Decomposing Polygon Meshes for Interactive Applications

1
Decomposing Polygon Meshes for Interactive
Applications

• Li Xuetao
• Computer Graphics Laboratory

2
Polygon Mesh
3
Objective

• Automatically decompose a polygon mesh into
  meaningful components

Polygon Mesh
Decomposition
4
Issues

• How to define a component by features on the mesh
• How to compute these features
• How to extract components automatically

5
Basic Idea
6
Basic Idea
7
Basic Idea
8
Geometric Topological Functions

• Geometric Function
• Topological Function

9
Profiles of Geometric Function
10
Derivatives of Geometric Function
11
Critical Point Component
Critical Point
Component
12
Approach
Computing Skeleton
Defining sweep path
Space Sweeping
Decomposition
Result
13
Approach

• Skeletonization
• Sweep Order
• Space Sweep

14
Skeletonization
15
Related Structures

• Medial Axis
• Axis of generalized cylinder
• Skeletal Curves

16
Simplification
17
Skeletonization based on Simplification
18
Associated Triangle List (ATL)
ATL(v1, v5) T1
ATL(v2, v5) T2
Edge collapse
19
2D Example
V4
V5
V4
V5
V4
V5
T4
T4
T4
T3
T5
T5
T5
V8
V3
V6
V6
V8
V6
V7
T2
T1
T1
V1
V2
V1
V2
V9
V11
V4
T4
V10
V8
V9
20
3D Example
21
Skeleton of Polygon Mesh
22
Sweep Order

• Skeletal tree
• Traversal order of the skeletal tree

23
Adding Virtual Edges
24
Skeletal Tree
25
Traversal Order
v
u
26
Skeletal Tree
27
Space Sweep
28
Sweep Plane
29
Sweep Operation

• Compute
• The cross sections
• The topological function
• The geometric function
• Check if critical point is reached
• If reached, extract component. If not, move the
  sweep plane to the next position

30
Computing Cross Sections

• Intersecting triangles

31
Computing Cross Sections
32
Computing Geometric Function

33
Computing Topological Function
34
Advancing the Sweep Plane
35
Extracting Components
36
Decomposition Results
37
Decomposition Results
38
Decomposition Results
39
Decomposition Results
40
Conclusion

• A formal definition of component
• A framework for decomposing polygon meshes