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Efficient Boolean Operations for Free-form Models in Geometry Images

This paper presents a method for Boolean operations on solid models using geometry images. It covers mesh intersection, pixel classification, and triangulation, providing experimental results and future work suggestions. The approach is efficient, benefits from regular data organization, and is independent of image resolution.

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Efficient Boolean Operations for Free-form Models in Geometry Images

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  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

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