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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 Inertia tensor of triangle ： ウィキペディア英語版 Inertia tensor of triangle The inertia tensor $$ \mathbf of a triangle (like the inertia tensor of any body) can be expressed in terms of covariance $$ \mathbf of the body: :$$ \mathbf = \mathrm(\mathbf)\mathbf - \mathbf where covariance is defined as area integral over the triangle: :$$ \mathbf \triangleq \int_ \rho \mathbf\mathbf^ = a \mathbf^ \mathbf where * $\backslash mathbf$ represents 3 × 3 matrix containing triangle vertex coordinates $(\backslash mathbf\_0,\; \backslash mathbf\_1,\; \backslash mathbf\_2)$ in the rows, * $a\; =\; |(\backslash mathbf\_1\; -\; \backslash mathbf\_0)\; \backslash times\; (\backslash mathbf\_2\; -\; \backslash mathbf\_0)|$ is twice the area of the triangle, * $$ \mathbf= \frac \begin 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \\ \end Substitution of triangle covariance in definition of inertia tensor gives eventually :$$ \mathbf = \frac(\mathbf^2_0 + \mathbf^2_1 + \mathbf^2_2 + (\mathbf_0 + \mathbf_1 + \mathbf_2)^2)\mathbf - a \mathbf^ \mathbf == A proof of the formula == The proof given here follows the steps from the article.〔http://number-none.com/blow/inertia/bb_inertia.doc Jonathan Blow, Atman J Binstock (2004) "How to find the inertia tensor (or other mass properties) of a 3D solid body represented by a triangle mesh"〕 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「Inertia tensor of triangle」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.