origami design
TRANSCRIPT
MITNovember, 2004
Context
MITNovember, 2004
Background• Origami: Japanese paper-folding.
• Traditional form: Decorative abstract shapes & child’s craft
• Modern extension: a form of sculpture in which the primarymeans of creating the form consists of folding
• Most common version: a figure folded from one sheet of paper,usually a square, with no cuts.
MITNovember, 2004
Traditional Origami• Japanese newspaper from 1734: Crane, boat, table, “yakko-san”• By 1734, it is already well-developed
MITNovember, 2004
Modern Origami• The modern art form was reborn in the early 20th century
through the efforts of a Japanese artist, Akira Yoshizawa, whocreated new figures of artistic beauty and developed a writteninstructional language.
A. Yoshizawa, Origami Dokuhon I
MITNovember, 2004
The Design Revolution• “Creative” origami caught on worldwide in the 1950s and 1960s.
• Beginning in the 1970s, many geometric design techniqueswere developed that enabled the creation of figures ofundreamed-of complexity.
• The mathematical theory of origami was greatly expanded inthe 1990s, leading to computer-aided origami design.
MITNovember, 2004
Origamitoday
• “Black Forest Cuckoo Clock,”designed in 1987
• One sheet, no cuts• 216 steps
– not including repeats• Several hours to fold
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Ibex
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Dragonfly
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Scaled Koi
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Western Pond Turtle
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Rattlesnake
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White-tailed Deer
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Bull Moose
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Bull Elephant
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Hummingbird & Trumpet Vine
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(Hummingbird Close-up)
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Grizzly Bear
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Roosevelt Elk
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Tree Frog
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Tarantula
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Murex
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Spindle Murex
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12-Spined Shell
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Banana Slug
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Spiral Tessellation
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Egg17 Tessellation
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Molecular Tessellation
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Chalk time…
MITNovember, 2004
A Tree & Active Polygons
aaa
1
234
56 7 8
91011
1213 14
1516
17
181920
21
222324
25 26
(root)
9
15
16
9
15
14
5 8
11
15
1617
20
21
23
25 26
MITNovember, 2004
Subtrees
MITNovember, 2004
Chalk time…
MITNovember, 2004
Molecules• Crease patterns that collapse a polygon so that all edges lie on a
single line are called “bun-shi,” or molecules (Meguro)• Different bun-shi are known from the origami literature.• Triangles have only one possible molecule.
aaa
A
CB
DD
D
a a
b
b c
cE
A
C
BD
a
bc
E A
C
BD
a
bc
the “rabbit ear” molecule
MITNovember, 2004
Quadrilateral molecules• There are two possible trees and several different molecules for a
quadrilateral.• Beyond 4 sides, the possibilities grow rapidly.
a
“4-star” “sawhorse”
Husimi/Kawasaki Maekawa Lang
MITNovember, 2004
Four is enough• It is always possible to add flaps (circles) to a base so that the
only polygons are triangles and quadrilaterals, so thesemolecules suffice.
MITNovember, 2004
Universal molecule• An algorithm that produces the crease pattern to collapse an
arbitrary valid convex polygon into a base whose projection is aspecified tree.
aa
0.449
0.354
0.194
0.325
0.393
0.372
0.627
MITNovember, 2004
A pentagonal UM
aa
TA B
C
D
E F
P
pB
pC
pD
pE
pA
pF,2
pF,1
pF,4
pF,3
MITNovember, 2004
Insetting
MITNovember, 2004
Gusset formation
aa
v2v 1
v3
v4
v5
Mv2v 1
v3
v4
v5
M
′v1 ′v2
′v3′v4
′v5hmax
MITNovember, 2004
Finished gussets
aa
v2v1
v3
v4
v5
M
MITNovember, 2004
Creases & Folded Form
aa
P
pB
pC
pA pF,1
pE
pF,3
pD
pF,4
pF,2
pF,5
pF,6
pBpC
pA
pEpD
MITNovember, 2004
Chalk time…
MITNovember, 2004
Universal Molecule 1
a
1
2
3
45
6
7 8
1
1
1
3
5
5
7 85
5
3
3
6
1
42
MITNovember, 2004
Universal Molecule 2
a
1
23 4 5
6 7
8 9 10 11
12 13 14 15
1
1 11
2 3
4
4
4
5
7
7
11
10
1514
13
12
6
8
8
8 6 9 9
9
6
7
MITNovember, 2004
Resources• Origami design software TreeMaker (with 170 pp manual) can
be downloaded from:– http://origami.kvi.nl/programs/treemaker
• …or Google-search for “TreeMaker”• Version 5.0 (Mac/Linux/Windows) is under construction.• Other origami-related software, including ReferenceFinder, is
at the same site• Theory described in 12 ACM SCG paper, “An Algorithm for
Origami Design” (1996) by Robert J. Lang.
MITNovember, 2004
More Resources• Origami Design Secrets, my new book teaching how to design
origami (and more), was published by A. K. Peters in October2003.
• Origami Insects II, my latest, contains a collection of fairlychallenging insect designs
• Both (and other books) available from the OrigamiUSA Source(www.origami-usa.org).
• Further information may be found athttp://www.langorigami.com, or email me [email protected]