Occlusivity (Ov) expresses the proportion of edges of an isovist that are not physically defined. It represents how previously unseen space may be revealed during movement (Benedikt, 1979). Occlusivity fields show moments of dramatic visual change as a user passes between spaces. A forest or hypostyle hall has high Occlusivity; a convex room has none; flat surfaces tend to extend occlusive edges into space.
To determine occlusivity, the Isovist_App calculates ‘occlusive importance’; the square of the length of occlusive edge detected at each iteration, divided by the length of radial at the same point. The result provides a value for occlusivity weighted in favour of nearer, longer occlusive edges, i.e. those with greater visual impact. It is then summated over successive radial iterations for every point ‘V’, and the final sum is divided by perimeter ‘Pv’. The outcome is a relative value between 0 and 1.
In notation form the calculation for Occlusivity is expressed as:
Where ‘Li’ provides radial length, ‘Ei_occ’ is the fraction of occluded edge detected, ’Pv’ the perimeter value, ’n’ the total number of radials sampled and ‘k’ the number of samples in one 360 degree cycle.