From 2ea88a51e4288cc32d3a4851a9280f1b88e130e1 Mon Sep 17 00:00:00 2001 From: Renge Date: Thu, 10 Nov 2022 20:22:27 -0500 Subject: [PATCH] feat: finish hw5 & hw6 --- HW5/2_1_1.png | Bin 0 -> 45918 bytes HW5/2_2_1.png | Bin 0 -> 81474 bytes HW5/HW5.html | 828 ++++++++++ HW5/HW5.md | 26 + HW5/HW5.pdf | Bin 0 -> 177789 bytes HW5/hw5.xcf | Bin 0 -> 157935 bytes HW6/1_1_1.png | Bin 0 -> 39305 bytes HW6/1_2_1.png | Bin 0 -> 38608 bytes HW6/2_1_1.png | Bin 0 -> 35440 bytes HW6/2_1_2.png | Bin 0 -> 38237 bytes HW6/2_1_3.png | Bin 0 -> 35852 bytes HW6/2_1_4.png | Bin 0 -> 57985 bytes HW6/2_2_1.png | Bin 0 -> 171813 bytes HW6/HW6.html | 840 ++++++++++ HW6/HW6.md | 20 + HW6/HW6.pdf | Bin 0 -> 358741 bytes HW6/hw6-p1.ipe | 594 +++++++ HW6/hw6-p2.ipe | 3246 ++++++++++++++++++++++++++++++++++++++ HW6/hw6-pts-disperse.ipe | 534 +++++++ HW6/hw6-pts-mst.ipe | 380 +++++ HW6/hw6-pts-nng.ipe | 384 +++++ HW6/hw6-pts-rng.ipe | 391 +++++ HW6/hw6-pts-tsp.ipe | 420 +++++ HW6/hw6-pts.ipe | 344 ++++ HW6/hw6.pdf | Bin 0 -> 115936 bytes HW6/hw6.png | Bin 0 -> 173841 bytes HW6/hw6.xcf | Bin 0 -> 273034 bytes 27 files changed, 8007 insertions(+) create mode 100644 HW5/2_1_1.png create mode 100644 HW5/2_2_1.png create mode 100644 HW5/HW5.html create mode 100644 HW5/HW5.md create mode 100644 HW5/HW5.pdf create mode 100644 HW5/hw5.xcf create mode 100644 HW6/1_1_1.png create mode 100644 HW6/1_2_1.png create mode 100644 HW6/2_1_1.png create mode 100644 HW6/2_1_2.png create mode 100644 HW6/2_1_3.png create mode 100644 HW6/2_1_4.png create mode 100644 HW6/2_2_1.png create mode 100644 HW6/HW6.html create mode 100644 HW6/HW6.md create mode 100644 HW6/HW6.pdf create mode 100644 HW6/hw6-p1.ipe create mode 100644 HW6/hw6-p2.ipe create mode 100644 HW6/hw6-pts-disperse.ipe create mode 100644 HW6/hw6-pts-mst.ipe create mode 100644 HW6/hw6-pts-nng.ipe create mode 100644 HW6/hw6-pts-rng.ipe create mode 100644 HW6/hw6-pts-tsp.ipe create mode 100644 HW6/hw6-pts.ipe create mode 100644 HW6/hw6.pdf create mode 100644 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HW5

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Problem 1

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    1. +
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      • k = 4: tetrahedron
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      • k = 5: F = 5, E = 7.5 (15 / 2), no dot exist
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      • k = 6: two tetrahedron merge one facet with each other
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    2. +
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    1. +
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      • F = 4, E = 10, V = 8, not possible, total V must less than 7 (3 * 7 = 21 > 20)
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      • F = 5, E = 10, V = 7, same reason
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      • Yes, cube
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    2. +
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    1. +
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      • consider four side faces as a whole 5 by 3 face, and the top/down/inside faces as 1 by 1 faces
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      • F = 4 + 21 * 2 + 4 * 8 + 12 + 8 + 4 = 102
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      • E = 4 + 5 * 6 * 2 * 2 + 4 * 8 + 4 + 4 * 8 + 12 + 2 * 4 * 2 = 220
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      • V = 6 * 6 * 2 + 4 * 8 = 104
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      • Euler characteristic = 104 + 102 - 220 = -14
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      • genus = (2 - (-14)) / 2 = 8 (-14 = 2 - 2g)
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    2. +
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Problem 2

