Abstract
The Minkowski sum of two sets A,B ∈ I Rd, denoted A ⊕B, is defined as \(\left\{ a + b ~\vert~ a \in A, b \in B \right\}\). We describe an efficient and robust implementation for the construction of Minkowski sums of polygons in I 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.
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Wein, R. (2006). Exact and Efficient Construction of Planar Minkowski Sums Using the Convolution Method. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_73
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DOI: https://doi.org/10.1007/11841036_73
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