The convexity coefficient 
of a region 
is the probability that the line
segment connecting two random points in 
is contained entirely within 
. For a convex region, 
.
For 
a subset of 
,
let the area of the visible region of a point 
be denoted 
, and let the area of 
be denoted 
. Then
 |
(Hodge et al. 2010).
The convexity coefficient is in general hard to compute exactly for concave regions even of simple shape. One closed form is that of an annulus
with inner radius 
and outer radius 
, which has
 |
(Hodge et al. 2010).
