GIS中统一于Q_i算子的多边形基本问题新算法

New Algorithms for Basic Issues of GIS Polygons Achieved by Q_i Operator

用Qi算子来描述多边形中边和连线两类矢量的方向角,归纳出由Qi算子所表示的矢量方向角在识别走向时的判断规则,从而成功建立了多边形4个基本问题的新算法。实现了4个算法在几何意义上的统一,并相对传统最优算法提高了执行效率,同时还保证了高可靠性和稳定性。

In this paper, Qi 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.