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Continuous Flattening of α-Trapezoidal Polyhedra
https://ipsj.ixsq.nii.ac.jp/records/182993
https://ipsj.ixsq.nii.ac.jp/records/18299331ad2dfc-5ac2-40fd-80b7-05b899ee75e0
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
IPSJ-JNL5808007.pdf (896.0 kB)
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Copyright (c) 2017 by the Information Processing Society of Japan
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| オープンアクセス | ||
| Item type | Journal(1) | |||||||||
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| 公開日 | 2017-08-15 | |||||||||
| タイトル | ||||||||||
| タイトル | Continuous Flattening of α-Trapezoidal Polyhedra | |||||||||
| タイトル | ||||||||||
| 言語 | en | |||||||||
| タイトル | Continuous Flattening of α-Trapezoidal Polyhedra | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| キーワード | ||||||||||
| 主題Scheme | Other | |||||||||
| 主題 | [特集：離散と計算の幾何・グラフ・ゲーム] polyhedron, continuous flattening, moving crease, zig-zag belt | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 著者所属 | ||||||||||
| Chuo Gakuin University | ||||||||||
| 著者所属 | ||||||||||
| Meiji University | ||||||||||
| 著者所属(英) | ||||||||||
| en | ||||||||||
| Chuo Gakuin University | ||||||||||
| 著者所属(英) | ||||||||||
| en | ||||||||||
| Meiji University | ||||||||||
| 著者名 |
Kazuki, Matsubara
× Kazuki, Matsubara
× Chie, Nara
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| 著者名(英) |
Kazuki, Matsubara
× Kazuki, Matsubara
× Chie, Nara
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| 論文抄録 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | It was proved that any orthogonal polyhedron is continuously flattened by using a property of a rhombus. We investigated the method precisely, and found that there are infinitely many ways to flatten such polyhedra. We prove that the infimum of the area of moving creases is zero for α-trapezoidal polyhedra, which is a generalization of semi-orthogonal polyhedra. Also we prove that, for any integer n, there exists a continuous flattening motion whose area of moving creases is arbitrarily small for any n-gonal pyramid with a circumscribed base and a top vertex being just above the incenter of the base. As a by-product we provide a continuous flattening motion whose area of moving creases is arbitrarily small for more general types of polyhedra. ------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.25(2017) (online) DOI http://dx.doi.org/10.2197/ipsjjip.25.554 ------------------------------ |
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| 論文抄録(英) | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | It was proved that any orthogonal polyhedron is continuously flattened by using a property of a rhombus. We investigated the method precisely, and found that there are infinitely many ways to flatten such polyhedra. We prove that the infimum of the area of moving creases is zero for α-trapezoidal polyhedra, which is a generalization of semi-orthogonal polyhedra. Also we prove that, for any integer n, there exists a continuous flattening motion whose area of moving creases is arbitrarily small for any n-gonal pyramid with a circumscribed base and a top vertex being just above the incenter of the base. As a by-product we provide a continuous flattening motion whose area of moving creases is arbitrarily small for more general types of polyhedra. ------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.25(2017) (online) DOI http://dx.doi.org/10.2197/ipsjjip.25.554 ------------------------------ |
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| 書誌レコードID | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | AN00116647 | |||||||||
| 書誌情報 |
情報処理学会論文誌 巻 58, 号 8, 発行日 2017-08-15 |
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| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1882-7764 | |||||||||
