Via topological mapping

the inclusion test of whether a set of points is in a polygon or not can be converted to comparing the projected points' position on the projection line. At first

the center point for topological mapping must be figured out

then the method maps vertices of the polygon onto the projection line. To each point of the set

according to the position of its mapping point and the mapping points of the vertices

it is confirmed that the point is in the area of two lines from the center point to the two vertices of one of the polygon's edges. And then

according to the two cases

whether the point is in the edge's box or not

we can draw a conclusion. If the point is out of the edge's box

the calculation of comparing its position with the edge's box's is only needed

and if the point is in or on the boundary of the edge's box

the calculation of cross product must be added. To the points of set

througth pre calculation of the polygon's vertices this algorithm can greatly reduce calculation of each point. Experiments show that this algorithm is rapid

robust and can be implemented easily.