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+
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+ HW5
+
+
+
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+
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+
+
+ HW5
+Problem 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
+
+
+
+
+
+
+
+
+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
+
+
+
+
+
+
+
+
+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
+
+
+
+
+
+generated by Ipe
+Delaunay edges: 18
+Voronoi edges: 18
+|Q| = 1: 10
+|Q| = 2: 18
+|Q| = 3: 7
+|Q| = 4: 2
+|Q| = 5: 0
+|Q| > 5: 0
+
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diff --git a/HW5/HW5.md b/HW5/HW5.md
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+# 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| = 4: 2
+ - |Q| = 5: 0
+ - |Q| > 5: 0
+ - 2. ![2_2_1](2_2_1.png)
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+
+
+
+
+ HW6
+
+
+
+
+
+
+
+
+
+
+ HW6
+Problem 1
+
+
+
+
+
+
+
+
+
+N D e l ( n ) = 3 n − 6 N_{Del(n)}=3n-6 N De l ( n ) ​ = 3 n − 6
+
+
+
+
+v D e l ( n ) = n − 1 v_{Del(n)}=n-1 v De l ( n ) ​ = n − 1
+
+
+
+
+N D e l ( n ) = 4 n − 6 N_{Del(n)}=4n-6 N De l ( n ) ​ = 4 n − 6
+
+
+
+
+v D e l ( n ) = n v_{Del(n)}=n v De l ( n ) ​ = n
+
+
+
+
+
+
+
+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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+(5, 6), (7, 10), (4, 7), (8, 9), (7, 9), (3, 5), (2, 8), (3, 10), (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 , 1 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 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 , 1
+
+
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+
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diff --git a/HW6/HW6.md b/HW6/HW6.md
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+# 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
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--- /dev/null
+++ b/HW6/hw6-p1.ipe
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+9
+
+
diff --git a/HW6/hw6-p2.ipe b/HW6/hw6-p2.ipe
new file mode 100644
index 0000000..81b13b5
--- /dev/null
+++ b/HW6/hw6-p2.ipe
@@ -0,0 +1,3246 @@
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+
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diff --git a/HW6/hw6-pts-disperse.ipe b/HW6/hw6-pts-disperse.ipe
new file mode 100644
index 0000000..e355c5b
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