2016/07/02 by Katie Clinch, Clinch, Katie, Bill Jackson +3
Engineering · #05C75 #52C25 #Advanced Antenna and Metasurface Technologies #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1607.00508
openalex publication_date 2016/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→\mathbb R2 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^∘. We show that the problem of characterising when a generic framework (G,p) is globally rigid can be reduced to the case when G belongs to a special family of `direction irreducible' mixed graphs, and prove that every generic realisation of a direction irreducible mixed graph G is globally rigid if and only if G is 2-connected, direction-balanced and redundantly rigid.