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    1. 2_1_1 +
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      • generated by Ipe
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      • Delaunay edges: 18
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      • Voronoi edges: 18
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      • |Q| = 1: 10
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      • |Q| = 2: 18
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      • |Q| = 3: 7
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      • |Q| = 4: 2
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      • |Q| = 5: 0
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      • |Q| > 5: 0
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    2. +
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    1. 2_2_1
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+ + + + + \ No newline at end of file diff --git a/HW5/HW5.md b/HW5/HW5.md new file mode 100644 index 0000000..924c3c4 --- /dev/null +++ b/HW5/HW5.md @@ -0,0 +1,26 @@ +# HW5 +## Problem 1 + - 1. - k = 4: tetrahedron + - k = 5: F = 5, E = 7.5 (15 / 2), no dot exist + - k = 6: two tetrahedron merge one facet with each other + - 2. - F = 4, E = 10, V = 8, not possible, total V must less than 7 (3 * 7 = 21 > 20) + - F = 5, E = 10, V = 7, same reason + - Yes, cube + - 3. - consider four side faces as a whole 5 by 3 face, and the top/down/inside faces as 1 by 1 faces + - F = 4 + 21 * 2 + 4 * 8 + 12 + 8 + 4 = 102 + - E = 4 + 5 * 6 * 2 * 2 + 4 * 8 + 4 + 4 * 8 + 12 + 2 * 4 * 2 = 220 + - V = 6 * 6 * 2 + 4 * 8 = 104 + - Euler characteristic = 104 + 102 - 220 = -14 + - genus = (2 - (-14)) / 2 = 8 (-14 = 2 - 2g) +## Problem 2 + - 1. ![2_1_1](2_1_1.png) + - generated by [Ipe](https://ipe.otfried.org/) + - Delaunay edges: 18 + - Voronoi edges: 18 + - |Q| = 1: 10 + - |Q| = 2: 18 + - |Q| = 3: 7 + - |Q| 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HW6

+

Problem 1

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    • 1_1_1
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      1. NDel(n)=3n−6N_{Del(n)}=3n-6
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      1. vDel(n)=n−1v_{Del(n)}=n-1
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      1. NDel(n)=4n−6N_{Del(n)}=4n-6
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      1. vDel(n)=nv_{Del(n)}=n
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    1. 1_2_1
      +Algorithm: First find the Voronoi diagram in O(nlogn), then for each intersection (both between edges and borders, including corners), find its distance to the point in the cell right next to it in O(n), and the one with the maximized distance is the P*
      +Based on Triangle inequality, any point that is not on the intersection must have less distance to the nearest point compare to the intersection point right next to it on the same edge, thus we can find P* in O(nlogn)
    2. +
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Problem 2

