Method

The tool can calculate up to 12 different metrics that each measure a particular aspect of a polygon's shape. Each metric has a normalized and unnormalized version. The normalized version is not affected by the polygon's area and provide a measure of the shape's compactness. The unnormalized versions of the metrics are affected by the polygon's area. The metric(s) used should make logical sense for the analysis. The Shape Metrics PowerPoint provides detailed descriptions of each metric along with example of their application. Brief descriptions of each metric follow...

Cohesion: the average Euclidean distance between all pairs of interior points. Click here for more details.

Proximity: the average Euclidean distance from all interior points to the centroid. Click here for more details.

Exchange: the area of the shape contained within a circle with an area equal to that of the polygon and centered on the polygon's centroid. Click here for more details.

Spin: the average of the square of the Euclidean distances between all interior points and the centroid. This metric is more sensitive to the outlying regions of the polygon. Click here for more details.

Perimeter: the perimeter of the shape. Click here for more details.

Depth: the average distance from the shape’s interior points to the nearest point on the perimeter. Click here for more details.

Girth: the radius of the largest circle that can be inscribed in the shape. Click here for more details.

Dispersion: the average distance from the centroid to all points on the perimeter. The metric is unaffected by gaps within the polygon. Click here for more details.

Range: the maximum distance separating two points on the shape perimeter. Click here for more details.

Detour: the perimeter of the shape’s convex hull.The convex hull is the convex polygon with the shortest possible perimeter that fully encompasses the shape. Click here for more details.

Traversal: the average distances of the shortest interior paths connecting any two points on the shape perimeter. Click here for more details.

Viable Interior: the area of the shape that is beyond the depth of the edge-effect. Requires an edge-width distance to be known. Click here for more details.