Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

Abstract

We define normal forms of regular closed polygonal curves in R², prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.