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.

翻译：矫形管由正对面粘结的正对面框组成,形成一条路径。1998年,Biedl等人显示,每个正对面管都有一个网格:在箱的边缘切开一个网格,使表面无重叠地展入一个相连的平板形状。我们给正对面管提供一个新的算法网格,其外形特性是,矩形脸被连接在一条路径上 -- -- 在正对面表面的长方形面上有一个汉密尔顿道。