6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

Prof. Erik Demaine       TA: Jayson Lynch


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[+] Rigidity theory: Pebble algorithms, rigid component decomposition, body-and-bar framework, angular rigidity, 5-connected double bananas.

This class focuses on one main question: how exactly and why does that pebble algorithm detect Laman's condition for minimal generic rigidity? We'll start with a simpler version of the algorithm that tests whether every k vertices induce at most 2k edges, and then extend to the needed 2k − 3 condition. Then I'll mention several extensions:
  • Decomposing any graph into minimally rigid components and redundant edges
  • Body and bar (and hinge) frameworks
  • Angular constraints between lines and planes, or between bodies
Finally, we'll see that the tricky 3D double bananas example, and indeed any graph in 3D, can be extended to be 5-connected while preserving Laman and generic flexibility.

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Handwritten notes, page 1/5[previous page][next page][PDF]

Handwritten notes, page 1/5[previous page][next page][PDF]

Slides, page 1/10[previous page][next page][PDF]

Slides, page 1/10[previous page][next page][PDF]

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