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Massachusetts Institute of Technology

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Massachusetts Institute of Technology via MIT OpenCourseWare

Overview

This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. Acknowledgments --------------- Thanks to videographers Martin Demaine and Jayson Lynch.

Syllabus

Lecture 1: Overview.
Class 1: Overview.
Lecture 2: Simple Folds.
Class 2: Universality & Simple Folds.
Lecture 3: Single-Vertex Crease Patterns.
Class 3: Single-Vertex Crease Patterns.
Lecture 4: Efficient Origami Design.
Class 4: Efficient Origami Design.
Lecture 5: Artistic Origami Design.
Class 5: Tessellations & Modulars.
Lecture 6: Architectural Origami.
Class 6: Architectural Origami.
Lecture 7: Origami is Hard.
Class 7: Origami is Hard.
Lecture 8: Fold & One Cut.
Class 8: Fold & One Cut.
Lecture 9: Pleat Folding.
Class 9: Pleat Folding.
Lecture 10: Kempe's Universality Theorem.
Class 10: Kempe's Universality Theorem.
Lecture 11: Rigidity Theory.
Class 11: Generic Rigidity.
Lecture 12: Tensegrities & Carpenter's Rules.
Class 12: Tensegrities.
Lecture 13: Locked Linkages.
Class 13: Locked Linkages.
Lecture 14: Hinged Dissections.
Class 14: Hinged Dissections.
Lecture 15: General & Edge Unfolding.
Class 15: General & Edge Unfolding.
Lecture 16: Vertex & Orthogonal Unfolding.
Class 16: Vertex & Orthogonal Unfolding.
Lecture 17: Alexandrov's Theorem.
Class 17: D-Forms.
Lecture 18: Gluing Algorithms.
Lecture 19: Refolding & Smooth Folding.
Class 19: Refolding & Kinetic Sculpture.
Lecture 20: Protein Chains.
Class 20: 3D Linkage Folding.
Lecture 21: HP Model & Interlocked Chains.

Taught by

Prof. Erik Demaine

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