1. The Domain of a Point Set Surface Nina Amenta and Yong J. Kil University of California at Davis

2. Introduction x (x) x

3. Motivation

4. MLS

5. Our Line Integral

6. Understanding MLS MLS Amenta, Kil, SIGGRAPH 2004 e(x,a) n(x)

7. Energy Field of MLS a Amenta, Kil, SIGGRAPH 2004 Gaussian Weight a

8. Vector Field of MLS a n MLS (x) Amenta, Kil, SIGGRAPH 2004

9. Extremal Surface Amenta, Kil, SIGGRAPH 2004 Energy on

10. An Energy and Vector Field (not MLS) e n

11. Circular plot x n(x) a ||e(x,a)||

12. MLS Vector Field

13. MLS Best Fitting Plane

14. MLS Corner Example

15. Ideal Stream Lines

16. MLS Circular Plot

17. MLS Vector Field

18. MLS Surface and Vector Field

19. Optimal Direction via Center of Mass c c c Normalized Gaussian Weight

20. n COM

21. Vector Field and Surface

22. Estimated Distance Function x

23. Estimated Distance Field

25. Estimated Distance Function

26. Line Integral Intro

27. Line Integral n I (x) a x

28. n I Vector Field

29. Ideal Stream Lines

30. n I Stream Lines

31. Surface and Stream Lines

32. Overall View MLSCenter of Mass e DIST & n I Vector Field Energy Field Surface

33. Conclusion Analyze various energy and vector fields. n COM works well except at sharp corners. e DIST approximates distance well. n I works well, but expensive (Not recommend for 3D).

34. Thank you. Updated paper and slide: http://graphics.cs.ucdavis.edu/~yjkil/pub/domain.html Defining Surface plugin (to appear): http://www.pointshop3d.com

35. Estimated Distance and Line Integral

36. MLS

37. e DIST n I

39. MLS Circular plot example

40. MLS Energy e(x,a)

41. Energy + Field

42. MLS Surface

43. Surface with maxima

44. MLS Surface with maxima