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Computational origami design typically focuses on achieving a desired shape of folding, treating multiple layers of paper like a single layer. In this paper, we study when we can achieve a desired shape with a desired constant number of layers throughout the shape, or a specified pattern of layer thicknesses. Specifically, we study the case of a rectangular strip of paper, which is the setting of the first universal computational origami design algorithm [SoCG’99]. Depending on the generality of the target surface and on the number of layers modulo 4, we give a variety of universal design algorithms, polynomial-time decision algorithms characterizing what is possible to fold, and NP-hardness results.

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Folding a Strip of Paper into Shapes with Specified Thickness

  • 会议论文

  • 发表日期：

    2026年

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  • Lily Chung,
  • Erik D. Demaine,
  • Martin L. Demaine,
  • Jenny Diomidova,
  • Jayson Lynch,
  • Klara Mundilova,
  • Hanyu Alice Zhang

摘要

Computational origami design typically focuses on achieving a desired shape of folding, treating multiple layers of paper like a single layer. In this paper, we study when we can achieve a desired shape with a desired constant number of layers throughout the shape, or a specified pattern of layer thicknesses. Specifically, we study the case of a rectangular strip of paper, which is the setting of the first universal computational origami design algorithm [SoCG’99]. Depending on the generality of the target surface and on the number of layers modulo 4, we give a variety of universal design algorithms, polynomial-time decision algorithms characterizing what is possible to fold, and NP-hardness results.