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

作者：Avvakumov S^*; Sossinsky A^*

来源：Mathematical Notes, 2018, 103(3-4): 466-473.

DOI：10.1134/S0001434618030124

• regular closed polygonal curve
• regular homotopy
• normal form of a polygonal curve
• local moves
• winding number of a plane curve
• Euler functional
• gradient descent

We define normal forms of regular closed polygonal curves in R-2, 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.

• 出版日期2018-3