Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT...

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1 Edge unfolding vs. general unfolding

Transcript of Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT...

Page 1: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

1Edge unfolding vs. general unfolding

Page 2: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]

(16)

(36)

(56)

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.

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Page 3: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]

(76)

(96)

(146)

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.

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[Demaine, Eppstein, Erickson, Hart, O’Rourke 2001/2003]

(A)

(B)

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.

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Page 5: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/VertexUnfolding_Kuperberg2003/.

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Page 6: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

z

x

y

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Page 7: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Damian, Flatland, O’Rourke 2007]

Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.

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[Damian, Flatland, O’Rourke 2007]Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.8

Page 9: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Damian, Flatland, O’Rourke

2007]Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.

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Page 10: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Damian, Flatland, O’Rourke

2007]Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.

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Page 11: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Damian, Flatland, O’Rourke 2007]Courtesy of Mirela Damian, Robin Flatland, and Joseph O’Rourke. Used with permission.11

Page 12: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

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[Damian, Flatland, O’Rourke 2008]

To view video: "Reverse-direction suture" at http://cs.smith.edu/~orourke/Unf/Orthog.Anims.html.

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Page 14: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[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.

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[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

Page 16: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[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.16

Page 17: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/CCCG98b/.

z

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z2

y

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[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/CCCG98b/.

z4

z3

B4

B3+

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Page 19: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Demaine, Iacono, Langerman 2010]Courtesy of Erik D. Demaine, John Iacono, and Stefan Langerman. Used with permission.19

Page 20: Edge unfolding vs. general unfolding 1 - MIT OpenCourseWare · (76) (96) (146) Image by MIT OpenCourseWare. See also . 3

[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/CCCG98b/.

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[Biedl, Demaine, Demaine, Lubiw, Overmars, O’Rourke, Robbins, Whitesides 1998]

Image by MIT OpenCourseWare.See also http://erikdemaine.org/papers/CCCG98b/.

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Image by MIT OpenCourseWare.

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Image by MIT OpenCourseWare.

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Image by MIT OpenCourseWare.

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Image by MIT OpenCourseWare.

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6.849 Geometric Folding Algorithms: Linkages, Origami, PolyhedraFall 2012

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