Abstract
Suppose a finite configuration of labeled points p = (p1,. . . ,pn) in Ed is given along with certain pairs of those points determined by a graph G such that the coordinates of the points of p are generic, i.e., algebraically independent over the integers. If another corresponding configuration q = (q1,. . . ,qn) in Ed is given such that the corresponding edges of G for p and q have the same length, we provide a sufficient condition to ensure that p and q are congruent in Ed. This condition, together with recent results of Jackson and Jordán, give necessary and sufficient conditions for a graph being generically globally rigid in the plane.
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Connelly, R. Generic Global Rigidity. Discrete Comput Geom 33, 549–563 (2005). https://doi.org/10.1007/s00454-004-1124-4
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DOI: https://doi.org/10.1007/s00454-004-1124-4