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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Conversion between quaternions and Euler angles ： ウィキペディア英語版 Conversion between quaternions and Euler angles Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of magic squares. For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". ==Definition== A unit quaternion can be described as: : :$|\backslash mathbf|^2\; =\; q\_0^2\; +\; q\_1^2\; +\; q\_2^2\; +\; q\_3^2\; =\; 1$ We can associate a quaternion with a rotation around an axis by the following expression :$\backslash mathbf\_0\; =\; \backslash cos(\backslash alpha/2)$ :$\backslash mathbf\_1\; =\; \backslash sin(\backslash alpha/2)\backslash cos(\backslash beta\_x)$ :$\backslash mathbf\_2\; =\; \backslash sin(\backslash alpha/2)\backslash cos(\backslash beta\_y)$ :$\backslash mathbf\_3\; =\; \backslash sin(\backslash alpha/2)\backslash cos(\backslash beta\_z)$ where α is a simple rotation angle (the value in radians of the angle of rotation) and cos(β''x''), cos(β''y'') and cos(β''z'') are the "direction cosines" locating the axis of rotation (Euler's Theorem). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Conversion between quaternions and Euler angles」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.