1. Boolean Operations for Free-form Models Represented in Geometry Images
Yan Fu and Bingfeng Zhou
(Presented by Jie Feng)
Institute of Computer Science & Technology
Peking University
April 17, 2008

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Outline
Motivation
Geometry Images
Boolean Operation on Geometry Images
Mesh Intersection
Pixel Classification
Triangulation
Experimental Results
Summary
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Motivation
Boolean operation of solid models is a key algorithm for geometry modeling
Boolean operation algorithms based on different representations
Level-set
Multi-resolution meshes
Hybrid of implicit and explicit models
Volumetric representation
Geometry images –– higher efficiency
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Geometry Images
Geometry Images [Gu et al. 2002]
Store the geometry information as (r,g,b) in a 2D image
Avoid the storage of connectivity information
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5. Boolean Operation on Geometry Images
Reconstructed meshes
gA-1
gB-1
Boolean operation GA GB
Geometry images
Resulting model gA gB
Definition:
p: M->D (M: 3d model, D: 2d domain)
M~G (geometry image)
D~g (2d grid)
g projected back to 3d surface -> g-1
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6. Step 1. Mesh Intersection
Calculate intersection lines between gA-1 and gB-1
→ Boundary grid lines (3D)
Project boundary grid lines to gA and gB
→ Closed paths in the parameter domain (2D)
Quadtree scheme to accelerate the triangle intersection
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7. Step 2. Pixel Classification
Closed paths in parameter domain divide the pixels of a geometry image into subsets
Decide the inside/outside property of each subset by a boundary-fill scheme
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Step 3. Triangulation
Intersection lines are used as the constrained edges in constrained Delaunay triangulation
Resulting triangle meshes are transformed into 3D space and merged together
The final triangle mesh can be further converted into a geometry image
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Experimental Results
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Experimental Results
Timing for Boolean operations
Results
Size of G.I.
G.I. Without quadtree
G.I. With quadtree
Mesh
64×64
59.2 s
0.140 s
1.547 s
108.5 s
0.328 s
1.563 s
128×128 s
0.906 s
4.453 s
58.3
0.078 s
5.234 s
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Summary
An efficient Boolean operation method
Free-form solid models represented by geometry images
Benefits from regular data organization
Accelerated intersection by using hierarchical quadtrees
Independent of resolutions of geometry images
Future works
To improve the robustness of intersection computation
To achieve better performance of Boolean operation by utilizing graphics hardware
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12. Thank you for your attention!
Questions?
Contact:
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