Unfolding Orthotubes with a Dual Hamiltonian Path

01/28/2022

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by   Erik D. Demaine, et al.

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MIT

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Princeton University

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An orthotube consists of orthogonal boxes (e.g., unit cubes) glued face-to-face to form a path. In 1998, Biedl et al. showed that every orthotube has a grid unfolding: a cutting along edges of the boxes so that the surface unfolds into a connected planar shape without overlap. We give a new algorithmic grid unfolding of orthotubes with the additional property that the rectangular faces are attached in a single path – a Hamiltonian path on the rectangular faces of the orthotube surface.