Origami Design - Massachusetts Institute Of Technology

Origami DesignTree Theory for Uniaxial BasesRobert J. Langrobert@langorigami.comMITNovember, 2004

ContextMITNovember, 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-developedMITNovember, 2004

Modern Origami The modern art form was reborn in the early 20th centurythrough the efforts of a Japanese artist, Akira Yoshizawa, whocreated new figures of artistic beauty and developed a writteninstructional language.A. Yoshizawa, Origami Dokuhon IMITNovember, 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 foldMITNovember, 2004

IbexMITNovember, 2004

DragonflyMITNovember, 2004

Scaled KoiMITNovember, 2004

Western Pond TurtleMITNovember, 2004

RattlesnakeMITNovember, 2004

White-tailed DeerMITNovember, 2004

Bull MooseMITNovember, 2004

Bull ElephantMITNovember, 2004

Hummingbird & Trumpet VineMITNovember, 2004

(Hummingbird Close-up)MITNovember, 2004

Grizzly BearMITNovember, 2004

Roosevelt ElkMITNovember, 2004

Tree FrogMITNovember, 2004

TarantulaMITNovember, 2004

MurexMITNovember, 2004

Spindle MurexMITNovember, 2004

12-Spined ShellMITNovember, 2004

Banana SlugMITNovember, 2004

Spiral TessellationMITNovember, 2004

Egg17 TessellationMITNovember, 2004

Molecular TessellationMITNovember, 2004

Chalk time MITNovember, 2004

A Tree & Active Polygons541891 (root)2346571011891112201713 141819212521172223241616151520232625MITNovember, 200426

SubtreesMITNovember, 2004

Chalk time MITNovember, 2004

Molecules Crease patterns that collapse a polygon so that all edges lie on asingle line are called “bun-shi,” or molecules (Meguro) Different bun-shi are known from the origami literature. Triangles have only one possible molecule.AaaDEaDEbAABcbaBDcCBbDcCthe “rabbit ear” moleculeMITNovember, 2004bDcC

Quadrilateral molecules There are two possible trees and several different molecules for aquadrilateral. Beyond 4 sides, the possibilities grow aekawaMITNovember, 2004Lang

Four is enough It is always possible to add flaps (circles) to a base so that theonly polygons are triangles and quadrilaterals, so thesemolecules suffice.MITNovember, 2004

Universal molecule An algorithm that produces the crease pattern to collapse anarbitrary valid convex polygon into a base whose projection is aspecified r, 2004

A pentagonal UMpAEBFpBPTApF,1pF,2pECpF,3pF,4DpDMITNovember, 2004pC

InsettingMITNovember, 2004

Gusset ��v3v4v3v4MITNovember, 2004

Finished gussetsv1v2Mv5v3v4MITNovember, 2004

Creases & Folded FormpApF,1pBpAPpF,2pF,6pF,5pEpF,3pCp F,4pDMITNovember, 2004pEpD pCpB

Chalk time MITNovember, 2004

Universal Molecule 121411113234536653578575MITNovember, 20048

Universal Molecule 22121514711475667810 111212 1314 15313 48 91107481369869MITNovember, 200414915

Resources Origami design software TreeMaker (with 170 pp manual) canbe 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, isat the same site Theory described in 12 ACM SCG paper, “An Algorithm forOrigami Design” (1996) by Robert J. Lang.MITNovember, 2004

More Resources Origami Design Secrets, my new book teaching how to designorigami (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 atrobert@langorigami.comMITNovember, 2004

Origami Design Secrets, my new book teaching how to design origami (and more), was published by A. K. Peters in October 2003. Origami Insects II, my latest, contains a collection of fairly challenging insect designs Both (and other books) available from the OrigamiUSA Source (www.origami-usa.org). Further information may be found at