Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh...
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![Page 1: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/1.jpg)
Martin IsenburgUC Berkeley
Jack SnoeyinkUNC Chapel Hill
Early Split Coding ofTriangle Mesh Connectivity
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Geometry
Connectivity
– Efficient Rendering
– Progressive Transmission
– Compact Storage
Mesh Compression“Geometry Compression” [Deering, 95]
• Surface Meshes– triangular
– polygonal
• Volume Meshes– tetrahedral, hexahedral
storage / network
main memory
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Connectivity
Triangle Mesh Connectivityv -9.7 1.6 -0.2v -6.6 1.4 3.3v -1.6 1.4 2.3v -3.3 -1.4 3.0v 5.6 1.7 4.5v -6.6 1.4 6.1v -3.3 –4.4 3.7v -1.6 1.4 2.1v -5.4 -1.6 6.4...
f 1 2 3f 3 2 4f 2 1 5f 2 5 4f 6 4 5f 6 5 7f 5 1 8f 4 8 7f 7 8 9f 9 8 10f 10 11 7...
Geometry
each index uses log2 (v) bits
6 log2 (v) bpv
3.24 bpv
enumeration of triangulatedplanargraphs
[Tutte 62]
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“Out-of-Core Compression” [Isenburg & Gumhold ‘03]
“Delphi Coding” [Coors and Rossignac ‘04]
“FreeLence” [Kälberer et al. ‘05]
Compression Schemes“Cut-Border Machine” [Gumhold & Strasser ‘98]
“Triangle Mesh Compression” [Touma & Gotsman ‘98]
“Edgebreaker” [Rossignac ‘99]
“Face Fixer” [Isenburg & Snoeyink ‘00]
“Angle Analyzer” [Lee, Alliez & Desbrun ‘02]
“Degree Duality Coder” [Isenburg ‘02]
“Near-optimal Coding” [Khodakovsky et al. ‘02]
“Valence-Driven Encoding” [Alliez & Desbrun ‘01]ComputerGraphics
“Succinct encodings of planar graphs” [He, Yao, & Hu ‘99]
“Short encodings of planar graphs” [Keeler & Westbrook ‘95]
“Succinct Representations of Graphs” [Turan ‘84]
“Optimal Coding” [Poulahlon & Schaeffer ‘03]
PlanarGraphCoding
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Connectivity Graph Traversal
split offset
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Connectivity Graph Traversal
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CBM – Edgebreaker – TG coder• label-based
split offset
“Cut-Border Machine” [Gumhold & Strasser ‘98]
“Edgebreaker” [Rossignac ‘99]
“Early Split Coding” [this paper]
C R C R R S. . . R C R E R C . . .
• degree-based
“Triangle Mesh Compression” [Touma & Gotsman ‘98]
3. . . . . .64 4 44 5 44S
split offset
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CBM and Edgebreaker
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
![Page 10: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/10.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
C
C
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
C C
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
R
C C R
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
C C R C
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
R
C C R C R
![Page 15: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/15.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
C C R C R S
12
3
4
5
6
7
89
10
11
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L
C C R C R S L
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L C
C C R C R S L C
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR
C C R C R S L C R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
C C R C R S L C R C
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R
C C R C R S L C R C R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
C C R C R S L C R C R C
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R
C C R C R S L C R C R C R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
C C R C R S L C R C R C R R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
R
C C R C R S L C R C R C R R R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
C C R C R S L C R C R C R R R L
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
C
C C R C R S L C R C R C R R R L C
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
C C R C R S L C R C R C R R R L C R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
R
C C R C R S L C R C R C R R R L C R R
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
RR
C C R C R S L C R C R C R R R L C R R R
offset = 11
![Page 30: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/30.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
RR
S
C C R C R S L C R C R C R R R L C R R R S
1
2
offset = 3
offset = 11
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CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
R
C C R C R S L C R C R C R R R L C R R R S R
S
L CR C
R C
R R
RL
CR
RR
SR
offset = 3
offset = 11
![Page 32: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/32.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
RR
SE
R
C C R C R S L C R C R C R R R L C R R R S R E
offset = 3
offset = 11
![Page 33: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/33.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
RR
SE
R
E
C C R C R S L C R C R C R R R L C R R R S R E E
offset = 11
offset = 3
![Page 34: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/34.jpg)
CBM and Edgebreaker
5
processedregion
unprocessed region
compressionboundary
CC
RC
RS
L CR C
R C
R R
RL
CR
RR
SE
R
E
C C R C R S L C R C R C R R R L C R R R S R E E C
offset = 11
offset = 3
+1 +3
+1 -1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -1 +1 +3 +3-1 -1 -1
= 4
= 12
C
...
