Transcript http://www.cs.unc.edu/~isenburg/trianglestripcompression/ Triangle Strip Compression Martin Isenburg University of North Carolina at Chapel Hill.

http://www.cs.unc.edu/~isenburg/trianglestripcompression/
Triangle Strip Compression
Martin Isenburg
University of North Carolina at Chapel Hill
Introduction
A new edge-based encoding scheme
for mesh connectivity.
Introduction
A new edge-based encoding scheme
for mesh connectivity.
 compact mesh representations
Introduction
A new edge-based encoding scheme
for mesh connectivity.
 compact mesh representations
 simple implementation
Introduction
A new edge-based encoding scheme
for mesh connectivity.
 compact mesh representations
 simple implementation
 fast decoding
Introduction
A new edge-based encoding scheme
for mesh connectivity.
 compact mesh representations
 simple implementation
 fast decoding
Introduction
A new edge-based encoding scheme
for mesh connectivity.
 compact mesh representations
 simple implementation
 fast decoding
 include triangle strip information
at little additional costs
A Triangle Mesh
A Stripified Triangle Mesh
Triangle Strips
Triangle Strips
• Technique for efficient rendering of
triangle meshes.
• Reduce data transfer between main
memory and render engine.
• Requires built-in buffer for two
(previous) vertices.
• Supported in today’s graphic boards.
Rendering with Triangles
Rendering with Triangles
Rendering with Triangle Strips
Rendering with Triangle Strips
Rendering with Triangle Strips
Sequential Triangle Strip
v0
v0 v1 v2 v 3 v4 v5 v6 v 7 v8
v2
7 triangles
v1
v4
v3
v6
v5
v7
9 vertices
v8
Sequential
Generalized
Generalized Triangle Strip
v0
7 triangles
v2
v1
10 vertices
v4
v3
v6
v5
v0 v 1 v2 v3 v2 v 5 v4 v7 v6 v8
v7
v8
Generalized Triangle Strip
v0
7 triangles
v2
v1
10 vertices
v4
v3
v6
v5
v0 v 1 v2 v3 v2 v 5 v4 v7 v6 v8
v7
v8
Generalized Triangle Strip
v0
v2
7 triangles
swap
v2
v1
10 vertices
v4
v3
v6
v5
v0 v 1 v2 v3 v2 v 5 v4 v7 v6 v8
v7
v8
Stripification Algorithms
• finding good set of triangle strips
(e.g. few swaps, restarts) isn’t easy
• computing optimal solution is NP hard
• proposed tools with good heuristics:
– STRIPE
(96, Evans et al.)
– SWAPS
(97, Speckmann & Snoeyink)
– FGTS
(99, Xiang et al.)
Storing a Mesh
Storing a Mesh
• Where are the vertices located ?
 mesh geometry
• Which vertices form a triangle?
 mesh connectivity
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangles
1 4 20
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangles
1 4 20
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangles
1 4 20
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangles
1 4 20
Standard Representation
list of vertices
list of triangles
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
x4 y4 z4
.....
xn yn zn
1 4 2
2 3 0
4 0 5
3 4 5
5 0 2
.....
.....
.....
4
u2 v 2 w 2
u3 v 3 w 3
u4 v 4 w 4
3 4
3 4
3 6
Connectivity
list of vertices
x0 y0 z0
x
y
z
1
1
1
Storage costs:
x2 y2 z2 u2 v2 w2
6xlog(n)
3 y3 z3bpvu3 v3 w3
4 x4 y4 z4 u4 v4 w4
.....
xn yn zn
list of triangles
1 4 2
2 3 0
4 0 5
3 4 5
5 0 2
.....
.....
.....
3 4
3 4
3 6
Storing a Stripified Mesh
Storing a Stripified Mesh
• Where are the vertices located ?
 mesh geometry
• Which vertices form a triangle?
 mesh connectivity
Storing a Stripified Mesh
• Where are the vertices located ?
 mesh geometry
• Which vertices form a triangle?
 mesh connectivity
• Which triangles form a strip?
 mesh stripification
Storing a Stripified Mesh
• Where are the vertices located ?
 mesh geometry
• Which vertices form a triangle strip?
 mesh connectivity
 mesh stripification
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
Standard Representation
list of vertices
x0 y0 z0
x1 y1 z1
x2 y2 z2
x3 y3 z3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangle strips
1 4 20 30 0 . . .
