2017/03/11 by Shiyu Zhao, Zhao, Shiyu, Zhiyong Sun +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Combinatorics (math.CO) #FOS: Electrical engineering #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1703.04035
openalex publication_date 2017/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses the problem of constructing bearing rigid networks in arbitrary dimensions. We first show that the bearing rigidity of a network is a generic property that is critically determined by the underlying graph of the network. A new notion termed generic bearing rigidity is defined for graphs. If the underlying graph of a network is generically bearing rigid, then the network is bearing rigid for almost all configurations; otherwise, the network is not bearing rigid for any configuration. As a result, the key to construct bearing rigid networks is to construct generically bearing rigid graphs. The main contribution of this paper is to prove that Laman graphs, which can be generated by the Henneberg construction, are generically bearing rigid in arbitrary dimensions. As a consequence, if the underlying graph of a network is Laman, the network is bearing rigid for almost all configurations in arbitrary dimensions.