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Problems In Generic Combinatorial Rigidity: Sparsity, Sliders, And Emergence Of Components, Louis Simon Theran
Problems In Generic Combinatorial Rigidity: Sparsity, Sliders, And Emergence Of Components, Louis Simon Theran
Open Access Dissertations
Rigidity theory deals in problems of the following form: given a structure defined by geometric constraints on a set of objects, what information about its geometric behavior is implied by the underlying combinatorial structure. The most well-studied class of structures is the bar-joint framework, which is made of fixed-length bars connected by universal joints with full rotational degrees of freedom; the allowed motions preserve the lengths and connectivity of the bars, and a framework is rigid if the only allowed motions are trivial motions of Euclidean space. A remarkable theorem of Maxwell-Laman says that rigidity of generic bar-joint frameworks depends …