feat: finish hw5 & hw6
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# HW5
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## Problem 1
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- 1. - 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. - 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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- 3. - 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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## Problem 2
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- 1. 
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- generated by [Ipe](https://ipe.otfried.org/)
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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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# HW6
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## Problem 1
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- 1.
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- 
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- 1. $N_{Del(n)}=3n-6$
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- 2. $v_{Del(n)}=n-1$
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- 3. $N_{Del(n)}=4n-6$
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- 4. $v_{Del(n)}=n$
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- 2. 
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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*
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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)
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## Problem 2
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- 1.
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- 1. 
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- 2. 
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- 3. 
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(5, 6), (7, 10), (4, 7), (8, 9), (7, 9), (3, 5), (2, 8), (3, 10), (1, 4)
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- 4. 
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$1, 4, 7, 9, 8, 2, 8, 9, 7, 10, 3, 5, 6, 5, 3, 10, 7, 4, 1 \rArr 1, 4, 7, 9, 8, 2, 10, 3, 5, 6, 1$
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- 2. 
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3246
HW6/hw6-p2.ipe
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3246
HW6/hw6-p2.ipe
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HW6/hw6-pts-disperse.ipe
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396 420 l
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</ipe>
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380
HW6/hw6-pts-mst.ipe
Normal file
380
HW6/hw6-pts-mst.ipe
Normal file
|
|
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384
HW6/hw6-pts-nng.ipe
Normal file
384
HW6/hw6-pts-nng.ipe
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391
HW6/hw6-pts-rng.ipe
Normal file
391
HW6/hw6-pts-rng.ipe
Normal file
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@ -0,0 +1,391 @@
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420
HW6/hw6-pts-tsp.ipe
Normal file
420
HW6/hw6-pts-tsp.ipe
Normal file
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@ -0,0 +1,420 @@
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</ipe>
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344
HW6/hw6-pts.ipe
Normal file
344
HW6/hw6-pts.ipe
Normal file
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@ -0,0 +1,344 @@
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-1 0 m
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||||
-2 0.333 l
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-2 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="arrow/double(spx)">
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<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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||||
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-1 -0.333 l
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||||
h
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-1 0 m
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-2 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="arrow/mid-normal(spx)">
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<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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-0.5 0.333 l
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-0.5 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="arrow/mid-fnormal(spx)">
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||||
<path stroke="sym-stroke" fill="white" pen="sym-pen">
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0.5 0 m
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||||
-0.5 0.333 l
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-0.5 -0.333 l
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h
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</path>
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</symbol>
|
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<symbol name="arrow/mid-pointed(spx)">
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||||
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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0.5 0 m
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||||
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-0.3 0 l
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-0.5 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="arrow/mid-fpointed(spx)">
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<path stroke="sym-stroke" fill="white" pen="sym-pen">
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||||
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-0.3 0 l
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-0.5 -0.333 l
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h
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</path>
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||||
</symbol>
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<symbol name="arrow/mid-double(spx)">
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<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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1 0 m
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||||
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||||
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h
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-1 0.333 l
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h
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</symbol>
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<symbol name="arrow/mid-fdouble(spx)">
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<path stroke="sym-stroke" fill="white" pen="sym-pen">
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</path>
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</symbol>
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<anglesize name="22.5 deg" value="22.5"/>
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||||
<anglesize name="30 deg" value="30"/>
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||||
<anglesize name="45 deg" value="45"/>
|
||||
<anglesize name="60 deg" value="60"/>
|
||||
<anglesize name="90 deg" value="90"/>
|
||||
<arrowsize name="large" value="10"/>
|
||||
<arrowsize name="small" value="5"/>
|
||||
<arrowsize name="tiny" value="3"/>
|
||||
<color name="blue" value="0 0 1"/>
|
||||
<color name="brown" value="0.647 0.165 0.165"/>
|
||||
<color name="darkblue" value="0 0 0.545"/>
|
||||
<color name="darkcyan" value="0 0.545 0.545"/>
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||||
<color name="darkgray" value="0.663"/>
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||||
<color name="darkgreen" value="0 0.392 0"/>
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||||
<color name="darkmagenta" value="0.545 0 0.545"/>
