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
Extremal reaches in polynomial time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Flattening fixed-angle chains is strongly NP-hard
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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We explore which classes of linkages have the property that each pair of their flat states--that is, their embeddings in R2 without self-intersection--can be connected by a continuous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein models. Our positive results include proofs that open chains with nonacute angles are flat-state connected, as are closed orthogonal unit-length chains. Among our negative results is an example of an orthogonal graph linkage that is flat-state disconnected. Several additional results are obtained for other restrictedclasses of linkages. Many open problems are posed.