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Subsequences of Labels areself-contained Encodings
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
reversible
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
reversible
E
E
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
… …
![Page 40: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/40.jpg)
S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
L
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
R
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
C
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
CR
… …
![Page 55: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/55.jpg)
S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
CR
C
… …
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S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
CR
CR
… …
![Page 57: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/57.jpg)
S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
CR
CR
… …
C
![Page 58: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/58.jpg)
S L C R C R C R R R L C R R R S R E E
Subsequences are self-contained
E
reversible
RE
S
R R
R
C
LR
RR
CR
CR
… …
CL
we did not needsplit offsets !!!
![Page 59: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/59.jpg)
TG coder
![Page 60: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/60.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
slot counts
![Page 61: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/61.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
7
![Page 62: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/62.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
7 6
zero slot
![Page 63: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/63.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
7 6
![Page 64: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/64.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
7 6 5
zero slot
![Page 65: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/65.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
7 6 5
![Page 66: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/66.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S 24
6
7
8
11
12
1315
16
18
offset = 18
7 6 5 S
![Page 67: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/67.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7 6 5 S
offset = 18
![Page 68: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/68.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
7 6 5 S 7
offset = 18
![Page 69: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/69.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
7 6 5 S 7
offset = 18
zero slot
![Page 70: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/70.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
7 6 5 S 7
offset = 18
zero slot
![Page 71: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/71.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
7 6 5 S 7
offset = 18
![Page 72: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/72.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
7 6 5 S 7 6
offset = 18
![Page 73: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/73.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
7 6 5 S 7 6
offset = 18
![Page 74: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/74.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
7 6 5 S 7 6 5
offset = 18
![Page 75: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/75.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
7 6 5 S 7 6 5
offset = 18
![Page 76: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/76.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
7 6 5 S 7 6 5
offset = 18
![Page 77: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/77.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
7 6 5 S 7 6 5
offset = 18
![Page 78: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/78.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
7 6 5 S 7 6 5
offset = 18
![Page 79: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/79.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 80: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/80.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 81: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/81.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 82: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/82.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 83: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/83.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 84: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/84.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6
offset = 18
![Page 85: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/85.jpg)
TG coder
5
processedregion
unprocessed region
compressionboundary
7
6
5
S
7
6
5
6
7 6 5 S 7 6 5 6 7
offset = 18
7
…
E
![Page 86: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/86.jpg)
Subsequences of Degrees arenot self-contained Encodings
![Page 87: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/87.jpg)
Subsequences are not self-contained
… S 7 6 5 6 E …
5
S
![Page 88: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/88.jpg)
… S 7 6 5 6 E …
5
S
Subsequences are not self-contained
![Page 89: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/89.jpg)
… S 7 6 5 6 E …
5
S
Subsequences are not self-contained
![Page 90: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/90.jpg)
… S 7 6 5 6 E …
5
S
Subsequences are not self-contained
![Page 91: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/91.jpg)
… S 7 6 5 6 E …
5
S
Subsequences are not self-contained
![Page 92: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/92.jpg)
… S 7 6 5 6 E …
5
S
Subsequences are not self-contained
![Page 93: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/93.jpg)
Not unique without split offsets
… S 4 3 E 4 3 E
4
3
34 4
34
3
6 6 5 6 6 5 6 … 5 7 5 6 6 6 5 …
![Page 94: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/94.jpg)
Early Split Coder
![Page 95: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/95.jpg)
Early Split Coder• encode with labels or degrees
• traverse triangles in same order – new label W
– earlier split operations
• one-to-one mapping insights:
– how to turn degree subsequences into self-contained encodings
– decoding strategy decides success
![Page 96: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/96.jpg)
RCR
CCR
The new label W
![Page 97: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/97.jpg)
R
C
CRCC
R
The new label W
![Page 98: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/98.jpg)
R
C
CRCC
R
The new label W
C
![Page 99: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/99.jpg)
R
CC R
CRCC
R
The new label W
wart
wart
RCR
CCR
![Page 100: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/100.jpg)
The new label W
RCR
CCR
C
R
CC R
CRCC
R
wart
wart
zero slot
![Page 101: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/101.jpg)
The new label W
RCR
CCR
CW
R
CC R
CRCC
R
wart
wart
![Page 102: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/102.jpg)
The new label W
RCR
CCR
CWC
R
CC R
CRCC
R
wart
wart
![Page 103: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/103.jpg)
The new label W
RCR
CCR
CWC R
R
CC R
CRCC
R
wart
wart
