Average Radial (Qv) expresses the mean view length of all space visible from a location. In visibility graph terminology, it relates to the ‘through vision’ at a location (Turner, 2007). In isovist terminology, it represents the mean radial length at a location.
To determine Average Radial at point ‘V’, the Isovist_App calculates the average distance between each edge of the polygon of the isovist, and the origin point of the isovist calculated at V. It subsequently finds the mean average of all such values, as weighted by the angle subtended by each edge. The outcome is an absolute value of length.
In notation form the calculation for Average Radial is expressed as:
Where xi, yi is the vector from V to each vertex of the isovist polygon, n the total number of vertexes of the isovist, alpha the angle subtended by the edge and theta the total sweep of the isovist.