## Creating Optimized Cut-Out Sheets for Paper Models from Meshes

Citations: | 2 - 0 self |

### BibTeX

@MISC{Straub_creatingoptimized,

author = {R. Straub and H. Prautzsch},

title = {Creating Optimized Cut-Out Sheets for Paper Models from Meshes},

year = {}

}

### OpenURL

### Abstract

### Citations

896 |
Approximation Algorithms
- Vazirani
- 2004
(Show Context)
Citation Context ...(e) . The minimum set cover problem is NP-hard, but fortunately there are some approximation algorithms that are sufficiently efficient in practice. We implemented the greedy set cover algorithm from =-=[18]-=- given in Algorithm 1. Algorithm 1 Greedy set cover algorithm. E := ∅ {set of new cut edges} C := ∅ {set of already covered paths} while C �= P1 ∪ . . . ∪ Pn do {Determine the edge with minimum averag... |

157 |
A linear-time algorithm for testing the truth of certain quantified boolean formulas
- Aspvall, Plass, et al.
- 1979
(Show Context)
Citation Context ...i by xi ∨ xi . With the help of an implication graph, both the satisfiability of a 2CNF formula can be decided and—if the formula is satisfiable—a fulfilling assignment can be computed in linear time =-=[2]-=-. Definition 3 (Implication graph). Let F = c1 ∧ . . . ∧ cn be a formula in 2CNF. Then the implication graph GF = (V, E) of F is a directed graph that has two vertices x and x for each variable x in F... |

111 | Solving geometric problems with the rotating calipers, in
- Toussaint
- 1983
(Show Context)
Citation Context ...oo large to fit on a paper sheet. To determine the size of each part, the minimum area bounding box—which is not necessarily axis aligned—of each part is computed with the rotating calipers algorithm =-=[17]-=-. Each bounding box that is too large, is iteratively subdivided along its x- or y-axis until it fits on a paper sheet. In each step, the axis that does not fit is selected. Then the path in the dual ... |

70 |
Bounds on backtrack algorithms for listing cycles, paths, and spanning trees
- Read, Tarjan
- 1975
(Show Context)
Citation Context ...hout a non-overlapping unfolding. On the other hand, for polyhedra that have a nonoverlapping unfolding, the only known algorithm to obtain such an unfolding is to try all possibilities. According to =-=[14]-=-, the number n of spanning trees of a graph with |VD| vertices and |ED| edges satisfies n ≥ 2 l “ 1 2 −1+ √ ”m 1+8(|ED|−|VD|+1) 1 ≈ 2⌈ 2(−1+ √ 9+8v)⌉ if we assume that the mesh is almost regular and t... |

57 | Unsolved problems in geometry - Croft, Falconer, et al. - 1991 |

53 | Folding and unfolding in computational geometry
- O’Rourke
- 1998
(Show Context)
Citation Context ...folding polyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding [3, 4, 5]. Other authors discuss cuts across faces [1] or the folding problem =-=[13]-=-. In [15] several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeeded in finding a non-overlapping unfolding for every test case. In this pap... |

51 |
H.: Making Papercraft Toys from Meshes using Strip-based Approximate Unfolding
- Mitani, Suzuki
- 2004
(Show Context)
Citation Context ...ce in the last few years. This has led to significant rise in the number of related publications recently, such as [10], which presented new ideas and theories about paper modeling. Mitani and Suzuki =-=[12]-=- presented a method for producing an unfolded papercraft from a 3D computer model, represented by a triangular mesh, by approximating the mesh ∗ Universität Karlsruhe (TH), Germany. {raphael,prau}@ira... |

37 | Schevon, “Star unfolding of a polytope with applications
- Agarwal, Aronov, et al.
- 1997
(Show Context)
Citation Context ...te on special cases like unfolding polyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding [3, 4, 5]. Other authors discuss cuts across faces =-=[1]-=- or the folding problem [13]. In [15] several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeeded in finding a non-overlapping unfolding for ... |

35 | Unfolding some classes of orthogonal polyhedra - Biedl, Demaine, et al. - 1998 |

