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線形計画法を用いた直交多面体の復元可能性の判定
https://doi.org/10.14988/pa.2019.0000000270
https://doi.org/10.14988/pa.2019.00000002709628a410-88e1-41cc-90b6-595fe2afbb3d
名前 / ファイル | ライセンス | アクション |
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023060020004.pdf (1.7 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||||||
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公開日 | 2019-08-30 | |||||||||||
タイトル | ||||||||||||
言語 | ja | |||||||||||
タイトル | 線形計画法を用いた直交多面体の復元可能性の判定 | |||||||||||
タイトル | ||||||||||||
言語 | ja-Kana | |||||||||||
タイトル | センケイ ケイカクホウ オ モチイタ チョッコウ タメンタイ ノ フクゲン カノウセイ ノ ハンテイ | |||||||||||
タイトル | ||||||||||||
言語 | en | |||||||||||
タイトル | Criteria for recoverability of rectangular polyhedra in terms of linear programming | |||||||||||
言語 | ||||||||||||
言語 | jpn | |||||||||||
キーワード | ||||||||||||
主題 | 3次元復元, 直交多面体, 線形計画問題 3D recovery, rectangular polyhedra, linear programming |
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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 | departmental bulletin paper | |||||||||||
ID登録 | ||||||||||||
ID登録 | 10.14988/pa.2019.0000000270 | |||||||||||
ID登録タイプ | JaLC | |||||||||||
アクセス権 | ||||||||||||
アクセス権 | open access | |||||||||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||||
著者 |
網野, 誠晃
× 網野, 誠晃× 西田, 優樹× 渡邊, 芳英
WEKO
15621
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著者所属 | ||||||||||||
ja | ||||||||||||
網野, 誠晃 / Rakunan Elementary School | ||||||||||||
著者所属 | ||||||||||||
ja | ||||||||||||
西田, 優樹 / Graduate School of Science and Engineering, Science of Environment and Mathematical Modeling, Doshisha University | ||||||||||||
著者所属 | ||||||||||||
ja | ||||||||||||
渡邊, 芳英 / 同志社大学理工学部数理システム学科教授 | ||||||||||||
抄録 | ||||||||||||
内容記述タイプ | Abstract | |||||||||||
内容記述 | 直交多面体とはすべての角が互いに直交する3つ面からなる多面体のことである.本論文では,与えられた特別な性質をもつラベル付き線画の直交多面体としての復元可能性問題を論じる.ここでラベルは各頂点につけられており,それらの頂点の周りの3次元的な構造を表している.多面体に対する直交制約条件は2次であり線形ではないので扱いにくいため,直交条件を平行条件に緩和することにより制約条件を線形化する.そのことにより,考える問題は平行多面体としての復元可能性の問題へとなり,平行多面体としての復元可能性問題は線形計画法の実行可能解の存在に帰着する.さらに,平行多面体としての復元可能性は,直交多面体としての復元可能性と同値であることを,線画における辺の角度に関する条件の下で,平行多面体を直交多面体へうつすラベルを保つアフィン変換を構成することによって示す. | |||||||||||
言語 | ja | |||||||||||
抄録 | ||||||||||||
内容記述タイプ | Abstract | |||||||||||
内容記述 | A rectangular polyhedron is a polyhedron whose corners consist of three mutually perpendicular faces. In the present paper, we consider the recoverability problem of a rectangular polyhedron from a given labeled line drawing that has certain special properties. Here the labels attached to junctions signify the 3D structures around them. Since the orthogonality constraints are quadratic, that is, not linear and it is hard to deal with, we relax the orthogonality constraints into the parallel constraints so that they become linear. Then our problem is changed to the recoverability of parallel polyhedra. The recoverability of parallel polyhedra is reduced to the existence of a feasible solution of the linear programming problem. Further, we prove that the recoverability of parallel polyhedra is equivalent to that of rectangular polyhedra by constructing a label preserving affine transformation from a parallel polyhedron to a rectangular polyhedron under the suitable conditions for angles between lines in the drawings. | |||||||||||
言語 | en | |||||||||||
書誌情報 |
ja : 同志社大学ハリス理化学研究報告 en : The Harris science review of Doshisha University 巻 60, 号 2, p. 79-86, 発行日 2019-07-31 |
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出版者 | ||||||||||||
言語 | ja | |||||||||||
出版者 | 同志社大学ハリス理化学研究所 | |||||||||||
出版者(英) | ||||||||||||
言語 | en | |||||||||||
出版者 | Harris Science Research Institute of Doshisha University | |||||||||||
ISSN | ||||||||||||
収録物識別子タイプ | PISSN | |||||||||||
収録物識別子 | 21895937 | |||||||||||
書誌レコードID | ||||||||||||
収録物識別子タイプ | NCID | |||||||||||
収録物識別子 | AA12716107 | |||||||||||
権利者情報 | ||||||||||||
権利者名 | 同志社大学ハリス理化学研究所 | |||||||||||
言語 | ja | |||||||||||
権利者名 | Harris Science Research Institute of Doshisha University | |||||||||||
言語 | en | |||||||||||
関連サイト | ||||||||||||
関連タイプ | isFormatOf | |||||||||||
識別子タイプ | URI | |||||||||||
関連識別子 | https://doors.doshisha.ac.jp/opac/opac_link/bibid/SB12902196/?lang=0 | |||||||||||
言語 | ja | |||||||||||
関連名称 | 掲載刊行物所蔵情報へのリンク / Link to Contents | |||||||||||
フォーマット | ||||||||||||
内容記述タイプ | Other | |||||||||||
内容記述 | application/pdf | |||||||||||
出版タイプ | ||||||||||||
出版タイプ | VoR | |||||||||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||
日本十進分類法 | ||||||||||||
主題 | 417 |