Graphical queries for the purpose of searching for pictorial information are of growinginterestinareaswherepicturesprovidevaluableinformation, including, for instance, design, architecture, and engineering. Sketching graphical queries is a natural way of revealing the visual appearance of objects one has in mind. The problem which arises is identifying necessary shape properties of sketches, thatis,thosepropertieswhicharenotaccidentalbutarenecessaryforspecifying a particular object property. This problem arises in particular because sketches are imprecise, and often distorted by the artistic limitations of the sketcher. From the theoretical point of view the concept of pictorial space applies. In this context, new concepts are required, in particular for dealing with imp- cise shape information in the plane. Taking into account constraints imposed by pictorial space, a relation algebra of intersection-free relations is proposed, which allows reasoning about qualitative line arrangements in the plane. The theory is further developed for characterising polygons, by deriving a number of qualitative properties which aid in describing polygons qualitatively. Applying this theory, only line arrangements which are both readily sketched and easily perceivable are considered to be di?erent. The notion of positional-contrast is introduced, which points out that the particular arrangements of line segments, i. e. their positions relative to each other, provide an expressive means of ch- acterising necessary shape properties. The method developed in this work is applied in using graphical queries to search for historical objects.