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:一个正交管道由正交盒子(例如单位立方体)组成,面对面粘合形成路径。1998年,Biedl等人表明每个正交管道都有一个网格展开:沿着盒子的边缘切割,使表面展开成为一个连通的平面形状,没有重叠。我们提供了一个新的算法网格展开正交管道,具有额外的特性:矩形面以单一路径相连,即正交管道平面上的汉密尔顿路径。