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- W2964335289 abstract "We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset F of creases is forcing if the global folding mountain/valley assignment can be deduced from its restriction to F. In this paper we focus on one particular class of foldable patterns called Miura-ori, which divide the plane into congruent parallelograms using horizontal lines and zigzag vertical lines. We develop efficient algorithms for constructing a minimum forcing set of a Miura-ori map, and for deciding whether a given set of creases is forcing or not. We also provide tight bounds on the size of a forcing set, establishing that the standard mountain-valley assignment for the Miura-ori is the one that requires the most creases in its forcing sets. Additionally, given a partial mountain/valley assignment to a subset of creases of a Miura-ori map, we determine whether the assignment domain can be extended to a locally flat-foldable pattern on all the creases. At the heart of our results is a novel correspondence between flat-foldable Miura-ori maps and 3-colorings of grid graphs." @default.
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- W2964335289 date "2015-01-04" @default.
- W2964335289 modified "2023-09-27" @default.
- W2964335289 title "Minimum forcing sets for Miura folding patterns" @default.
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- W2964335289 doi "https://doi.org/10.5555/2722129.2722140" @default.
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