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Published byDarwin Keeton Modified about 1 year ago

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CS504 Presentation Chan’s algorithm

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Planar Convex Hull CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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

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

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Chan’s Algorithm CS504 Presentation

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

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

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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)

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

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

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

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

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Chan’s Algorithm CS504 Presentation

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

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

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

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

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Chan’s Algorithm CS504 Presentation 1 2 3 4 5

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Chan’s Algorithm CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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Chan’s Algorithm CS504 Presentation

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