Interactive Boolean Operations on Surfel-Bounded Solids

1. Interactive Boolean Operations on Surfel-Bounded Solids Bart Adams Philip DutréKatholieke Universiteit Leuven

2. A B Goal: CSG on free-form solids • union, difference and intersection • on free-form solids • at interactive rates A-B AB AB

3. 90k surfels 94k surfels 8FPS “Bond of Union”

4. Related work Kristjansson et al. [2001] • subdivision surfaces Museth et al. [2002] • level set framework Pauly et al. [2003] • points and moving least squares surface ACM SIGGRAPH

5. Surfels are considered as small disks • position x • normal n • radius r n x r surfels shown at half size

6. Three categories of surfels head surfels that lie completely helix outside surfels with the other solid’s surface intersecting helix surfels that lie completely head inside

7. Algorithm overview inside-outside partitioning Preprocess classification of surfels Interactive loop keep appropriate set of surfels resamplingoperator

8. Algorithm overview inside-outside partitioning Preprocess classification of surfels Interactive loop keep appropriate set of surfels resamplingoperator

9. depth = 3 depth = 2 depth = 1 For each solid an octree is constructed

10. s ns ns points away from the empty cell  interior Classification of empty leaf cell as interior

11. ns s ns points towards the empty cell  exterior Classification of empty leaf cell as exterior

12. Interior Boundary Exterior Three types of leaf cells in the resulting octree

13. Partitioning of boundary cells using parallel planes P2 P1 All surfels between P1 and P2

14. The empty half-space of P1 is interior P2 P1 ns s ns points away from the empty space  interior

15. ns points towards the empty space  exterior The empty half-space of P2 is exterior P2 P1 ns s

16. In 3D, the boundary cell is partitioned in three volumes Exterior Boundary Interior

17. Algorithm overview inside-outside partitioning Preprocess classification of surfels Interactive loop keep appropriate set of surfels resamplingoperator

18. s1 s2 s3 s5 s4 Classification of surfels • s1 outside octree  outside • s2 in exterior cell  outside • s3 in interior cell  inside

19. s4 s5 Classification of surfels • surfels s4 and s5 in empty half-spaces:  s4outside  s5inside boundary cell

20. Classification of surfels • surfel s between parallel planes: • search for nearest neighbor surfel t • test disks of s and t for intersection s t boundary cell

21. Use octree as acceleration structure solid B root node intersects with boundary cells  test children solid A

22. Use octree as acceleration structure solid B child node only intersects with exterior cells  all surfels outside solid A

23. Use octree as acceleration structure solid B child node intersects with boundary cells  test children solid A

24. Use octree as acceleration structure solid B leaf node only intersects with exterior cells  all surfels outside solid A

25. Use octree as acceleration structure solid B leaf node still intersects with boundary cells  test surfels individually solid A

26. 200k surfels Inside-outside classification

27. 200k surfels Inside-outside classification NN search for only 5%, 80% of this 5% is intersecting

28. Algorithm overview inside-outside partitioning Preprocess classification of surfels Interactive loop keep appropriate set of surfels resamplingoperator

29. Algorithm overview inside-outside partitioning Preprocess classification of surfels Interactive loop keep appropriate set of surfels resamplingoperator

30. Resampling operator: motivation Intersection of two spheres Include surfels Resample surfels Exclude surfels

31. Resample surfel by smaller surfels • clip surfels: • irregularly shaped surfels • our method: resample surfels: • surfel replaced by smaller surfels • only one type of primitive

32. Close-up of resampled surfels surfels shown at half size

33. 350k surfels 230k surfels 46k surfels 4.4FPS Resampling results in sharp edges and corners

34. Local smoothing eliminates sharp creases no smoothing smoothing 340k surfels 250k surfels 650k surfels 3.3FPS

35. 350k surfels 370k surfels 2FPS “Bond of Union”

36. Discussion Advantages • fast classification • sharp edges and corners • only one type of primitive • octree is easy to update Limitations • partitioning might fail in case of incorrectly oriented surfels • choice of parallel planes is not always optimal

37. Conclusion Contributions • fast inside-outside test • resampling operator Future work • CSG operations on mixed polygon-surfel models • implementation on GPU

38. Acknowledgements • graphics group K.U.Leuven • the reviewers • aspirant F.W.O.-Vlaanderen

40. Remark: surfels are considered being disks, not just points enlarge bounding boxes for overlap tests

41. Remark: surfels are considered being disks, not just points translate planes in boundary cells

42. Choice of parallel planes is not always optimal

43. Comparison with the technique of Pauly et al.

44. Surfels close to surface of other solid • Inside with our technique, • outside with the technique of Pauly et al. • Solutions: • denser sampling • differential points (Kalaiah and Varshney)