# 4.2.2 Perimeter & Closed Perimeter

Perimeter (Pv) expresses the length of the edge of all space visible from a location. In isovist terminology, it represents the geometric isovist perimeter at said location (Benedikt, 1979).

To determine perimeter, the Isovist_App calculates the mean distance between successive radial-plan intersections for every point ‘V’ in plan. The outcome is multiplied by the number of samples in one full cycle to give an absolute value of length.

In notation form the calculation for Perimeter is expressed as:

Where  ‘Ei’ provides ‘edge’ length between radial ends, ’Xi and Yi’ are the coordinates of the nearest radial intersection, ’n’ the total number of radials sampled, and ‘k’ the number of samples in one 360 degree cycle.

Closed Perimeter (Uv) expresses the length of the closed edges (i.e. solid walls) of all space visible from a location. In isovist terminology, it represents the non occluded perimeter at said location (Benedikt, 1979).

To determine closed perimeter, the Isovist_App subtracts the total length of any occluded edges from the length of all perimeter edges, for every point ‘V’ in plan.

In notation form the calculation for Closed Perimeter is expressed as:

Where  ‘E occ’ provides ‘edge’ length between radial ends detected as being occlusive, ’n’ the total number of radials sampled, and ‘k’ the number of samples in one 360 degree cycle.