DETERMINATION OF TOPOLOGICAL RELATIONSHIP BETWEEN POINT AND POLYGON BASED ON VECTOR ALGEBRA
Liu Deer 1,2) ; Wang Yongjun 1) ; and Lü Guonian 1)
1)Jiangsu Provincial Key Lab. of GISC, Nanjing Normal University, Nanjing 210046 2)Faculty of Architectural and Survey Engineering,Jiangxi University of Science and Technology,Ganzhou 341000
Abstract：Through the analysis of the geometric sense of vector algebra, vector crossproduct is used to determine the topological relationship between point and polygon. A horizontal vector is made based on the determination of point and then the cross multiplication between it and each vector of the polygon is made. Futhermore, the signal of kcomponent is employed to determine the spatial relationship between point and polygon. An appropriate weight value is given to a bare possibility. The parity of the weight sum is to decide the spatial relationship between point and polygon. The intersectant point is avoided to be computed, and some special cases are resolved with geometric equivalence. Software implementation verifies the high robustness and efficiency of this algorithm.
Liu Deer,Wang Yongjun ,and Lü Guonian . DETERMINATION OF TOPOLOGICAL RELATIONSHIP BETWEEN POINT AND POLYGON BASED ON VECTOR ALGEBRA[J]. jgg, 2011, 31(2): 89-93.
