Japanese Writing: Kanji

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(No Transcript)
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SPIRALE REVERSI
Reverse Decoding of theEdgebreaker Encoding
Martin Isenburg Jack Snoeyink University
of North Carolina at Chapel Hill
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Introduction

• Mesh compression is hip
• Edgebreaker encodes mesh connectivity
• Original decoding algorithm
• worst case time complexity O(n2)
• Wrap Zip decoding algorithm
• worst case time complexity O(n)
• Spirale Reversi decoding algorithm

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Overview

• Connectivity Compression
• Edgebreaker
• Four Examples
• Edgebreaker Encoding
• Edgebreaker Decoding
• Wrap Zip Decoding
• Spirale Reversi Decoding
• Holes and Handles

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Connectivity Compression
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Standard Representation
vertex1 (x,y,z) vertex2 (x,y,z) vertex3
(x,y,z) vertexn
triangle1 1 2 3 triangle2 3 4 3 triangle3
5 2 1 trianglem
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Compression Schemes

• Geometry Compression, Deering, 1995
• Short Encodings of Planar Graphs and Maps, Keeler
  and Westbrook, 1995
• Geometric Compression through Topological
  Surgery, Taubin and Rossignac, 1996
• Good orders for incremental (re)construction,
  Snoeyink and vanKrefeld, 1997
• Encoding a triangulation as a permutation of its
  point set, Denny and Sohler, 1997
• Triangle Mesh Compression, Touma and Gotsman,
  1998
• Real time compression of triangle mesh
  connectivity, Gumhold and Strasser, 1998
• Mesh Connectivity Coding by Dual Graph Approach,
  Li and Kuo, 1998
• Edgebreaker Connectivity Compression for
  Triangle Meshes, Rossignac, 1998
• Mesh Collapse Compression, Isenburg and Snoeyink,
  1999
• Single Resolution Compression of Arbitrary
  Triangular Meshes with Properties, Bajaj,
  Pascucci, and Zhuang, 1999
• Triangle Strip Compression, Isenburg, 2000
• Face Fixer Compressing Polygon Meshes with
  Properties, Isenburg and Snoeyink, 2000
• Efficient Coding of non-triangular Meshes,
  Kronrod and Gotsman

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Compression Schemes
time

• Geometry Compression, Deering, 1995
• Short Encodings of Planar
  Westbrook, 1995
• Geometric Compression
  ubin and Rossignac, 1996
• Good orders for increm
  nd vanKrefeld, 1997
• Encoding a triangulation
  y and Sohler,
  1997
• Triangle Mesh Compre
• Real time compression
  d and Strasser,
  1998
• Mesh Connectivity Co
  o, 1998
• Edgebreaker Connectivity
  ossignac, 1998
• Mesh Collapse Compressi
• Single Resolution Compres
  hes with Properties,
  Bajaj, Pascucci, and Zhuang, 1999
• Triangle Strip Compression, Isenburg, 2000
• Face Fixer Compressing Polygon Meshes with
  Properties, Isenburg and Snoeyink, 2000
• Efficient Coding of non-triangular Meshes,
  Kronrod and Gotsman

esh Connec
Edgebreaker
esh Collaps
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Edgebreaker
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Encoding

• Encodes meshconnectivity asa sequence oflabels
• Best worst casebound for meshconnectivity
• Less than 4 bits per vertex for meshes without
  holes and handles

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Decoding

• Original decoding replays encoding traversal
• but O(n2) worst case time complexity
• Wrap Zip decoding sort of replays encoding
  traveral
• only O(n) time complexity
• but multiple traversals of labels (triangles) for
  mesh with boundary (handles)
• zipping is un-necessary overhead

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Edgebreaker Encoding
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EdgebreakerDecoding
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• Changes in boundary length
• Computing initial boundary length

0
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• Changes in boundary length
• Computing initial boundary length

1
1
0
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• Changes in boundary length
• Computing initial boundary length

1
-1
1
0
0
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• Changes in boundary length
• Computing initial boundary length

1
-1
-1
1
0
-1
0
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• Changes in boundary length
• Computing initial boundary length

1
-1
-1
-1
1
0
-1
-2
0
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• Changes in boundary length
• Computing initial boundary length

1
-1
-1
-1
-1
1
0
-1
-2
-3
0
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• Changes in boundary length
• Computing initial boundary length

1
-1
-1
-1
-1
1
1
0
-1
-2
-3
-2
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
1
1
0
-1
-2
-3
-2
0
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
1
1
0
-1
-2
-3
-3
-2
0
-1
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
-3
1
1
0
-1
-2
-3
-3
-6
-2
0
-1
-4
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
-3
1
1
1
0
-1
-2
-3
-3
-6
-5
-2
0
-1
-4
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
-3
-1
1
1
1
0
-1
-2
-3
-3
-6
-6
-5
-2
0
-1
-4
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
-3
-1
-1
1
1
1
0
-1
-2
-3
-3
-6
-7
-6
-5
-2
0
-1
-4
0
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• Changes in boundary length
• Computing initial boundary length
• Computing offset for label

1
-1
-1
-1
-1
-1
-3
-3
-1
-1
1
1
1
0
-1
-2
-3
-3
-6
-10
-7
-6
-5
-2
0
-1
-4
0
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Wrap ZipDecoding
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zip ...

























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zip ...






























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zip ...






































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zip ...































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zip ...












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Spirale ReversiDecoding
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Holes andHandles
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Encoding a hole



























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Encoding a hole

































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Encoding a handle




























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Encoding a handle




























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Encoding a handle




























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Yeez this bunny again!
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Acknowledgements

• Davis King for details on Edgebreaker during our
  pool session at SCG 99
• Jarek Rossignac for suggesting the name Spirale
  Reversi