Anthony Nixon, Lancaster University

Abstract

A (bar-joint) framework (G;p) in Rd is the combination of a graph G and a map p assigning positions to the vertices of G. A framework is rigid if the only edgelength-preserving continuous motions of the vertices arise from isometries of Rd. The framework is globally rigid if every other framework with the same edge lengths arises from isometries of Rd. Both rigidity and global rigidity, generically, are well understood when d = 2.

A linearly constrained framework in Rd is a generalisation of a framework in which some vertices are constrained to lie on one or more given hyperplanes. Streinu and Theran characterised rigid linearly constrained generic frameworks in R2 in 2010. In this talk I will describe an analogous result for the global rigidity of linearly constrained generic frameworks in R2.

This is joint work with Hakan Guler and Bill Jackson.

Video