Configuration spaces of convex and embedded polygons in the plane

Details Configuration spaces of convex and embedded polygons in the plane Configuration spaces of convex and embedded polygons in the plane

2008-11-10

arxiv.org/abs/0811.1365v1

Computer Science

Computational Geometry

16 pages

Scientific paper

This paper studies the configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote.

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