Qualitative line arrangements
2007
In this chapter we will investigate line arrangements from a qualitative point of view. The proposed representation and reasoning processes rely on those sort of distinctions which are easily comprehensible by natural perceptual systems. For instance, it will be possible to distinguish whether two lines are on the same side with respect to another one, or whether they are on different sides-but we will not be able to obtain their precise positions. From an information theory point of view, possible arrangements of lines are systematically investigated, making use of distinctions which are both easily perceivable and easily sketchable: left and right, back and front, during and contains. We shall learn that such coarse classifications will nevertheless allow a vast number of distinctions to be made, and finally arrive at a theory of line arrangements which is based on a small set of relations between intervals within the plane. This theory forms the basis for a qualitative geometry using which we will consider the qualitative characterisation of polygons in the next chapter.