1 0 40 20 4 . . .
7 4 50 80 4 . . .
.........
.........
.........
Connectivity and Stripification
list of vertices
x0 y0 z0
x
y
z
1
1
1
Storage costs:
x2 y2 z2
x3 log(n)
y3 z3 bpv
2~3
4 x4 y4 z4
6 4 .....
xn yn zn
list of triangle strips
1 4 20 30 0 . . .
1 0 40 20 4 . . .
7 4 50 80 4 . . .
.........
.........
.........
Connectivity Compression
for Triangle Meshes
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Short Encodings of Planar
Graphs and Maps
4.6 bpv (4.6)
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Topological Surgery
2.4 ~ 7.0 bpv (--)
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Triangle Mesh Compression
0.2 ~ 2.9 bpv (--)
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Edgebreaker
3.2 ~ 4.0 bpv (4.0)
Compression Techniques
A Simple and Efficient
• Keeler Westbrook [95] Encoding for Triangle Meshes
4.2 ~ 5.4 bpv (6.0)
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Compression Techniques
• Keeler Westbrook [95]
• Taubin Rossignac [96]
• Tauma Gotsman [98]
• Rossignac [98]
• DeFloriani et al [99]
• Isenburg Snoeyink [99]
Mesh Collapse Compression
1.1 ~ 3.4 bpv (--)
strip-internal edges
strip-internal edges
1
1
1
1
1
1
1
1
1
1
1
1
strip-internal edges
3 bpv
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1 0
0
Triangle Fixer
Encoding scheme
Define initial active boundary around
arbitrary edge of mesh.
Encoding scheme
Define initial active gate as one of the
two boundary edges.
Encoding scheme
Label active gate with T, R, L, S, or E.
Encoding scheme
Label active gate with T, R, L, S, or E.
Which label ? Depends on its adacency
relation with the boundary.
Encoding scheme
Label active gate with T, R, L, S, or E.
Which label ? Depends on its adacency
relation with the boundary.
Update active boundary and active gate.
Encoding scheme
Label active gate with T, R, L, S, or E.
Which label ? Depends on its adacency
relation with the boundary.
Update active boundary and active gate.
Boundary is expanded (T), is shrunk (R and
L), is split (S), or is terminated (E).
Label T
Active gate not adjacent to other boundary
edge.
before
Label T
before
after
Label R
Active gate adjacent to next edge along
active boundary.
before
Label R
before
after
Label L
Active gate adjacent to previous edge along
active boundary.
before
Label L
before
after
Label S
Active gate adjacent to some other edge
of active boundary.
before
Label S
Active gate adjacent to some other edge
of active boundary.
Label S
Active gate adjacent to some other edge
of active boundary.
before
Label S
before
after
Label E
Active gate adjacent to previous and next
edge along active boundary.
before
Label E
before
after
Example Run: Encoding
T
T
T
T
T
R
T
T
T
T
R
T
T
T
T
R
T
H10
R
R
R
R
R
R
R
R
E
Example Run: Decoding
E
R
R
R
R
R
R
R
R
H10
T
R
T
T
T
T
R
T
T
T
T
R
T
T
T
T
T
Holes and Handles
Simple Mesh
Mesh with Holes
Mesh with Handle
Mesh with Handle and Holes
Encoding a hole
• use new label H
• associate integer called size with
label H that specifies number of
edges/vertices around hole
• one label Hsize per hole
• total number of labels remains equal
to number of mesh edges
Label Hsize
Active gate adjacent to hole of size
edges/vertices.
before
hole
Label Hsize
before
hole
after
Encoding a handle
• use new label M
• associate three integers called index,
offset1, and offset2 with label M that
specify current configuration
• one label Midx,off1,off2 per handle
• total number of labels remains equal
to number of mesh edges
Label Midx,off1,off2
Active gate adjacent to some edge of
boundary in stack.