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<color name="darkorange" value="1 0.549 0"/>
|
||||
<color name="darkred" value="0.545 0 0"/>
|
||||
<color name="gold" value="1 0.843 0"/>
|
||||
<color name="gray" value="0.745"/>
|
||||
<color name="green" value="0 1 0"/>
|
||||
<color name="lightblue" value="0.678 0.847 0.902"/>
|
||||
<color name="lightcyan" value="0.878 1 1"/>
|
||||
<color name="lightgray" value="0.827"/>
|
||||
<color name="lightgreen" value="0.565 0.933 0.565"/>
|
||||
<color name="lightyellow" value="1 1 0.878"/>
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<color name="navy" value="0 0 0.502"/>
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<color name="orange" value="1 0.647 0"/>
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<color name="pink" value="1 0.753 0.796"/>
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<color name="purple" value="0.627 0.125 0.941"/>
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<color name="red" value="1 0 0"/>
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<color name="seagreen" value="0.18 0.545 0.341"/>
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<color name="turquoise" value="0.251 0.878 0.816"/>
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<color name="violet" value="0.933 0.51 0.933"/>
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<color name="yellow" value="1 1 0"/>
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<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
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<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
|
||||
<dashstyle name="dashed" value="[4] 0"/>
|
||||
<dashstyle name="dotted" value="[1 3] 0"/>
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||||
<gridsize name="10 pts (~3.5 mm)" value="10"/>
|
||||
<gridsize name="14 pts (~5 mm)" value="14"/>
|
||||
<gridsize name="16 pts (~6 mm)" value="16"/>
|
||||
<gridsize name="20 pts (~7 mm)" value="20"/>
|
||||
<gridsize name="28 pts (~10 mm)" value="28"/>
|
||||
<gridsize name="32 pts (~12 mm)" value="32"/>
|
||||
<gridsize name="4 pts" value="4"/>
|
||||
<gridsize name="56 pts (~20 mm)" value="56"/>
|
||||
<gridsize name="8 pts (~3 mm)" value="8"/>
|
||||
<opacity name="10%" value="0.1"/>
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||||
<opacity name="30%" value="0.3"/>
|
||||
<opacity name="50%" value="0.5"/>
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<opacity name="75%" value="0.75"/>
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||||
<pen name="fat" value="1.2"/>
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||||
<pen name="heavier" value="0.8"/>
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<pen name="ultrafat" value="2"/>
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<symbolsize name="large" value="5"/>
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<symbolsize name="small" value="2"/>
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<symbolsize name="tiny" value="1.1"/>
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<textsize name="Huge" value="\Huge"/>
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<textsize name="LARGE" value="\LARGE"/>
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<textsize name="Large" value="\Large"/>
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<textsize name="footnote" value="\footnotesize"/>
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<textsize name="huge" value="\huge"/>
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<textsize name="large" value="\large"/>
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<textsize name="small" value="\small"/>
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<textsize name="tiny" value="\tiny"/>
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<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
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<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
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<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
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<tiling name="falling" angle="-60" step="4" width="1"/>
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<tiling name="rising" angle="30" step="4" width="1"/>
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</ipestyle>
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<page>
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<layer name="alpha"/>
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<view layers="alpha" active="alpha"/>
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<use layer="alpha" name="mark/disk(sx)" pos="192 512" size="normal" stroke="black"/>
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<use matrix="1 0 0 1 32 -16" name="mark/disk(sx)" pos="128 448" size="normal" stroke="black"/>
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<use name="mark/disk(sx)" pos="192 384" size="normal" stroke="black"/>
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<use name="mark/disk(sx)" pos="256 448" size="normal" stroke="black"/>
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<use matrix="1 0 0 1 0 -16" name="mark/disk(sx)" pos="320 448" size="normal" stroke="black"/>
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<use matrix="1 0 0 1 0 16" name="mark/disk(sx)" pos="320 384" size="normal" stroke="black"/>
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<use matrix="1 0 0 1 -16 0" name="mark/disk(sx)" pos="256 368" size="normal" stroke="black"/>
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<use name="mark/disk(sx)" pos="128 368" size="normal" stroke="black"/>
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<use name="mark/disk(sx)" pos="64 368" size="normal" stroke="black"/>
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<use name="mark/disk(sx)" pos="64 448" size="normal" stroke="black"/>
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||||
<path stroke="darkcyan" arrow="normal/normal">
|
||||
48 384 m
|
||||
352 384 l
|
||||
</path>
|
||||
<path stroke="darkcyan" arrow="normal/normal">
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||||
192 352 m
|
||||
192 544 l
|
||||
</path>
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<text transformations="translations" pos="182.379 515.166" stroke="black" type="label" width="7.895" height="11.097" depth="0" valign="baseline" size="LARGE">1</text>
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<text matrix="1 0 0 1 128 28" transformations="translations" pos="197.254 374.656" stroke="black" type="label" width="7.895" height="11.097" depth="0" valign="baseline" size="LARGE">6</text>
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<text transformations="translations" pos="53.5399 376.257" stroke="black" type="label" width="7.895" height="11.097" depth="0" valign="baseline" size="LARGE">8</text>
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<text transformations="translations" pos="121.278 376.486" stroke="black" type="label" width="7.895" height="11.097" depth="0" valign="baseline" size="LARGE">9</text>
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<text matrix="1 0 0 1 -132 -20" transformations="translations" pos="326.322 390.675" stroke="black" type="label" width="7.895" height="11.097" depth="0" valign="baseline" size="LARGE">7</text>
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<text transformations="translations" pos="246.913 374.656" stroke="black" type="label" width="15.791" height="11.097" depth="0" valign="baseline" size="LARGE">10</text>
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</page>
|
||||
</ipe>
|
||||
BIN
HW6/hw6.pdf
Normal file
BIN
HW6/hw6.pdf
Normal file
Binary file not shown.
BIN
HW6/hw6.png
Normal file
BIN
HW6/hw6.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 170 KiB |
BIN
HW6/hw6.xcf
Normal file
BIN
HW6/hw6.xcf
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user