Flat-state connectivity of linkages under dihedral motions

Written with Greg Aloupis*, Erik D. Demaine, Vida Dujmovic'*, Stefan Langerman, Henk Meijer, Ileana Streinu, Joseph O'Rourke, Mark Overmars, Michael Soss, and Godfried Toussaint.

Proceedings of the 13th Annual International Symposium on Algorithms and Computation, 369-380, 2002.

We explore which classes of linkages have the property that each pair of flat states---that is, their embeddings the in the plane without self-intersections---can be connected by a continous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein modles. 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 other results are obtained for other restricted classes of linkages. Many open problems are posed.

Publications - Jeff Erickson (jeffe@cs.uiuc.edu) 02 Jan 2003