A characterisation of the generic rigidity of 2-dimensional point-line frameworks

TL;DR

This paper characterizes the conditions under which 2D point-line frameworks are generically rigid, providing a polynomial algorithm to decide rigidity based on the framework's structure.

Contribution

It offers a new combinatorial characterization of generic rigidity for 2D point-line frameworks and introduces an efficient decision algorithm.

Findings

Characterization of generic rigidity conditions

Polynomial-time algorithm for rigidity decision

Applicable to 2D point-line frameworks

Abstract

A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if every continuous motion of the points and lines which preserves the constraints results in a point-line framework which can be obtained from the initial framework by a translation or a rotation. We characterise when a generic point-line framework is rigid. Our characterisation gives rise to a polynomial algorithm for solving this decision problem.