A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Straightening polygonal arcs and convexifying polygonal cycles
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Single-Vertex origami and spherical expansive motions
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, to a flat position, in such a way that the paper is not torn, stretched and, for rigid origami, not bent anywhere except along the given creases. Streinu and Whiteley showed how to reduce the single-vertex origami problem to the Carpenter's Rule Problem for spherical polygons. Using spherical expansive motions, they solved the cases of open