Abstract: Taking the test point as the origin and using vertical and horizontal coding chain consisting of 1 and 0 to represent each consecutive vertex of the planar polygon lying above the x-axis and on the right side of y-axis,or below the x-axis and on the left side of y-axis respectively,each sequence of three consecutive 1s or 0s appearing in the vertical or horizontal coding chain is replaced by the first or last digit and the other two are deleted in both chains,at the same time the corresponding vertices are deleted in polygon.Through recursive procedures,a simplified equivalent eigenpolygon is obtained and the in-out polygon test can be readily accomplished by checking the relationships of adjacent 1 and 0digits in the two chains.