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CS504 Presentation Chan’s algorithm. Planar Convex Hull CS504 Presentation.

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Presentation on theme: "CS504 Presentation Chan’s algorithm. Planar Convex Hull CS504 Presentation."— Presentation transcript:

1 CS504 Presentation Chan’s algorithm

2 Planar Convex Hull CS504 Presentation

3 Chan’s Algorithm CS504 Presentation

4 Chan’s Algorithm CS504 Presentation

5 Chan’s Algorithm CS504 Presentation Stage 1 n = 32 Set m = 8

6 Chan’s Algorithm CS504 Presentation Stage 1 n = 32 Set m = 8 r = 4

7 Chan’s Algorithm CS504 Presentation

8 Chan’s Algorithm CS504 Presentation Stage 2 (After Stage 1) m = 8 r = 4

9 Chan’s Algorithm CS504 Presentation Stage 2 Using Graham’s Scan

10 Chan’s Algorithm CS504 Presentation Stage3 : Jarvis’s March How to merge these r hulls into a single hull? IDEA : treat each hull as a “fat point” and run Jarvis’s March! # of iteration is at most m –to guarantee the time complexity O(nlogh)

11 Chan’s Algorithm CS504 Presentation (-inf,0) -> lowest pt lowest pt

12 Chan’s Algorithm CS504 Presentation Find the point that maximize the angle in each hull lowest pt 1

13 Chan’s Algorithm CS504 Presentation Find the point that maximize the angle in each hull lowest pt 1 2

14 Chan’s Algorithm CS504 Presentation Find the point that maximize the angle in each hull lowest pt 1 2 3

15 Chan’s Algorithm CS504 Presentation

16 Chan’s Algorithm CS504 Presentation FAIL EXAMPLE – too small value m m = 4 4 iteration

17 Chan’s Algorithm CS504 Presentation In 4(a), how to find such points?

18 Chan’s Algorithm CS504 Presentation Find the point that maximize the angle in each hull lowest pt 1

19 Chan’s Algorithm CS504 Presentation Find the point that maximize the angle in a hull

20 Chan’s Algorithm CS504 Presentation

21 Chan’s Algorithm CS504 Presentation

22 Chan’s Algorithm CS504 Presentation

23 Chan’s Algorithm CS504 Presentation

24 Chan’s Algorithm CS504 Presentation

25 Chan’s Algorithm CS504 Presentation


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