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On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2023-11-24 , DOI: 10.1134/s0037446623060022 V. A. Alexandrov
中文翻译:
欧几里得$d$-空间中两个具有规定边长的仿射等价框架的存在性
更新日期:2023-11-24
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2023-11-24 , DOI: 10.1134/s0037446623060022 V. A. Alexandrov
We study the existence of the two affine-equivalent bar-and-joint frameworks in Euclidean \( d \)-space which have some prescribed combinatorial structure and edge lengths. We show that the existence problem is always solvable theoretically and explain why to propose a practical algorithm for solving the problem is impossible.
中文翻译:
欧几里得$d$-空间中两个具有规定边长的仿射等价框架的存在性
我们研究了欧几里得\(d\)空间中两个仿射等价的杆关节框架的存在性,它们具有一些规定的组合结构和边长。我们证明了存在问题在理论上总是可以解决的,并解释了为什么提出解决该问题的实用算法是不可能的。