15 lines
1.1 KiB
Markdown
15 lines
1.1 KiB
Markdown
# HW4
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## Problem 1
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- 1. 
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A star is an example. P(g1) can see all of P, but on all direction of the circle, it is not monotone.
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- 2. Same as 3. 3 is a subset of 2.
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- 3. 
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This is an example. It is a orthogonal simple polygon, and it is montain monotone on X direction, but it is not one gaurdable(two witness points do not share any common view).
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- 4. 
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- 5. True. Simple 4-gon with exactly 3 convex vertices must be a fox. If we rotate it and put its nose on origin and one of its ear on positive x-axis, it will look something like this:
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Note that if we go through y direction, the nose must be t because its at (0,0) which is the lowest y coordinate. Also the ear that is not on the x-axis must be b because it has highest y coordinate or otherwise this polygon won't be a fox. Besides, other than the line at $y=0$, no more than two points will share the same y value. Thus we have t and b join the same line so this must be mountain monotone on some direction d.
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## Problem 2
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- 1. 
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- 2. 
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- 3.  |