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.
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 . The second main result is an O(n polylog n)-time algorithm for deciding whether a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.