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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 Support function ： ウィキペディア英語版 Support function In mathematics, the support function ''h''''A'' of a non-empty closed convex set ''A'' in $\backslash mathbb^n$ describes the (signed) distances of supporting hyperplanes of ''A'' from the origin. The support function is a convex function on $\backslash mathbb^n$. Any non-empty closed convex set ''A'' is uniquely determined by ''h''''A''. Furthermore, the support function, as a function of the set ''A'' is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition. Due to these properties, the support function is one of the most central basic concepts in convex geometry. ==Definition== The support function $h\_A\backslash colon\backslash mathbb^n\backslash to\backslash mathbb$ of a non-empty closed convex set ''A'' in $\backslash mathbb^n$ is given by :$h\_A(x)=\backslash sup\backslash ,$ $x\backslash in\backslash mathbb^n$; see 〔T. Bonnesen, W. Fenchel, '' Theorie der konvexen Körper,'' Julius Springer, Berlin, 1934. English translation: ''Theory of convex bodies,'' BCS Associates, Moscow, ID, 1987.〕 〔R. J. Gardner, ''Geometric tomography,'' Cambridge University Press, New York, 1995. Second edition: 2006.〕 .〔R. Schneider, ''Convex bodies: the Brunn-Minkowski theory,'' Cambridge University Press, Cambridge, 1993.〕 Its interpretation is most intuitive when ''x'' is a unit vector: by definition, ''A'' is contained in the closed half space :$\backslash$ and there is at least one point of ''A'' in the boundary :$H(x)=\; \backslash$ of this half space. The hyperplane ''H''(''x'') is therefore called a ''supporting hyperplane'' with ''exterior'' (or ''outer'') unit normal vector ''x''. The word ''exterior'' is important here, as the orientation of ''x'' plays a role, the set ''H''(''x'') is in general different from ''H''(-''x''). Now ''h''''A'' is the (signed) distance of ''H''(''x'') from the origin. 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「Support function」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.