Boolean Operations for Free-form Models Represented in Geometry Images

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

2. Outline • Motivation • Geometry Images • Boolean Operation on Geometry Images • Mesh Intersection • Pixel Classification • Triangulation • Experimental Results • Summary ICST, Peking University

3. 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 ICST, Peking University

4. 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 ICST, Peking University

5. Reconstructedmeshes Boolean operation Geometry images Resulting model gA gA-1 GA gB gB-1 GB Boolean Operation on Geometry Images ICST, Peking University

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 ICST, Peking University

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 ICST, Peking University

8. 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 ICST, Peking University

9. Experimental Results ICST, Peking University

10. Experimental Results • Timing for Boolean operations ICST, Peking University

11. 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 ICST, Peking University

12. Thank you for your attention! • Questions? Contact: zhoubingfeng@icst.pku.edu.cn ICST, Peking University