منابع مشابه
Characterizing generic global rigidity
A d-dimensional framework is a graph and a map from its vertices to Ed . Such a framework is globally rigid if it is the only framework in Ed with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a generic framework globally rigid? We answer this question by proving a conjecture by Connelly, that his sufficient condition is also necessary: a generic framework...
متن کاملGeneric Global Rigidity
Suppose a finite configuration of labeled points p = (p1, . . . , pn) inEd 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...
متن کاملGeneric global rigidity of body-bar frameworks
A basic geometric question is to determine when a given framework G(p) is globally rigid in Euclidean space Rd, where G is a finite graph and p is a configuration of points corresponding to the vertices of G. G(p) is globally rigid in Rd if for any other configuration q for G such that the edge lengths of G(q) are the same as the corresponding edge lengths of G(p), then p is congruent to q. A f...
متن کاملGeneric Global Rigidity in Complex and Pseudo-Euclidean Spaces
In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rig...
متن کاملOperations Preserving Global Rigidity of Generic Direction-Length Frameworks
A two-dimensional direction-length framework is a pair (G, p), where G = (V ;D,L) is a graph whose edges are labeled as ‘direction’ or ‘length’ edges, and a map p from V to R. The label of an edge uv represents a direction or length constraint between p(u) and p(v). The framework (G, p) is called globally rigid if every other framework (G, q) in which the direction or length between the endvert...
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2019
ISSN: 2050-5094
DOI: 10.1017/fms.2019.16