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The Minkowski sum of two sets A,B ∈ Rd, denoted A ⊕ B, is defined as {a+b|a ∈ A,b ∈ B}. We describe an efficient and robust implementation for the construction of Minkowski sums of polygons in R2 using the convolution of the polygon boundaries. This method allows for faster computation of the sum of non-convex polygons in comparison with the widely-used methods for Minkowski-sum computation that decompose the input polygons into convex sub-polygons and compute the union of the pairwise sums of these convex sub-polygon. Partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-006413 (ACS - Algorithms for Complex Shapes), and by the Hermann Minkowski-Minerva Center for Geometry at Tel Aviv University.