Abstract: This paper presents a new and more effective algorithm to determine the directional relationship between arbitrarily-shaped polygons which is based on the rasterization of polygons and well conforms to spatial cognitive models.The results are identical to that of visual interpretation by human.Then the calculability of the directional relationship between arbitrarily-shaped polygons is discussed.And an approach to determine the calculability based on the number of zero values of the degree of membership of direction is provided.