Abstract: According to large numbers of experiments,observations and deduction analysis,the theories and rules of k-order Voronoi polygon's existence of point set S are discussed.Thus we conclude and advance many ways to judge the k-order Voronoi polygon's existence,such as the ways of distance probability Judgment,recursion induce method,most nearest judgement principle and obstruct area judgement principle.Finially the relation between image resolution and the existence is discussed.