summary of Contributions
• Compress polygonal connectivityCompress polygonal connectivity• simpler, more compact, extensions
• Capture structural informationCapture structural information• face groupings
• mesh partitions
• discontinuity curves
• Model LibrariesModel Libraries• “rich” meshes
• storage / network transmission
Current and Future Work
• Triangle Strip CompressionTriangle Strip Compression Graphics Interface 2000Graphics Interface 2000
• Tetrahedral and Hexahedral meshes Tetrahedral and Hexahedral meshes “cell fixer”“cell fixer”
Acknowledgements
Davis KingDavis King
Jarek RossignacJarek Rossignac
Mike ManiscalcoMike Maniscalco
Stefan GumholdStefan Gumhold
SS66
Viewpoint DatalabsViewpoint Datalabs
Thank you.Thank you.
Regular Irregular Connectivity
• Re-meshableRe-meshable• Bunnies, Horses, various Roman Statues, …
• Highly detailed, dense, scanned data sets
• Not Re-meshableNot Re-meshable• Cessnas, Spanish Galleons, Sandals, …
• Careful designed meshes with sharp features
• CAD models, Viewpoint models
Predictive Coding
good not convex bad not planar bad
Attaching Geometry