![Page 104: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/104.jpg)
The “early split” operation
RR
CRC
![Page 105: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/105.jpg)
The “early split” operation
S
RR
CRC
![Page 106: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/106.jpg)
The “early split” operation
S
RR
CRC
R
![Page 107: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/107.jpg)
The “early split” operation
S
RR
CRC
RL
![Page 108: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/108.jpg)
The “early split” operation
S
RR
CRC
RL R
![Page 109: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/109.jpg)
The “early split” operation
S
RR
CRC
RL R
Lzero slot
![Page 110: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/110.jpg)
The “early split” operation
S
RR
CRC
RL R
L
![Page 111: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/111.jpg)
The “early split” operation
S
RR
CRC
RL R
L
![Page 112: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/112.jpg)
The “early split” operation
S
RR
CRC
RL R
L
![Page 113: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/113.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
![Page 114: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/114.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
![Page 115: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/115.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
Szero slot
![Page 116: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/116.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
SW
zero slot
![Page 117: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/117.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
WS W
![Page 118: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/118.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
WS W
C
![Page 119: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/119.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
WS W
CR
![Page 120: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/120.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
WS W
CR
R
zero slot
![Page 121: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/121.jpg)
The “early split” operation
S
RR
CRC
RL R
L
RR
CRC
C
WS W
CR
R
W
![Page 122: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/122.jpg)
Complete Example
![Page 123: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/123.jpg)
One Scheme & Four Encodings
label-based
degree-based
![Page 124: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/124.jpg)
Forward Decodingwith offsets
![Page 125: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/125.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 126: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/126.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 127: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/127.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 128: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/128.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 129: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/129.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
zero slot
![Page 130: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/130.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 131: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/131.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
zero slot
![Page 132: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/132.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 133: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/133.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
zero slot
![Page 134: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/134.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
zero slot
![Page 135: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/135.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 136: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/136.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 137: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/137.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 138: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/138.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 139: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/139.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 140: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/140.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 141: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/141.jpg)
Forward Decoding with offsets
V5 V4 V5 V5 V6 V6 V4 V8 V5 V5 S1,0,0
C C C C R C R C R W C R C S1 C R R E C R E
![Page 142: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/142.jpg)
Reverse Decodingwithout offsets
![Page 143: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/143.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 144: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/144.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 145: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/145.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 146: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/146.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 147: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/147.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 148: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/148.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 149: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/149.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 150: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/150.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 151: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/151.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 152: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/152.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 153: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/153.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 154: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/154.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 155: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/155.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 156: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/156.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 157: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/157.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 158: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/158.jpg)
Reverse Decoding w/o offsets
E V3 E V4 S V5 V5 W V8 V4 V6 V6 V5 V5
E R C E R R C S C R C W R C R C R C C C C
![Page 159: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/159.jpg)
Results
![Page 160: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/160.jpg)
Compression Results
![Page 161: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/161.jpg)
Improving the TG coder
5
“Valence-Driven Encoding” [Alliez & Desbrun ‘01]
degree of vertexmust beat least 5
(at least 6 for early-split)
degree of vertexmust beat least 4
(at least 5 for early-split)
![Page 162: Martin Isenburg UC Berkeley Jack Snoeyink UNC Chapel Hill Early Split Coding of Triangle Mesh Connectivity.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d5f5503460f94a3f0ca/html5/thumbnails/162.jpg)
Thank You