Bill Jackson: Rigidity of point-line frameworks

Abstract:

A point-line framework is a collection of points and lines in the Euclidean plane which are linked by constraints which fix the angles between some pairs of lines, and the distances between some pairs of points and between some pairs of points and lines. A framework is rigid if the only continuous motion of the points and lines which preserve the constraints are translations or rotations of the whole plane. The rigidity of a framework depends only on its underlying `point-line graph' when the framework is generic i.e there are no algebraic dependencies between the coordinates of its points and lines. We characterize when a generic point-line framework is rigid. This is joint work with John Owen (Siemens).