34 | Openmesh - a generic and efficient polygon mesh data structure
- Botsch, Steinberg, et al.
- 2002
(Show Context)
Citation Context ...ith planar faces that are simple polygons without holes. If there are faces with holes, they can be subdivided to get rid of the holes. For efficient traversal of the mesh, a half-edge data structure =-=[7]-=- is used to represent the mesh internally such that any adjacent entity of the mesh can always be computed in constant time. 2.1 Initial Unfolding To create the cut-out sheets, we first unfold the mod... |

34 | Adaptive unwrapping for interactive texture painting
- Igarashi, Cosgrove
- 2001
(Show Context)
Citation Context ...problem is known to be NP-hard. Although exact algorithms for solving small bin packing problems in a reasonable amount of time exist [11], we apply the approximative 2D bin packing algorithm used in =-=[9]-=- for packing textures on a texture atlas.sd α β Figure 5. A trapezoidal glue tab with base angles α and β and width d. 2.4 Computing Glue Tabs So far, we did not consider glue tabs which need to be ad... |

34 | The three-dimensional bin packing problem
- Martello, Pisinger, et al.
(Show Context)
Citation Context ...mple geometry—in our case we have rectangular bounding boxes—this problem is known to be NP-hard. Although exact algorithms for solving small bin packing problems in a reasonable amount of time exist =-=[11]-=-, we apply the approximative 2D bin packing algorithm used in [9] for packing textures on a texture atlas.sd α β Figure 5. A trapezoidal glue tab with base angles α and β and width d. 2.4 Computing Gl... |

26 | Ununfoldable polyhedra with convex faces
- Bern, Demaine, et al.
(Show Context)
Citation Context ... a non-overlapping unfolding. Many papers concentrate on special cases like unfolding polyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding =-=[3, 4, 5]-=-. Other authors discuss cuts across faces [1] or the folding problem [13]. In [15] several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeede... |

15 | Ununfoldable polyhedra
- Bern, Demaine, et al.
- 1999
(Show Context)
Citation Context ... a non-overlapping unfolding. Many papers concentrate on special cases like unfolding polyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding =-=[3, 4, 5]-=-. Other authors discuss cuts across faces [1] or the folding problem [13]. In [15] several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeede... |

12 |
Origami Design Secrets: Mathematical Methods for an Ancient Art. A K Peters Ltd
- Lang
- 2003
(Show Context)
Citation Context ...to create complex models. Origami and paper modeling in general have seen a renaissance in the last few years. This has led to significant rise in the number of related publications recently, such as =-=[10]-=-, which presented new ideas and theories about paper modeling. Mitani and Suzuki [12] presented a method for producing an unfolded papercraft from a 3D computer model, represented by a triangular mesh... |

9 | R.E.: A linear-time algorithm for testing the truth of certain quantified boolean formulas - Aspvall, Plass, et al. - 1979 |

8 | H.: Improving exact algorithms for MAX-2-SAT
- Shen, Zhang
- 2005
(Show Context)
Citation Context ...quivalence clauses xi ↔ xj to the tab arrangement formula. However, by adding equivalence clauses for all cuts, the formula often becomes unsatisfiable. As a consequence, we use a MAX-2-SAT algorithm =-=[16]-=- to guarantee that all original clauses and as many added equivalence clauses as possible are fulfilled. Now we have a valid assignment with minimally sized tabs. In the last step of our glue tab arra... |

7 | Nets of polyhedra - Schlickenrieder - 1997 |

3 | Ununfoldable polyhedra with triangular faces
- Bern, Demaine, et al.
- 1999
(Show Context)
Citation Context ... a non-overlapping unfolding. Many papers concentrate on special cases like unfolding polyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding =-=[3, 4, 5]-=-. Other authors discuss cuts across faces [1] or the folding problem [13]. In [15] several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeede... |

2 | Imaging maths—unfolding polyhedra - Polthier |

1 |
Nets of polyhedra. Diplomarbeit, Technische Universität
- Schlickenrieder
- 1997
(Show Context)
Citation Context ...olyhedra with orthogonal faces [6], or prove that some special polyhedra do not have a non-overlapping unfolding [3, 4, 5]. Other authors discuss cuts across faces [1] or the folding problem [13]. In =-=[15]-=- several heuristic methods to get a nonoverlapping edge unfolding are studied. But no heuristic algorithm has succeeded in finding a non-overlapping unfolding for every test case. In this paper, we pr... |

1 | Optimierte Bastelbögen aus Netzen - Bertram |

1 | Optimierte Bastelbögen aus Netzen - Römer |