Approximate merging of two curves

1. Approximate merging of two curves Speaker: Jun Chen Nov. 28, 2007

2. References Approximate merging of a pair of Bezier curves Shi-Min Hu, Ruo-Feng Tong, Tao Ju, Jia-Guang Sun (CAD,2001)

4. Results of “merging”

5. Results of “merging”

6. Background Approximate conversion of spline curves. Josef Hoschek (CAGD 1987) • Reducing the amount of communicating data: • 1.Degree reduction • 2.Merging

7. Background Approximate conversion of spline curves. Josef Hoschek (CAGD 1987)

8. Perturbation in degree reduction

9. Perturbation in degree reduction

11. Precise merging

12. Perturbation

13. Perturbation

14. Method (1)

17. Method (2)

19. Matching endpoints and derivatives

20. Merging with points constraints

22. Degree elevation(?)

25. Remarks ?

26. Future work

27. Merging & degree reduction Perturbation Degree reduction Merging

28. 降阶：一条低阶曲线逼近一条高阶曲线，附带端点的插值条件。降阶：一条低阶曲线逼近一条高阶曲线，附带端点的插值条件。 • 合并：一条高阶曲线逼近两条低阶曲线，附带端点的插值条件。

29. New method(郭,2005)

30. Key points

32. Merging a Pair of Disk Bezier Curves (陈发来,2004)

33. Precise merging

34. Something different

35. Methed (Linear programming)

37. References Approximate merging of B-spline curves via knot adjustment and constrained optimization Chiew-Lan Tai, Shi-Min Hu, Qi-Xing Huang (CAD,2003)

38. Hong Kong University of Science and Technology • Geometric modeling, computer graphics, and graphics recognition.

40. Problem

41. Precise merging

43. ?

45. Knot adjustment

46. Error estimation and examples

47. Future work • Squared difference integral norm • 3次，且G2连续(梁清清,2006)

48. Thank you!