Suppose a two-member team is required to navigate through dangerous territory (a plane with polygonal obstacles) along two preselected polygonal paths. The team could consist of police officers, soldiers, or even robots on the surface of Mars. Team members are allowed to coordinate their movements, and it is imperative to keep the team close together during the mission so that if an emergency o...

Abstract. We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of general constant area speed motion of polygons. Accuracy and efficiency o...

We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme to analyse general constant area speed motion of polygons. Accuracy and efficiency of our numerical sch...