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Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

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Class 9: Pleat Folding

This class covers creases in context of smoothness and a proof from the lecture involving Taylor expansion. Algorithms for the numbers of folding operations necessary for an MV string are presented. The class ends with a hypar folding exercise.

46mins

24 Jun 2015

Rank #1

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Lecture 8: Fold & One Cut

This lecture presents the fold and cut problem, and both the straight skeleton method and disk-packing method. Simple fold and cut is then generalized for folding surface of polyhedra.

1hr 20mins

24 Jun 2015

Rank #2

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Class 6: Architectural Origami

This class begins with a folding exercise and demonstration involving Origamizer. A high-level overview of the mathematical constraints for Freeform and Rigid software are presented, followed by examples of origami robots and current open problems.

45mins

24 Jun 2015

Rank #3

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Class 7: Origami is Hard

This class begins with several examples of box-pleating and maze-folding. Clarifications on NP-hardness are provided with a walkthrough of a proof. Additional folding gadgets are introduced and non-simple folds are addresed.

49mins

24 Jun 2015

Rank #4

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Lecture 5: Artistic Origami Design

This lecture presents both the traditional and non-traditional style of origami with many visual examples. The lecture then moves onto applying tree method to design origami, and includes a design example for a crab using TreeMaker.

1hr 26mins

24 Jun 2015

Rank #5

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Lecture 7: Origami is Hard

This lecture introduces universal hinge patterns with the cube and maze gadget. NP-hardness problems involving partition and satisfiability are presented with examples of simple folds, global flat foldability, and disk packing.

1hr 22mins

24 Jun 2015

Rank #6

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Class 5: Tessellations & Modulars

This class introduces more examples of origami models that use a variety of techniques and media. At the end of the session, the class participates in a folding exercise that uses business cards to make modular cubes.

38mins

24 Jun 2015

Rank #7

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Lecture 6: Architectural Origami

This lecture presents Origamizer, freeform origami, and rigid origami applied to architectural and three-dimensional design contexts. Geometric constraints, demonstration videos, and physical models are shown for each portion of the lecture.

1hr 18mins

24 Jun 2015

Rank #8

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Class 4: Efficient Origami Design

This class begins with folded examples produced by TreeMaker and Origamizer. Explanation of the triangulation algorithm, checkerboard folding, the Lang Universal Molecule, and Origamizer tucking molecules are offered.

49mins

24 Jun 2015

Rank #9

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Lecture 4: Efficient Origami Design

This lecture continues to discuss the tree method and characterizing a uniaxial base. Another algorithm, Origamizer, is presented with introductory examples of folding a cube, checkerboard, and arbitrary polyhedra.

1hr 26mins

24 Jun 2015

Rank #10

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Lecture 2: Simple Folds

This lecture begins with definitions of origami terminology and a demonstration of mountain-valley folding. Turn, hide, color reversal gadgets, proofs for folding any shape, Hamiltonian refinement, and foldability with 1D flat folding are presented.

1hr 23mins

24 Jun 2015

Rank #11

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Class 3: Single-Vertex Crease Patterns

This class reviews algorithms for testing flat-foldability for a 1D MV pattern and for single-vertex MV pattern. An exercise walks through determining local flat-foldability, and questions cover higher dimensions and motivations for flat-foldability.

46mins

24 Jun 2015

Rank #12

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Lecture 3: Single-Vertex Crease Patterns

This lecture explores the local behavior of a crease pattern and characterizing flat-foldability of single-vertex crease patterns. Kawasaki's theorem and Maekawa's theorem are presented as well as the tree method with Robert Lang's TreeMaker.

1hr 23mins

24 Jun 2015

Rank #13

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Class 2: Universality & Simple Folds

This class begins with a folding exercise of numerical digits. Questions discussed cover strip folding in the context of efficiency, defining pseudo-polynomial, seam placement, and clarifications about simple folds and flat-foldability.

53mins

24 Jun 2015

Rank #14

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Lecture 19: Refolding & Smooth Folding

This lecture begins with a problem involving unfolding and refolding. Examples of smooth foldings and unfoldings are given, followed by a problem involving the wrapping of a sphere and a proof that the wrappings are contractive.

1hr 25mins

24 Jun 2015

Rank #15