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Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

Origamizing polyhedral surfaces.

Tomohiro Tachi1

  • 1The University of Tokyo, Tokyo, Japan. ttachi@siggraph.org

IEEE Transactions on Visualization and Computer Graphics
|January 16, 2010
PubMed
Summary
This summary is machine-generated.

Researchers developed a practical method for creating 3D origami by determining the folding pattern for polyhedral surfaces without cuts. This computational origami approach enables the design of complex, previously unrealizable spatial models.

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Area of Science:

  • Computational geometry
  • Origami engineering
  • Computer-aided design

Background:

  • Traditional origami design often relies on manual methods or is limited to simpler shapes.
  • Creating complex 3D polyhedral surfaces from a single sheet without cuts presents significant geometric challenges.

Purpose of the Study:

  • To present the first practical computational method for deriving folding patterns (origamizing) for arbitrary polyhedral surfaces.
  • To solve the inverse problem of generating a crease pattern from a target 3D shape.
  • To develop a system for interactive design of complex 3D origami models.

Main Methods:

  • Formulating the problem as a polygon layout on a planar surface using 'tucking molecules'.
  • Investigating the necessary conditions for valid crease pattern construction.
  • Developing a two-step mapping and edge-splitting algorithm to satisfy these conditions.

Main Results:

  • A novel algorithm that successfully generates folding patterns for given polyhedral surfaces.
  • The introduction of 'tucking molecules' to facilitate the planar layout of surface polygons.
  • Demonstration of a system enabling interactive design of complex 3D origami.

Conclusions:

  • The developed method provides a practical solution for computational origami and the design of complex 3D folded structures.
  • This work opens new possibilities for creating intricate origami designs that were previously difficult or impossible to achieve.
  • The interactive system facilitates broader accessibility to advanced 3D origami design.