Optimal Degree Distribution for LT Codes with Small Message Length
[Istrail, Schwartz, King 1999] - MIT OpenCourseWare · Aichholzer, Bremner, Demaine, Meijer,...
Transcript of [Istrail, Schwartz, King 1999] - MIT OpenCourseWare · Aichholzer, Bremner, Demaine, Meijer,...
[Istrail,Schwartz,King 1999]
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Image by MIT OpenCourseWare.
[Newman 2002]
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Counterclockwise Chain
Length >1 to next
Length 1 to nextodd-parity H node
odd-parity H node
Length 1 to next even-parity H node
Length >1 to next even-parity H node
Clo
ckw
ise
Ch
ain
Image by MIT OpenCourseWare.See also http://portal.acm.org/citation.cfm?id=545495/.
Aichholzer, Bremner, Demaine,
Meijer, Sacristán, Soss 2003
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Length 18
Unique optimal folding
Unique optimal folding
Length 20
Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/RedBlue_CGTA2003/.
Aichholzer, Bremner, Demaine,
Meijer, Sacristán, Soss 20034
X
X
Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/RedBlue_CGTA2003/.
Aichholzer, Bremner, Demaine,
Meijer, Sacristán, Soss 20035
Uniqueoptimalfolding
Twooptimalfoldings
Length 18
Length 16
Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/RedBlue_CGTA2003/.
[Demaine, Langerman, O’Rourke, Snoeyink 2003]6
Glass, Langerman, O’Rourke, Snoeyink, Zhong 2004
Brunet, Irving, O’Rourke 2004
Courtesy of Joseph O'Rourke.Used with permission.
Courtesy of Julie Glass, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink, Jianyuan K. Zhong. Used with permission.7
Glass, Lu, O’Rourke, Zhong 2006
Courtesy of Joseph O'Rourke. Used with permission.8
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v’0
sv2
sv0
v2
v’2
sv1
s0
(0,0,0)
Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/InterlockedLinkages_SoCG2002/.
[Demaine, Langerman, O’Rourke, Snoeyink 2002]10
a2 a1
b1
b1
xy
Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/InterlockedLinkages_SoCG2002/.
[Demaine, Langerman,
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2002]11
[Demaine, Langerman, O’Rourke, Snoeyink 2002]
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O’Rourke, Snoeyink
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012 21
2 412 51
2
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[Demaine, Langerman,
O’Rourke, Snoeyink
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locked chains?
2 3 4 5
univ. rigid univ. fixed angle rigid univ. fixed
angle rigid rigid
2univ. − − − − − − − − +rigid − − − − + + + + +
3
univ. − − − − + + + + +fixedangle − − − + + + + + +
rigid − + + + + + + + +
4
univ. − + + + + + + + +fixed angle − + + + + + + + +
rigid − + + + + + + + +5 rigid + + + + + + + + +
[Demaine, Langerman, O’Rourke, Snoeyink 2002]16
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6.849 Geometric Folding Algorithms: Linkages, Origami, PolyhedraFall 2012
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