论文标题
线约束框架的全球刚度
Global Rigidity of Line Constrained Frameworks
论文作者
论文摘要
我们考虑了针对酒吧连接框架的全局刚度问题，其中每个顶点都被限制在$ \ Mathbb r^d $中的特定行上。在我们的环境中，我们允许将多个顶点限制为同一行。在给定线路集的温和假设下，我们给出了在这种情况下通常具有全球刚性的图形的完整组合表征。这给出了$ d $维度的一维全球刚性表征的延伸。
We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $\mathbb R^d$. In our setting we allow multiple vertices to be constrained to the same line. Under a mild assumption on the given set of lines we give a complete combinatorial characterisation of graphs that are generically globally rigid in this setting. This gives a $d$-dimensional extension of the well-known combinatorial characterisation of 1-dimensional global rigidity.
