On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space

Abstract

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.