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      1. 2_1_1
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      1. 2_1_2
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      1. 2_1_3
        +(5, 6), (7, 10), (4, 7), (8, 9), (7, 9), (3, 5), (2, 8), (3, 10), (1, 4)
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      1. 2_1_4
        +1,4,7,9,8,2,8,9,7,10,3,5,6,5,3,10,7,4,1⇒1,4,7,9,8,2,10,3,5,6,11, 4, 7, 9, 8, 2, 8, 9, 7, 10, 3, 5, 6, 5, 3, 10, 7, 4, 1 \rArr 1, 4, 7, 9, 8, 2, 10, 3, 5, 6, 1
      2. +
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    1. 2_2_1
    2. +
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+ + + + + \ No newline at end of file diff --git a/HW6/HW6.md b/HW6/HW6.md new file mode 100644 index 0000000..9751e70 --- /dev/null +++ b/HW6/HW6.md @@ -0,0 +1,20 @@ +# HW6 +## Problem 1 + - 1. + - ![1_1_1](1_1_1.png) + - 1. $N_{Del(n)}=3n-6$ + - 2. $v_{Del(n)}=n-1$ + - 3. $N_{Del(n)}=4n-6$ + - 4. $v_{Del(n)}=n$ + - 2. ![1_2_1](1_2_1.png) + Algorithm: First find the Voronoi diagram in O(nlogn), then for each intersection (both between edges and borders, including corners), find its distance to the point in the cell right next to it in O(n), and the one with the maximized distance is the P* + Based on Triangle inequality, any point that is not on the intersection must have less distance to the nearest point compare to the intersection point right next to it on the same edge, thus we can find P* in O(nlogn) +## Problem 2 + - 1. + - 1. ![2_1_1](2_1_1.png) + - 2. ![2_1_2](2_1_2.png) + - 3. ![2_1_3](2_1_3.png) + (5, 6), (7, 10), (4, 7), (8, 9), (7, 9), (3, 5), (2, 8), (3, 10), (1, 4) + - 4. ![2_1_4](2_1_4.png) + $1, 4, 7, 9, 8, 2, 8, 9, 7, 10, 3, 5, 6, 5, 3, 10, 7, 4, 1 \rArr 1, 4, 7, 9, 8, 2, 10, 3, 5, 6, 1$ + - 2. ![2_2_1](2_2_1.png) \ No newline at end of file diff --git a/HW6/HW6.pdf b/HW6/HW6.pdf new file mode 100644 index 0000000000000000000000000000000000000000..28a93b89b79d85705743bcdf74f68af63db58e9a GIT binary patch literal 358741 zcmeFYXH=70*C=W)C?G{q1d&Klsz~o!i3LJ&O9_Gy34%aCdQZR_5>OD3-nK}Q8j6t~ z6aq+>8hVo+I)oD1S#iJbd+&ShId_cv=X~FH$LH8X_nOaKv(LHK^JGrJ`_Mb$QWCOE zg2egUZ6=w^*DpIF?U+53Z_y;6CS)=Q~}^@@BUiM@$D5k;RdqUe*sKnEKD{~8TI~+Y_i`Y+Hj!Sm8 z9($t7q)u%=VecEyVHFv<<&8n{onG^)kUTexZyWJ_+#TRGc%h2_>@Hl`;`l@LdJj|S z;V(a5PIfwIudd6rlsX=J6@EW_F=Y1jRTjYmPRk~8d>+y-Czn@ueNfKp`Myu{o=7P~ za2zUrJ1(o;H2wY-bHKKfXnU04hz0xj5oxdd7mrSmxy!cgxZOSpepN7jsiFJ+lS7C$ z;lKgH-F_*f#oaVf@uk_t-jn!=(@Y2+RAj`B^f{)4M?ojml=(DHn}qq)Y6pLs5=;Gf z7^%D;GvEB_A!m2``Qo}WmrV{jmmJXaWhaI`eV_&{w71S#zf8N%v~q=;`{(T=-`5Vk zDGXc77BGX<8?qBqBkn1F9N|1VPaA@(s&!t`>nWe@3WM3kxA@eitQwjK8F4CId$z(c z8b{lGXlrBCY)p5g2I%)&%Thgm6`xOd%zNBHGO4rE>8yhA!z~Fyt|{bFarfz9*DKG) z1d6(qwa$FG)_2MJZRsJa+kTJ!&~?lDbv;4gIE>z!Z#&tL>Grl9CN`zyap8LWAboP|egicfES_5Z2ElEgfb3S3k@>y4XJz};#_h6{ zwDk4gYYj(xM;Co33rj!TX?54d!u$6l&1awrI5{$kz-2cV_rIy#vUPL4Z{?!l z=-}k|%nF!L;onNbT*C4A&d$Do!m>5w!9VkZTyFl%!Ugi4Jr#*6^H?MX1s*lv{ImS= z&52~=GZpI+J%7gHa7h&#Omgc9Mo$W8TJT4!u?h z->;8LAc`IM`_B)HC^d{nhna>|-oqrdyVJP`4U~#bEUOR78XT)Tv7E8M{YUCyM8r8c(J}tXx~1$?0w+lcghlj&T;(eyr~vlC)eGl6iY>a ze78Xe%kK<-rY7xTa0^NzFEh8hBlI-j3m^Rk>uJPgVORI4_pjPWYP&&amWy8aQFU_(Q*U1pK3=fO$$uz4c-w&KZs73=ebjOc-Cekw!jc~H5MWVf-;}o zcZ$nq*=|pU#nWbY1NJ&Gic_^N1mmEhtyV=T*m@Sbz$Ajpj4ABDim-)XR4Jq~7E)w$ zXJw{a)cuL0nK5eh})7__o#3xcc zlvv83=oM*1hv_}5r4_c8RTT3q;f!z_JWA?EwM9uztzX{*o{uHKUHb<;E)BsSeexST zxlXHBcZa`!RZsFLy{-1u@0au78-rup!>*I-gU4Gg-T&m*rAZ^supDn{fSf`JgX*gim%(; 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