We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way, we solve a handful of related problems: orthogonal fold & punch, 1D fold & cut, signed 1D fold & cut, and 1D interval fold & cut.
翻译:我们定义了正交折叠与切割能够产生的切割图形:将一张矩形纸张沿水平和竖直褶痕折叠,然后在任意角度上进行一次切割。在此过程中,我们解决了一些相关问题:正交折叠与穿孔、1D折叠与切割、有符号1D折叠与切割、以及1D区间折叠与切割。