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このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/13761
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| タイトル: | Flat Foldings of Plane Graphs with Prescribed Angles and Edge |
| 著者: | Abel, Zachary
Demaine, Erik D.
Demaine, Martin
Eppstein, David
Lubiw, Anna
Ryuhei Uehara |
| キーワード: | plane graph
folding problem
single-vertex flat origami |
| 発行日: | 2014-09-24 |
| 出版者: | Springer |
| 誌名: | Lecture Notes in Computer Science |
| 巻: | 8871 |
| 開始ページ: | 272 |
| 終了ページ: | 283 |
| DOI: | 10.1007/978-3-662-45803-7_23 |
| 抄録: | When can a plane graph with prescribed edge lengths and prescribed angles (from among {0,180°, 360°}) be folded at to lie in an infinitesimally thick line, without crossings? This problem generalizes the classic theory of single-vertex at origami with prescribed mountain-valley assignment, which corresponds to the case of a cycle graph. We characterize such at-foldable plane graphs by two obviously necessary but also sufficient conditions, proving a conjecture made in 2001: the angles at each vertex should sum to 360°, and every face of the graph must itself be at foldable. This characterization leads to a linear-time algorithm for testing at foldability of plane graphs with prescribed edge lengths and angles, and a polynomial-time algorithm for counting the number of distinct folded states. |
| Rights: | This is the author-created version of Springer, Zachary Abel, Erik D. Demaine, Martin Demaine, David Eppstein, Anna Lubiw and Ryuhei Uehara, Lecture Notes in Computer Science, 8871, 2014, 272-283. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-662-45803-7_23 |
| URI: | http://hdl.handle.net/10119/13761 |
| 資料タイプ: | author |
| 出現コレクション: | b10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
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| 20593.pdf | | 1414Kb | Adobe PDF | 見る/開く |
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