Mutual visibility of points in building plans

In this paper, attempts are made to characterise building plans based on mutual visibility of points defined by the lines composing these plans. Since lines in building plans represent real walls and their surfaces, points defined by these lines are considered to have certain perceivable significance. The paper considers two overlapping sets of points: vertices and coordination points. Vertices are tangible points defined by the free ends and the intersections of lines, while coordination points are the tangible and intangible points defined by intersecting lines and/or diagonals. A coordination point helps to coordinate two or more points, either physically by direct access or visually by sightlines. The paper proposes graph-theoretic techniques to characterise vertices and coordination points based on their visual relationships defined in a number of ways. These techniques are applied to three sets of artificial building plans representing the cellular, deformed and free-plan types: types that are quite common in architectural literature. With the help of these techniques, several elusive properties of architectural space and experience are formally described highlighting similarities and differences among these plan types. The significance of these techniques is discussed in relation to architecture, perceptual psychology and cognitive science.