Abstract: In order to more easily calculate polygonal position relationships and expand the theories of simple polygon to general polygon,a method labeling node status is proposed.Firstly,11 positions are defined to describe each node status of poly-line chains.And both methods of "an endpoint of a line with another line" and "an endpoint of a line with an adjoining line" are used to label any poly-line chain.Meanwhile,after the division pretreatments of two lines,which make the intersections only occurring at endpoints,are implemented,the labeling method become more efficient.Finally,the node-labeling features of basic position relationships between two poly-line chains are given,and the labeling of three-dimensional vertex is also preliminarily studied.The labeling method is simple in principle,but practical in application,whose space and time complexities of algorithm are O(n) and O(n²) respectively.Experimental results show that this method can stably label poly-line chain with arbitrary shapes;and through searching the labeling feature of each node,the position relationships among poly-line chains can be solved,furthermore,some applications can be achieved for general poly-line chains,such as collision detection,intersection computing and polygonal simplification decomposition,etc.