Conditions for unique graph realizations
SIAM Journal on Computing
Discrete & Computational Geometry
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
Rigid realizations of graphs on small grids
Computational Geometry: Theory and Applications
Fast matching of large point sets under occlusions
Pattern Recognition
| Hi-index | 0.00 |
A straight-line realization of (or a bar-and-joint framework on) graph G in R^d is said to be globally rigid if it is congruent to every other realization of G with the same edge lengths. A graph G is called globally rigid in R^d if every generic realization of G is globally rigid. We give an algorithm for constructing a globally rigid realization of globally rigid graphs in R^2. If G is triangle-reducible, which is a subfamily of globally rigid graphs that includes Cauchy graphs as well as Grunbaum graphs, the constructed realization will also be infinitesimally rigid. Our algorithm relies on the inductive construction of globally rigid graphs which uses edge additions and one of the Henneberg operations. We also show that vertex splitting, which is another well-known operation in combinatorial rigidity, preserves global rigidity in R^2.