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00:00
1.
Geometric Reasoning and Applications: Arrangement and Duality
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02:06
2.
Outline of the Contents
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03:25
3.
Definition of Duality
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03:32
4.
Definition of Duality
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11:05
5.
Duality Properties
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14:02
6.
Geometric Interpretation of Duality
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21:26
7.
Duality for Other Objects
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24:34
8.
Why Study Duality?
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26:25
9.
Definition of Arrangement
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28:28
10.
Complexity of an Arrangement
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31:18
11.
Properties of Arrangements: Number of Vertices, Edges, and Faces
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34:12
12.
Properties of Arrangements : Number of Vertices, Edges, and Faces
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34:44
13.
Properties of Arrangements: Number of Vertices, Edges, and Faces
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38:27
14.
Zone Theorem
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41:26
15.
Zone Theorem
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41:59
16.
Proof of Zone Theorem
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49:14
17.
Constructing an Arrangement with Doubly-Connected Edge Lists
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50:43
18.
Doubly-Connected Edge Lists
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52:03
19.
Constructing an Arrangement
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52:19
20.
Constructing an Arrangement
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52:46
21.
Zone Theorem
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52:57
22.
Constructing an Arrangement
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1:00:28
23.
Constructing an Arrangement
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1:01:47
24.
Constructing an Arrangement
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1:04:03
25.
Constructing an Arrangement
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1:04:40
26.
Complexity Analysis of Arrangement Construction
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1:09:13
27.
Computing Discrepancy
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1:21:13
28.
Computing Levels of Vertices