CircleAreaField
CircleAreaField is a mathematical construct used in computational geometry and related fields to describe a scalar field derived from the geometry of a planar region. Given a compact region R in the plane with boundary ∂R, for every point p in R the function r(p) is defined as the Euclidean distance from p to ∂R. The CircleAreaField at p is defined as F(p) = π [r(p)]^2. Equivalently, F(p) equals the area of the largest circle centered at p that lies entirely within R.
The domain of F is R, and F vanishes on the boundary since r(p) = 0 there. The
Properties and relationships: F is continuous and 1-Lipschitz; away from sharp corners its gradient exists almost
Computations and applications: F can be computed by standard distance-transform algorithms on grids or meshes. Applications
See also: distance transform, signed distance function, medial axis, morphological erosion.