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David M. Mount. Ruth Silverman. Angela Y. Wu. On the Area of Overlap of Translated Polygons. (Also cross-referenced as CAR-TR-699) January 1994.
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. Department of Computer Science, University of Maryland, Center for Automation Research,
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