On the Area of Overlap of Translated Polygons

(Also cross-referenced as CAR-TR-699) Given two simple polygons P and Q in the plane and a translation
vector t E R2, the area-oJ-overlap function of P and Q is the function
Ar(t) = Area(P n (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 efficient algorithms for computing a
representation of this function, and for tracing contour curves of
constant area of o verlap.