Abstract: Any areal symbol of a thematic map is mace of a boundary line with certain symbols filled in it.The boundary line may be a polygon,a smooth curve of a combination of the two,and it can be drawn as those thiner elements,while the symbols to be filled are of different types,such as parallel lives,alphabets or other pictures,and the automatic drafting methods are quite different.The key point to draw parallel lines automatically within a boundary line is as follows:with the help of a computer,according to the digitized coordinates of the boundary points as well as the given parameters of parallel lines the position of their ends is to be found and then to connect them successively on the automatic drawing machine can be realized.In this paper,a mathematical method on the calculating of the coordinates of the ends of parallel lines within a polygon is introduced and the processes of lining,pairing and outputting are described.