# n 次元空間の回転と直投影について -高次元代数的図法幾何学IOn Rotations and Orthogonal Projections in n-Dimensional Euclidean Space

## 抄録

One of our purpose is to arrange and to analyze a method of visual perception of an object in n-dimensional Euclidean space <I>R</I><SUP>n</SUP> systematically and practically.<BR>When we study the process of visual perception of an object in <I>R</I><SUP>n</SUP>, we have to extend the process in 3-dimensional case to the general cases. If we try to perceive the unidentified object, usually we move (rotate) the object or we change the position (turn) around it, and we look it or press the shutter. In this paper, we will generalise these "moving" (rotation) and "looking" (projection) to n-dimensional cases, and we will give them, especially for the former, a practical expression.<BR>It is well known the theoretical expression of rotation in <I>R</I><SUP>n</SUP>, that is to decompose it to a product of at most n/2 2-dimensional rotations, so called the canonical form of the orthogonal transformation. This expression is useful and economical in mathematical sense, but it lacks practical use especially in high dimensional cases, since the axis of the 2 -dimensional rotation in each component is change depending on the given rotation. Then this expression is not satisfied our purpose.<BR>On the other hand, from our viewpoint to treat rotation and projection together, we obtain the following expression : any rotation in <I>R</I><SUP>n</SUP> which fixes the origin is decomposed to a product of at most n-1 2-dimensional rotations with the fixed axis and a rotation in the projection hyperplane ( ≅ <I>R</I><SUP>n-1</SUP>) . Of course our expression has practical value in exchange for a little waste.

## 収録刊行物

• 図学研究

図学研究 33(1), 33-43, 1999-03-01

日本図学会

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## 各種コード

• NII論文ID(NAID)
10002783657
• NII書誌ID(NCID)
AN00125240
• 本文言語コード
JPN
• 資料種別
ART
• ISSN
03875512
• NDL 記事登録ID
4690305
• NDL 雑誌分類
ZM1(科学技術--科学技術一般)
• NDL 請求記号
Z14-457
• データ提供元
CJP書誌  NDL  J-STAGE

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