Abstract
We study the problem of cutting a simple polygon with n vertices into two pieces such that — if we reposition one piece disjoint of the other, without rotation — they have the minimum possible bounding square. If we cut with a single horizontal or vertical segment, then we can compute an optimal solution for a convex polygon with n vertices in O(n) time. For simple polygons we give an O(n 4ga(n) log n) time algorithm.
Supported by the Berlin-Zürich Graduate Program “Combinatorics, Geometry, and Computation”, financed by the German Science Foundation (DFG) and ETH Zürich.
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van Kreveld, M., Speckmann, B. (2002). Cutting a Country for Smallest Square Fit. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_9
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DOI: https://doi.org/10.1007/3-540-36136-7_9
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