Convexifying Star-Shaped Polygons
Hazel Everett, Sylvain Lazard, Steven M. Robbins, H. Schröder, Sue H. Whitesides · 1998
1 Introduction The reconfiguration problem for chains is to determine whether a chain of n links can be moved from one given configuration to another. The links have fixed lengths and may rotate about their endpoints. Previous work on the reconfiguration of chains (e.g. [1]) has allowed links to pass over one another, so that the links act as distance constraints but not as obstacles. We study a variant of this problem, which we call polygon convexification: the initial configuration of the chain forms a simple polygon, the final configuration is a convex polygon, and the links are not allowed to cross. It is unknown whether every polygon can be convexified.