Orthogonal Fold & Cut

TL;DR

This paper characterizes the patterns achievable through orthogonal fold and cut on rectangular sheets, solving related problems like fold & punch and 1D fold & cut, advancing understanding of fold-and-cut techniques.

Contribution

It provides a complete characterization of orthogonal fold & cut patterns and addresses several related fold-and-cut problems, offering new theoretical insights.

Findings

Characterization of orthogonal fold & cut patterns

Solutions for fold & punch and 1D fold & cut problems

Advancement in fold-and-cut theoretical understanding

Abstract

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.