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The Domain of a Point Set Surface

The Domain of a Point Set Surface. Nina Amenta and Yong J. Kil University of California at Davis. x. (x). (x). x. Introduction. Motivation. MLS. Our Line Integral. Understanding MLS. MLS. e(x,a). n(x). Amenta, Kil, SIGGRAPH 2004. a. a. Gaussian Weight . Energy Field of MLS.

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The Domain of a Point Set Surface

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

  2. x (x) (x) x Introduction

  3. Motivation

  4. MLS

  5. Our Line Integral

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

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

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

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

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

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

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

  20. nCOM

  21. Vector Field and Surface

  22. x Estimated Distance Function

  23. Estimated Distance Field

  24. Estimated Distance Field

  25. Estimated Distance Function

  26. Line Integral Intro

  27. x a Line IntegralnI(x)

  28. nIVector Field

  29. Ideal Stream Lines

  30. nIStream Lines

  31. Surface and Stream Lines

  32. Overall View eDIST & nI MLS Center of Mass Vector Field Energy Field Surface

  33. Conclusion • Analyze various energy and vector fields. • nCOMworks well except at sharp corners. • eDIST approximates distance well. • nI works well, but expensive (Not recommend for 3D).

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

  35. Estimated Distance and Line Integral

  36. MLS

  37. eDIST nI

  38. eDIST nI

  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

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