Analytical and numerical aspects on motion of polygonal curves with constant area speed

Abstract

General area-preserving motion of polygonal curves is formulated as a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to the admissible class used in the crystalline curvature flow. The ODEs are discretized implicitly in time keeping a given constant area speed while solution polygonal curves keep belonging to the polygonal class.

Proceedings of Slovak-Austrian Mathematical Congress, within MAGIA 2007, Dept. of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, ISBN 978-80-227-2796-9 (2007) 127--141