Computational Origami

This page contains links to computational tools useful for origami design and for combining origami with mathematical or scientific applications. See here for additional links about origami math, science, and technology. See here for additional links not specifically related to mathematical and scientific origami.

If you’ve got a computational origami tool you’d like listed, send me a link. Please let me know if you find any broken links below or if there are any pages you think I’ve overlooked.

Design Tools

These links are for software that is primarily for origami design: you specify the shape or functionality that you want, and the software tool constructs the fold pattern and/or a 2D or 3D model of the result.

  • TreeMaker
    My own design tool for creating tree-like (branched) structures. I’ve not updated it in a while, but it’s still useful for getting a sense of the layout of efficient structures for such forms.
  • ReferenceFinder
    My design tool for finding short folding sequences to give any combination of points or lines. Includes source code, making it relatively easy to port to other platforms (there was an iPhone port for a while, though it’s no longer on the iOS app store).
  • ReferenceFinder Online
    Robby Kraft has written an online version of ReferenceFinder which, being web-based, should work from any platform.
  • Origami Mechanism Topology Optimizer
    Kazuko Fuchi and co-workers at AFRL have developed this Matlab program for origami mechanism design. The objective function is a desired displacement; it determines fold lines (on a user-defined grid) that produces the desired displacement.
  • Edwin Peraza Hernandez’s Kinematic Simulation
    Edwin Peraza Hernandez’s Matlab codes for kinematic simulation of sharp-crease and smooth-fold origami.
  • Tomohiro Tachi’s FreeForm Origami
    Tomohiro Tachi’s program allows you to grab and pull vertices of the 3D form and watch the corresponding crease pattern change in real time. It’s also useful for determining rigid foldability of existing patterns.
  • Tomohiro Tachi’s Origamizer
    Constructs a crease pattern that, when folded, conforms to an arbitrary user-specified triangulated surface.
  • Tomohiro Tachi’s Rigid Origami Simulator
    Performs simulation and analysis of (potentially) rigidly foldable origami mechanisms and allows 3D manipulation of the pattern on-screen.
  • Jun Mitani’s ORIPA
    ORIPA is a pattern editor for origami that provides a visual rendering of the folded form. The file format is starting to see adoption by other computational tools.
  • Jun Mitani’s ORI-REVO
    Jun Mitani’s interactive Java tool for constructing surfaces of revolution, including both crease patterns with rotational symmetry (like the “Origami Flanged Pot” demonstration above) as well as rectangular-translational symmetry. See a demonstration video here.
  • Jun Mitani’s ORI-REF
    Yet another cool tool from Mitani-san. This one generates curved folds whose folds are planar in 3D by repeatedly reflecting a curved surface through a user-definable plane.
  • Alex Bateman’s Tessellations
    Alex Bateman’s web page that includes extensive information about origami tessellations and a downloadable program, Tess, for generating them.
  • JOrigami
    An open source Java implementation of the “Fold and Cut” problem originally solved by Erik Demaine. Contains code and some good references on the problem.
  • Nonlinear truss model with topology optimization
    Andrew Gilman’s MatLab code for designing origami mechanisms based on topology optimization.
  • Wolfram Demonstrations
    The Wolfram demonstrations project includes several Mathematica notebooks for the creation of origami figures. I draw your attention to two that I’ve submitted:

    • Origami Flanged Pots — An interactive tool that lets you define the cross section of a rotationally symmetric pot and generate the crease pattern and an image of the folded form.
    • Interactive Rings Tessellation — Lets you define several characteristics of a rotationally symmetric simple flat twist tessellation and generate the crease pattern and image of the folded form.

    Analysis, Utilities, and API Tools

    These links are for software that is primarily for analysis of existing origami patterns and useful utilities if you are building your own software for origami design or analysis.

    • Glaucio Paulino and Chris Liu’s MERLIN, MERLIN2
      A Matlab package by Glaucio Paulino and his students for performing simulation within a truss-based model of origami mechanisms. Includes elastic energy, panel bending/deformation, analysis of nonlinear phenomena like snap-through, and more.
    • FOLD format
      The specification for the Flexible Origami List Datastructure format developed by Erik Demaine, Jason Ku, and myself, as an interchange format for origami software. Converters written by Erik Demaine for many popular formats (e.g., Oripa); supported natively by MERLIN2, Origami Simulator, and more.
    • Tessellatica
      My collection of Mathematica code for manipulating and analyzing origami forms. It’s open-source, but you’ll need Mathematica to use it.
    • Amanda Ghassaei’s Origami Simulator
      A Javascript implementation of an origami folding simulator, based on a “truss model” and using the FOLD format.
    • Rhino 3D
      Rhino 3D is a modeling tool for designers that has seen adoption by quite a few people for use in computational origami (do a search for the word “origami” on their website). Many of them use the Grasshopper plugin, which is a “generative modeler” for Rhino; put differently, it allows you to create structures algorithmically, using a visual editor.

    Computational Origamists

    Modern research in origami modeling and algorithms almost certainly requires some level of programming, which, with the growth in interest in computational origami, means there are tens, if not hundreds of people who have done some level of programming. These are a few of the more prominent researchers who have developed and posted publicly available tools (see above for specifics).

    • Erik Demaine (MIT)
      Erik Demaine is one of the leading computation origamists in the world; he and his co-authors have solved numerous computational origami problems, demonstrating both complexity classes and algorithms both existence-proving and efficient.
    • Glaucio Paulino (Georgia Tech)
      Professor Paulino’s research focuses on computational mechanics and spans development of methodologies to characterize deformation and fracture behavior of existing and emerging materials and structural systems, topology optimization for large-scale and multiscale/multiphysics problems, and origami.
    • Edwin Peraza-Hernandez (University of California Irvine)
      Professor Peraza Herandez’s research explores the modeling, analysis, and design aspects of morphing structures, especially those inspired by origami and tensegrity.
    • Jun Mitani (University of Tsukuba)
      Professor Mitani has developed the theory and tools of many origami structures; you can see examples of them and his papers on his website.
    • Tomohiro Tachi (University of Tokyo)
      Tomohiro Tachi has developed a number of origami computational tools and has developed fundamental theory in the area of rigid folding and the notoriously difficult field of thick origami.
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