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6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW). Instructor: Professor Erik Demaine. 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. (from ocw.mit.edu)

Lecture 16 - Vertex & Orthogonal Unfolding

This lecture continues with open problems involving general unfoldings of polyhedra and proof of vertex unfolding using construction of facet-paths. Approaches for unfolding orthogonal polyhedra, grid unfolding, and folding convex polyhedra are presented.


Class 16 - Vertex & Orthogonal Unfolding

This class reviews covers topologically convex vertex-unfoldable cases and unfolding for orthogonal polyhedra, including the approach of heavy-light decomposition. The class also reviews Cauchy's Rigidity Theorem.


Go to the Course Home or watch other lectures:

Lecture 01 - Overview
Lecture 02 - Simple Folds
Lecture 03 - Single-Vertex Crease Patterns
Lecture 04 - Efficient Origami Design
Lecture 05 - Artistic Origami Design
Lecture 06 - Architectural Origami
Lecture 07 - Origami is Hard
Lecture 08 - Fold & One Cut
Lecture 09 - Pleat Folding
Lecture 10 - Kempe's Universality Theorem
Lecture 11 - Rigidity Theory
Lecture 12 - Tensegrities & Carpenter's Rules
Lecture 13 - Locked Linkages
Lecture 14 - Hinged Dissections
Lecture 15 - General & Edge Unfolding
Lecture 16 - Vertex & Orthogonal Unfolding
Lecture 17 - Alexandrov's Theorem
Lecture 18 - Gluing Algorithms
Lecture 19 - Refolding & Smooth Folding
Lecture 20 - Protein Chains
Lecture 21 - HP Model & Interlocked Chains