Abstract
A grid unfolding without refinement method for a new sub-class of polycubes, called Manhattan Towers with a H-convex base, is proposed. Such polycubes can be seen both as a Manhattan Tower and as an orthostack. A direct extension of this algorithm to Up-and-Down Orthoterrains is also presented.
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The algorithms are presented in the paper and are rather straightforward to reimplement.
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We implement our algorithms in Mathematica and the notebooks are accessible on demand. The algorithms are presented in the paper and their implementation is straightforward.
References
Badagavi P, Pai V, Chinta A (2017) Use of origami in space science and various other fields of science. In: 2017 2nd IEEE international conference on recent trends in electronics, information & communication technology (RTEICT). IEEE, pp 628–632
Bern MW, Demaine ED, David E, Eric K, Andrea M, Jack S (2003) Ununfoldable polyhedra with convex faces. Comput Geom 24(2):51–62
Biedl TC, Demaine ED, Demaine ML, Lubiw A, Overmars MH, O’Rourke J, Robbins S, Whitesides S (1998) Unfolding some classes of orthogonal polyhedra. In: Proceedings of the 10th Canadian conference on computational geometry, McGill University, Montréal, Québec, Canada, August 10–12, 1998
Chambers EW, Sykes K, Traub C (2012) Unfolding rectangle-faced orthostacks. In: CCCG. pp 23–28
Chan HS, Dill KA (1993) The protein folding problem. Phys today 46(2):24–32
Damian M, Flatland R, Meijer H, O’Rourke J (2005) Unfolding well-separated orthotrees. In: 15th annual fall workshop on computational geometry and visualization. pp 23–25
Damian M, Flatland RY, O’Rourke J (2008) Unfolding manhattan towers. Comput Geom 40(2):102–114
Damian M, Demaine ED, Flatland RY, O’Rourke J (2017) Unfolding genus-2 orthogonal polyhedra with linear refinement. Graphs Comb 33(5):1357–1379
Demaine ED, O’Rourke J (2007) Geometric folding algorithms–linkages, origami, polyhedra. Cambridge University Press, Cambridge
Demaine ML, Hearn RA, Ku J, Uehara R (2019) Rectangular unfoldings of polycubes. J Inf Process 28:841–845
Johnson M, Chen Y, Hovet S, Sheng X, Wood B, Ren H, Tokuda J, Tse ZTH (2017) Fabricating biomedical origami: a state-of-the-art review. Int J Comput Assist Radiol Surg 12(11):2023–2032
Langerman S, Winslow A (2016) Polycube unfoldings satisfying conway’s criterion. In: Japan conference on discrete and computational geometry
O’Rourke J (2007) Unfolding orthogonal terrains. CoRR arXiv:0707.0610
O’Rourke J (2008) Unfolding orthogonal polyhedra. Contemp Math 453:307
Richaume L, Andres E, Largeteau-Skapin G, Zrour R (2019) Unfolding level 1 menger polycubes of arbitrary size with help of outer faces. In: Michel C, Jean C, Yukiko K, Nabil M (eds) Discrete geometry for computer imagery. Springer, Cham, pp 457–468
Streinu I (2000) A combinatorial approach to planar non-colliding robot arm motion planning. In: Proceedings 41st annual symposium on foundations of computer science. IEEE, pp 443–453
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The authors propose a novel method for unfolding a new class of polycubes without refinement.
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Richaume, L., Andres, E., Largeteau-Skapin, G. et al. Unfolding H-convex Manhattan Towers. J Comb Optim 44, 3023–3037 (2022). https://doi.org/10.1007/s10878-021-00829-8
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DOI: https://doi.org/10.1007/s10878-021-00829-8