Bringing closed polygonal curves in the plane to normal form via local moves
The key-concept in this paper is introduced as follows: a closed polygonal plane curve with \(n\) vertices is in normal form if: (1) it is a regular polygon; (2) its sides are of equal length and it is inscribed in a circle going around it several times; (3) its sides are of equal length, and it is inscribed in a ``figure eight'' curve and self-intersects only at the curve's double point. The authors prove that given a closed polygonal plane curve there is a regular homotopy that transforms it into normal form. Two algorithms performing this transformation via local moves are constructed: in case of closed polygonal curves with equal edges, and in case of closed polygonal plane curves with arbitrary edges. The problem and the algorithms are related to modeling the motion of a biological entity on a flat surface.
scientific article; zbMATH DE number 6909354