Flattening Polygonal Linkages via Uniform Angular Motion

Akitaya, Hugo A. and Jones, Matthew D. and Sandoval, Gregory A. and Souvaine, Diane L. and Stalfa, David and Tóth, Csaba D. (2017) Flattening Polygonal Linkages via Uniform Angular Motion. In: Graph Drawing and Network Visualization, GD 2017, September 25-27 , pp. 615-617(Official URL: https://link.springer.com/content/pdf/bbm%3A978-3-...).

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We study the motion of polygonal linkages under the restriction that the angles between adjacent edges change uniformly to 0, π, or 2π. We show that convex polygons, orthogonally convex polygons and orthogonal 2-terraines unfold without self-intersection to a straight line in this model, but there exists an orthogonal 12-gon that does not. Further, we show that regular polygons, triangles, quadrilaterals, and convex pentagons can be reconfigured into flat zigzag chains; and every m x n rectangle made of unit-length edges can be reconfigured into a unit-length zigzag.

Item Type: Conference Poster
Classifications: G Algorithms and Complexity > G.560 Geometry
P Styles > P.600 Poly-line
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1643

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