Abstract
The paper investigates the achievable cut patterns on paper using orthogonal folds followed by a single straight cut, addressing various related problems such as punch operations and 1D fold & cut techniques.
AI-generated summary
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.
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