Proceedings of the 30th Canadian Conference on Computational Geometry, CCCG 2018
We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a linear-time algorithm for deciding whether a polygonal curve is threadable—O(n) for a curve of n vertices—and if threadable, finding a sequence of rigid motions to thread it through a hole. We also sketch an argument that shows 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 can thread through a hole in a plane in R3, and if so, providing a description of the rigid motions that achieve the threading.
© the authors
O’Rourke, Joseph and Rogers, Emmely, "Threadable Curves" (2018). Computer Science: Faculty Publications, Smith College, Northampton, MA.