1
Edge unfolding vs. general unfolding
(16)
(36)
(56)
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.
2
[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]
(76)
(96)
(146)
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.
3
[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]
(A)
(B)
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.
4
[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.
5
z
y
x
6
Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.
7
[Damian, Flatland, O’Rourke 2007]
[Damian, Flatland, O’Rourke 2007]
8
Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.
9
Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.
[Damian,
Flatland,
O’Rourke
2007]
[Damian,
Flatland,
O’Rourke
2007]
10
Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.
[Damian, Flatland, O’Rourke 2007]
11
Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.
12
To view video: "Reverse-direction suture" at http://cs.smith.edu/~orourke/Unf/Orthog.Anims.html.
13
[Damian, Flatland, O’Rourke 2008]
Courtesy of Joseph O'Rourke. Used with permission.
To view videos: "Unfolding Orthogonal Terrains" at http://cs.smith.edu/~orourke/Unf/Orthog.Anims.html.
[O’Rourke 2007]
14
[O’Rourke 2007]
Courtesy of Joseph O'Rourke. Used with permission.
To view videos: "Unfolding Orthogonal Terrains" at http://cs.smith.edu/~orourke/Unf/Orthog.Anims.html.
15
Courtesy of Joseph O'Rourke. Used with permission.
To
16 view videos: "Unfolding Orthogonal Terrains" at http://cs.smith.edu/~orourke/Unf/Orthog.Anims.html.
[O’Rourke 2007]
z
y
z1
z4
z2
z3
z2
z0
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/CCCG98b/.
17
[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]
B4
B3
+
z4
z3
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/CCCG98b/.
18
[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]
[Demaine, Iacono, Langerman 2010]
19
Courtesy of Erik D. Demaine, John Iacono, and Stefan Langerman. Used with permission.
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/CCCG98b/.
20
[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]
Image by MIT OpenCourseWare.
See also http://erikdemaine.org/papers/CCCG98b/.
21
[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]
Image by MIT OpenCourseWare.
22
v
v
Image by MIT OpenCourseWare.
23
_
+
+
0
_
+
e’
0
+
s
e
s’
C
0
+
C+
_
+
0
Image by MIT OpenCourseWare.
24
+
_
+
v
_
_
+
f
+
_
+
Image by MIT OpenCourseWare.
25
Image by MIT OpenCourseWare.
26
MIT OpenCourseWare
http://ocw.mit.edu
6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Fall 2012
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