A Dynamical Systems Approach to the Polygonal Approximation of Plane Convex Compacts

A connection is described between the polygonal approximation of a compact convex set in R2 and some dynamical systems on the unit circumference in R2. Based on this a numerical procedure is proposed for finding a best approximating n-gon for an arbitrary compact convex set in R2 (w.r.t. Hausdorff metric). The algorithm provides a solution to a specific global optimization problem where the function to be minimized has more than one local minimum. In one of its equivalent formulations the above approximation problem can be considered as a specific spline approximation problem. From this point of view our algorithm provides also a solution to a specific variable knots spline approximation problem.