ABSTRACT
This chapter describes the rigidity properties of frameworks in which some of the points in a bar-joint framework are replaced by lines. A characterization of the generic rigidity matroid for point-line frameworks in on all point-line graphs would give a characterization for bar-joint frameworks as a special case, which is a significant unsolved problem. Any direction-length framework can be represented by a fixed-slope point-line framework by adding a fixed slope line for each pair of points which are constrained by a direction constraint, constraining this line to be at distance zero from the two points and deleting the direction constraint. A point-line framework is a realization of a point-line graph which is obtained by assigning appropriate coordinates to each point- and line-vertex in the graph. A framework is degenerate if there is an isometry which leaves all the points and lines in the framework unchanged.
