# The global rigidity of a framework is not an affine-invariant property

## TL;DR

This paper demonstrates that global rigidity of frameworks is not preserved under affine transformations in any Euclidean space, contrasting with the invariance of infinitesimal rigidity under projective transformations.

## Contribution

It proves that global rigidity is not an affine-invariant property in Euclidean spaces of any dimension, clarifying a previously less-understood aspect of rigidity theory.

## Key findings

- Global rigidity is not affine-invariant in Euclidean d-space for d ≥ 2.
- Infinitesimal rigidity remains invariant under projective transformations.
- The result extends known planar cases to higher dimensions.

## Abstract

It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework `to be globally rigid' is not invariant even under affine transformations of the Euclidean plane. In this note, we prove of the latter statement for Euclidean $d$-space for every $d\geqslant 2$.