Before revision:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time. Finally, we connect threadable curves to the problem known as "moving a chair through a doorway."
After revision:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane in R^3, and if so, providing a description of the rigid motions that achieve the threading.