Abstract: In this paper,Q_i operator is used to measure the azimuth of edges and connected lines which are vectors and related to the four basic issues.Principles judging to which side the following edge(connected line) turned relative to the current are founded.By deriving the direction relationship between the neighbouring edges(connected lines) based on these principles,the polygon's orientation,polygonal convexity-concavity can be identified,so does to point-in-polygon query.New algorithms are presented,the analysis shows that improved performance is achieved,and there is the unification of the geometry idea in solving those four issues.