Convexity is a measure of how close a polygon is to being convex. Convex polygons have convexity equal to 1.0, while the more concave the polygon is, the closer to 0.0 is its convexity.

Mathematically, the convexity is calculated as follows:

Note that if the input path is not a valid polygon (i.e. it has at least one self-intersection), the computation may lead to results that are not intuitive.

Area of the sample polygon (on the left) equals to 17529.730, while area of its convex hull (on the right) equals to 20176.250, so the convexity of the polygon equals to 17529.730/20176.250 = 0.867.

This filter can throw an exception to report error. Read how to deal with errors in Error Handling.

List of possible exceptions:

This filter is available on Advanced Complexity Level.

• RegionConvexity – Computes the area of a region divided by area of its convex hull.

• PathConvexHull – Computes the smallest convex shape that contains the given path.

• PolygonElongation – Computes the elongation factor of a polygon (perfect circle has minimal elongation equal 1.0).

• PolygonCircularity – Computes the area of a polygon divided by the area of a circle having the same feature.