This paper presents a model for space in which an autonomous agent acquires information about its environment. The agent uses a predefined exploration strategy to build a map allowing it to navigate and deduce relationships between points in space. The shapes of objects in the environment are represented qualitatively. This shape information is deduced from the agent's motion. Normally, in a qualitative model, directional information degrades under transitive deduction. By reasoning about the shape of the environment, the agent can match visual events to points on the objects. This strengthens the model by allowing further relationships to be deduced. In particular, points that are separated by long distances, or complex surfaces, can be related by line-of-sight. These relationships are deduced without incorporating any metric information into the model. Examples are given to demonstrate the use of the model.