One Approach for Computing Simple Polygons on a Given Point Set in the Plain
We consider the problem of computing all possible simple polygons embrasing every point of a given finite point set in the plane. The developed approach is based on topological analysis of mutual visibility graphs of all free points and end points of a constructed chain. We found several new necessary conditions for existence of simple polygonal chains which are based on checking collocations of articulation points, bridges and biconnected components of such graphs.