Topology determined between point and polygon based on Vector Algebra

Through study the geometric meaning of Vector Algebra, vector cross-product was used to determine the topological relationship between point and polygon. A horizontal vector was made based on the point determined. Cross multiplication between it and each edge of the polygon was made. Then, the signal of k-component was employed to determine the spatial relationship between point and polygon. An appropriate weight value was given to a bare possibility. The parity of the weight sum was to decide the spatial relationship between point and polygon. The intersectant point was avoided to compute, and some special cases were resolved with geometric equivalence. Software implementation verified the high robustness and efficiency of this algorithm. At last, this algorithm is compared with Ray Method, and the test result testifies that it has higher efficiency than Ray Method.