Combining Globally Rigid Frameworks

TL;DR

This paper presents a method for combining two globally rigid bar frameworks in d-dimensional space to produce a new globally rigid framework by identifying vertices and removing a common edge.

Contribution

It introduces a novel construction technique for combining globally rigid frameworks, expanding the toolkit for rigidity analysis in higher dimensions.

Findings

The construction preserves global rigidity after combining frameworks.

The method applies to frameworks in any dimension d.

It provides a systematic way to generate larger rigid structures.

Abstract

Here it is shown how to combine two generically globally rigid bar frameworks in $d$-space to get another generically globally rigid framework. The construction is to identify $d+1$ vertices from each of the frameworks and erase one of the edges that they have in common.