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+
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+ HW4
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HW4
+
Problem 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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+
Same as 3. 3 is a subset of 2.
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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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+
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:
+
+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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\ No newline at end of file
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+# HW4
+## Problem 1
+ - 1. 
+ A star is an example. P(g1) can see all of P, but on all direction of the circle, it is not monotone.
+ - 2. Same as 3. 3 is a subset of 2.
+ - 3. 
+ 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).
+ - 4. 
+ - 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:
+ 
+ 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.
+## Problem 2
+ - 1. 
+ - 2. 
+ - 3. 
\ No newline at end of file
diff --git a/HW4/HW4.pdf b/HW4/HW4.pdf
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diff --git a/HW4/hw4-sweep_1.ipe b/HW4/hw4-sweep_1.ipe
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diff --git a/HW4/hw4-sweep_2.ipe b/HW4/hw4-sweep_2.ipe
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