On the area of overlap of translated polygons

Given two simple polygons P and Q in the plane and a translation vector t 2R2, the area-of-overlap function of P and Q is the function Ar(t) = Area(P \(t + Q)), where t + Q denotes
Q translated by t. This function has a number of applications in areas such as motion planning
and object recognition. We present a number of mathematical results regarding this function.
We also provide e cient algorithms for computing a representation of this function, and for
tracing contour curves of constant area-of-overlap.