Two vectors compose of point and edge of polygon was defined

the normal direction of these two vectors was calculated

the normal direction is the reference for testing. A line was drawn through the point

there are some crossing points between line and some edges of polygon

the normal direction of point and these edges was calculated

if the number of positive normal and negative normal is same

the point is outside the polygon

otherwise the point is inside the polygon. This method didn’t make mistake like half-line method

and it is sample than other methods. The computation is decreased. It is proved be an effective and simple robust algorithm by programming

and it is suitable for most case self-intersection polygon.