Unfortunately, there is one serious

Unfortunately, there is one serious difficulty with the line segment method. When two surfaces intersect, or when a surface folds over on itself, segment chains must be reordered, possibly with the addition or removal of some chains. If such intersections are anticipated, the reordering process may not be difficult. In the general case, however, the detection of intersections and determining how a reordering should be done is not a trivial task.