Face Fixer Compressing Polygon Meshes with Properties Martin Isenburg Jack Snoeyink University of North Carolina at Chapel Hill

Polygon Models: Triceratops 356triangles 2266quadrangles 140pentagons 63hexagons 10heptagons 7octagons 2undecagons

Polygon Models: Others

Faces and Corners: Sandal

Fewer polygons  less connectivity information Fewer polygons  less connectivity information Polygons tend to be planar & convex  better geometry prediction Polygons tend to be planar & convex  better geometry prediction Better triangle strips Better triangle strips Do not triangulate!

Group Structures: Teapot & Cow

Group Structures: Others

Overview Do not triangulate! Do not triangulate! Connectivity Compression for Manifold Polygon Meshes Connectivity Compression for Manifold Polygon Meshes Compact mesh representations Simple implementation Beyond Faces: Quadrilateral grids Capture Structures! Capture Structures!

Previous Work

Fast Rendering Fast Rendering Progressive Transmission Progressive Transmission Maximum Compression Maximum Compression

Previous Work Fast Rendering Fast Rendering Progressive Transmission Maximum Compression graphics boardmain memory

Previous Work Fast Rendering Fast Rendering Progressive Transmission Maximum Compression Triangle Strips [?] Generalized Triangle Mesh[ Deering ] Transparent Vertex Caching[ Hoppe, n VIDIA ]

Previous Work Fast Rendering Progressive Transmission Progressive Transmission Maximum Compression Maximum Compression main memorystorage / network

Previous Work Fast Rendering Progressive Transmission Progressive 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 Compression Maximum Compression Topological Surgery [ Taubin, Rossignac ] Triangle Mesh Compression[ Costa, Gotsman ] Edgebreaker[ Rossignac, King et ] Cut-border Machine[ Gumhold, Strasser ]

ver 1 (x,y,z) ver 2 (x,y,z) ver 3 (x,y,z) ver n Standard Mesh Representation face face face face m connectivity n = 10, KB60 KB n = 100, KB600 KB n = 1,000, MB6 MB geometry

ver 1 (x,y,z) ver 2 (x,y,z) ver 3 (x,y,z) ver n Standard Mesh Representation face face face face m nor 1 (x,y,z) nor 2 (x,y,z) nor 3 (x,y,z) nor i tex 1 (u,v) tex 2 (u,v) tex 3 (u,v) tex k col 1 (r,g,b) col 2 (r,g,b) col 3 (r,g,b) col j

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 edges number of labels = number of edges reverse decoding reverse decoding Face Fixer F4F4 F5F5 R F3F3 LS E HnHn M

Encoding

F4F4

F4F4 F3F3

F4F4 F3F3 R

F4F4 F3F3 F5F5 R

F4F4 F3F3 F5F5 R F5F5

F4F4 F3F3 F5F5 R F5F5 R

F4F4 F3F3 F5F5 R F5F5 R R

Compressing Resulting label sequence: Resulting label sequence: non-uniform label frequencies correlation among subsequent labels Adaptive order-3 arithmetic coding Adaptive order-3 arithmetic coding Compact probability tables Fast bit-operations F4F4 F3F3 F5F5 R F5F5 R F4F4... RR F4F4 R

Decoding R

R

F5F5

F5F5

R

F3F3

F4F4

+2.0 TG Compression Results Triceratops2.1 Galleon2.6 Cessna2.8 Beethoven2.9 Shark1.7 Cupie2.3 bits vertex model

fragmented disks half-disk disk Non-Manifold Meshes (1)

Non-Manifold Meshes (2) cut

Beyond Faces

Extension: Quadrilateral Grids

Encoding a Quad Grid right left height

Encoding a Quad Grid QG

Triceratops Galleon Beethoven Shark Teapot Trumpet bits vertex model Compression with Quad Grids diff

Extension: Repeated Patches

Structures

Extension: Structures

case D case B case A case C Super Faces connected by an edge connected by a vertex

Encoding a Super Face

SF

Encoding a Super Face

F4F4

F4F4 F3F3

F4F4 F3F3 R

F4F4 F3F3 R F5F5

F4F4 F3F3 R F5F5 R

F4F4 F3F3 R F5F5 R R

F4F4 F3F3 R F5F5 R R F3F3

F4F4 F3F3 R F5F5 R R F3F3 R

Compression with Structures bits vertex model diff Triceratops Galleon Cessna Beethoven Shark Cupie

Summary

Summary of Contributions Compress polygonal connectivity Compress polygonal connectivity simpler, more compact, extensions Capture structural information Capture structural information face groupings mesh partitions discontinuity curves Model Libraries Model Libraries “rich” meshes storage / network transmission

Current and Future Work Triangle Strip Compression Graphics Interface 2000 Triangle Strip Compression Graphics Interface 2000 Tetrahedral and Hexahedral meshes  “cell fixer” Tetrahedral and Hexahedral meshes  “cell fixer”

Acknowledgements Davis King Jarek Rossignac Mike Maniscalco Stefan Gumhold S 6 Viewpoint Datalabs

Thank you.

Regular  Irregular Connectivity Re-meshable Re-meshable Bunnies, Horses, various Roman Statues, … Highly detailed, dense, scanned data sets Not Re-meshable Not 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