Area (Av) expresses the area of all space visible from a subject point in the plan (Benedikt, 1979). In visibility graph terminology, it represents the number of other subject points that said location is directly ‘connected’ to, called ‘Connectivity’ (Turner, 2001b). Isovist_App Area has been shown to correlate to DepthMap’s Connectivity.
To determine Area, the Isovist_App calculates the mean radial length squared for every subject point ‘V’ in plan. The outcome is multiplied by Pi and the number of samples in one full cycle to give an absolute value of area.
In notation form the calculation for Area is expressed as:
Where ‘Li’ provides radial length, Xi and Yi’ are the coordinates of the nearest radial intersection; ‘Xv and Yv’ the coordinates of V; n’ the total number of radials sampled, and ‘k’ the number of samples in one 360 degree cycle.