Flat-State Connectivity of Linkages Under Dihedral Motions

Authors

Greg Aloupis, Université McGill
Erik D. Demaine, Massachusetts Institute of Technology
Vida Dujmović, Université McGill
Jeff Erickson, University of Illinois Urbana-Champaign
Stefan Langerman, Université McGill
Henk Meijer, Queen’s University
Joseph O'Rourke, Smith CollegeFollow
Mark Overmars, Universiteit Utrecht
Michael Soss, Chemical Computing Group Inc
Ileana Streinu, Smith CollegeFollow
Godfried T. Toussaint, Université McGill

Document Type

Conference Proceeding

Publication Date

12-1-2002

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Abstract

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.

Volume

2518 LNCS

First Page

369

Last Page

380

DOI

10.1007/3-540-36136-7_33

ISSN

03029743

Rights

© Springer-Verlag Berlin Heidelberg 2002.

Comments

Archived as published.

Recommended Citation

Aloupis, Greg; Demaine, Erik D.; Dujmović, Vida; Erickson, Jeff; Langerman, Stefan; Meijer, Henk; O'Rourke, Joseph; Overmars, Mark; Soss, Michael; Streinu, Ileana; and Toussaint, Godfried T., "Flat-State Connectivity of Linkages Under Dihedral Motions" (2002). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/204