From 28f0551c27ac41c93153e6fd530aab42af8066b1 Mon Sep 17 00:00:00 2001 From: Renge Date: Thu, 6 Oct 2022 15:51:55 -0400 Subject: [PATCH] feat: finish hw4 --- HW4/1_1_1.png | Bin 0 -> 50934 bytes HW4/1_3_1.png | Bin 0 -> 11551 bytes HW4/1_4_1.png | Bin 0 -> 52751 bytes HW4/1_5_1.png | Bin 0 -> 9770 bytes HW4/2_1_1.png | Bin 0 -> 52423 bytes HW4/2_2_1.png | Bin 0 -> 69131 bytes HW4/2_3_1.png | Bin 0 -> 100503 bytes HW4/HW4.html | 815 +++++++++++++++++++++++++++++++++++++ HW4/HW4.md | 15 + HW4/HW4.pdf | Bin 0 -> 400993 bytes HW4/hw4-sweep_1.ipe | 418 +++++++++++++++++++ HW4/hw4-sweep_2.ipe | 518 +++++++++++++++++++++++ HW4/hw4-sweep_3.ipe | 518 +++++++++++++++++++++++ HW4/hw4p1.ipe | 482 ++++++++++++++++++++++ HW4/hw4p1.ipe.autosave.ipe | 491 ++++++++++++++++++++++ 15 files changed, 3257 insertions(+) create mode 100644 HW4/1_1_1.png create mode 100644 HW4/1_3_1.png create mode 100644 HW4/1_4_1.png create mode 100644 HW4/1_5_1.png create mode 100644 HW4/2_1_1.png create mode 100644 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    HW4

    +

    Problem 1

    +
      +
    • +
        +
      1. 1_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. +
      +
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        +
      1. Same as 3. 3 is a subset of 2.
      2. +
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        +
      1. 1_3_1
        +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).
      2. +
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        +
      1. 1_4_1
      2. +
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      1. 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: +1_5_1
        +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=0y=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.
      2. +
      +
    • +
    +

    Problem 2

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        +
      1. 2_1_1
      2. +
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      1. 2_2_1
      2. +
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      1. 2_3_1
      2. +
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    + + + + + \ No newline at end of file diff --git a/HW4/HW4.md b/HW4/HW4.md new file mode 100644 index 0000000..8c89c17 --- /dev/null +++ b/HW4/HW4.md @@ -0,0 +1,15 @@ +# HW4 +## Problem 1 + - 1. ![1_1_1](1_1_1.png) + 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. ![1_3_1](1_3_1.png) + 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. ![1_4_1](1_4_1.png) + - 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: + ![1_5_1](1_5_1.png) + 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_1_1](2_1_1.png) + - 2. ![2_2_1](2_2_1.png) + - 3. ![2_3_1](2_3_1.png) \ No newline at end of file diff --git a/HW4/HW4.pdf b/HW4/HW4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c8f1927a69af43995508b3f99094569ce33e3b0c GIT binary patch literal 400993 zcmc${2|Sc*_&0t!N=2PEOQ>j-45OoxrBOOcoDj(tlZ0eTwlHX+#hQ~y$dRN-WM48$ z4a%0iLX%Mmp|NC)W!~$4hK?!q{@(ZV{y+coIiGW^&-2{Recjjfy}sA?x~$j!Ymd}s z>8(8Lvw9wk@@x^45py_tf=5Y74F9)ps-v2%SNuOH9CjZuavWWoThtD=+o-gPaLn| z&MP;*n!_B}`=;lL%SFTNb-E;yR>-{Yy_c2z{(AYfYv1a!+?!@~2HUk>v~m@ZX?*D? zD^Kbup4M5i`jED}^pQutqDQn{@8ujhkj7e<@+vCRk7k}SPhaBEpBuNEFH>I9WooCH zASGp!q^0iTe%GIwsN!(Whrh^H$anbyZikd*^`;J~a}0N^Drn&npmwM7s8V?TS!ram zREM(V=ELVk8V!EPR>8kj*g)Oq0VUsG?`7e>XE)bN#_n7FC~s|1 zg<0sKCDNgBpUnRjQwynC?3XrZ=EA)Vzl0EULR_FwAHP^XGVKt_s@~M+jJ5rPlac=l z@g%Me5W(+fC6{w&&-E(VJMMb}};3ioUB}2w$k7t(+cc79A(*Zh6D8%<_5u)?DWeM=ue^g2qDn 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