before
offset2
index in stack
offset1
Label Midx,off1,off2
before
after
offset2
index in stack
offset1
Triangle Strip Compression
Triangle Strip Compression
• let triangle strips guide the mesh
traversal
• replace label T with labels TR, TL, TB,
and TE
• traversing along strip means progress
for both:
– encoding connectivity
– encoding stripification
Label TR
Triangle strip leaves triangle on the right.
before
Label TR
before
after
Label TL
Triangle strip leaves triangle on the left.
before
Label TL
before
after
Label TB
Triangle strip leaves triangle on the left
and on the right.
before
Label TB
before
after
Label TE (case 1)
Triangle strip ends in triangle.
before
AND
It’s the last triangle
of current strip.
It doesn’t follow a
label of type TB.
Label TE (case 1)
before
after
Label TE (case 2)
Triangle strip ends in triangle.
before
AND
Not the last triangle
of current strip.
It follows a label of
type TB.
Label TE (case 2)
before
after
Example Run: Encoding
TL
TR
TR
TR
TE
TB
TL
TR
TR
TL
TR
TR
TE
TE
H10
R
R
R
R
R
S
L
L
E
R
R
E
Example Run: Decoding
calculate offset
TL
TR
TL
TL
TE
TB
TL
TR
TR
TL
TR
TR
TE*
TE
H10
R
R
R
R
R
S
L
L
E
R
R
E
Offset = 6
E
R
R
E
L
L
S
R
R
R
R
R
H10
TE
TE
*
TE
*
TE
*
TE
*
TR
TR
TL
TR
TR
TL
TB
TE
TR
TR
TR
TL
Compressing the label sequence
Fixed-Bit Encoding
• map label types to unique bit-codes
example: T  0 R  01
S  0001
L  001
E  0011
• frequent labels are mapped to short
bit-codes
• make mapping dependent on last label
(e.g. one label memory)
• very simple implementation
Arithmetic Encoding
• approaches the entropy of the label
sequence
• adaptive version
• three label memory
• due to small number of different
symbols, probability tables require
less than 4 KB
• implemented with fast bit operations
Results
Fandisk
Eight
Bunny
Triceratops
Skull
Results
mesh
vertices
fixed
aac-3
250
3.99 2.98
2.36 1.78
shape
2562
4.00 3.09
0.77 0.62
fandisk
6475
4.01
3.61
1.67 2.25
triceratops
2832
4.00 4.12
2.52 3.49
eight
766
4.09 3.46
1.43 1.78
femur
3897
4.16 4.48
3.05 4.02
skull
10952
4.22 4.78
2.96 4.18
bunny
34834
4.00 3.69
1.73 2.40
bishop
Video
Mesh Properties
Many polygon meshes include additional
information
• Surface Normals
• Texture coordinates
• Colours
Mesh Properties
Mesh properties can be attached to
Mesh Properties
Mesh properties can be attached to
• vertices
Mesh Properties
Mesh properties can be attached to
• vertices
• faces
Mesh Properties
Mesh properties can be attached to
• vertices
• faces
• corners
Corner Attributes
• Make stripification process difficult.
• Corner attributes must be consistent
for vertices in strip.
• But . . . mapping attributes to strip
corners is cheaper than mapping to
triangle corners.
• Usually requires 1 bit per corner.
• Immediate savings of 50 % and more!
Number of Corners
mesh
vertices
triangles
strip
250
1488
498
shape
2562
15360
5124
fandisk
6475
38838
13394
triceratops
2832
16980
5948
eight
766
4608
1584
femur
3897
23394
8272
skull
10952
66312
23304
bunny
34834
208353
71909
bishop
Summary and Current Work
• Compact encodings for stripified
triangle meshes.
• Exploit existing correlation between
connectivity and stripification.
• Edge-based encoding has other useful
applications (non-triangular meshes).
Acknowledgements
• Bettina Speckmann for fruitful
discussions on triangle strips
• Xinyu Xiang for triangulating some
of my test models
• my supervisor Jack Snoeyink for
reviewing the paper