Global rigidity of direction-length frameworks

A 2-dimensional direction-length framework is a collection of points in the plane which are linked by pairwise constraints that fix the direction or length of the line segments joining certain pairs of points. We represent it as a pair (G, p), where G = (V; D, L) is a 'mixed' graph and p : V -> R-2 is a point configuration for V. It is globally rigid if every direction-length framework (G, q) which satisfies the same constraints can be obtained from (G, p) by a translation or a rotation by 180 degrees. We characterise the mixed graphs G with the property that every generic framework (G, p) is globally rigid. (C) 2020 Elsevier Inc. All rights reserved.