Compactness (Cv) expresses the shape property (relative to a circle) of all space visible from a location. In an isovist field, compactness identifies the regions of plan in which an observer’s spatial experience is contiguously consistent. Such regions identify and correlate to meaningful instances of Peponis’ S- and E-partitions (Peponis, 1997); identifying opportunities for the emergence of new surfaces in the visual field as a result of movement.

To determine compactness, the Isovist_App calculates a form of the isoperimetric quotient of the isovist for every point ‘V’ in plan. The outcome is a relative value between 0 and 1.

In notation form the calculation for Compactness is expressed as: 

Where ‘Av’ is the area value; and ‘Pv’ the perimeter value.