Before revision:  We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices  . Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.
After revision:  We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices . That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge . Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.