Global rigidity of 2-dimensional direction-length frameworks with connected rigidity matroids

A 2-dimensional direction-length framework (G,p) consists of a multigraph G=(V;D,L) with realisation p:V→R2. The edges G represent geometric constraints: in L have fixed length, and D gradient. is globally rigid if every (G,q) which satisfies the same constraints as can be obtained from by an isometry plane. We characterise global rigidity for class frameworks p generic matroid connected. Specifically, we show that such are only both non-empty, 2-separation direction-balanced. This extends previous work Jackson Jordán (2010).