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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 Circular surface ： ウィキペディア英語版 Circular surface In mathematics and, in particular, differential geometry a circular surface is the image of a map ''ƒ'' : ''I'' × ''S''1 → R3, where ''I'' ⊂ R is an open interval and ''S''1 is the unit circle, defined by :$f(t,\backslash theta)\; :=\; \backslash gamma(t)\; +\; r(t)(t)\backslash cos\backslash theta\; +\; r(t)(t)\backslash sin\backslash theta,\; \backslash ,$ where γ, u, v : ''I'' → R3 and ''r'' : ''I'' → R>0, when Moreover, it is usually assumed that u · u = v · v = 1 and u · v = 0, where dot denotes the canonical scalar product on R3, i.e. u and v are unit length and mutually perpendicular. The map γ : ''I'' → R3 is called the base curve for the circular surface and the two maps u, v : ''I'' → R3 are called the direction frame for the circular surface. For a fixed ''t''0 ∈ ''I'' the image of ''ƒ''(''t''0, ''θ'') is called a generating circle of the circular surface.〔S. Izumiya, K. Saji, and N. Takeuchi, "Circular Surfaces", ''Advances in Geometry'', de Gruyter, Vol 7, 2007, 295–313.〕 Circular surfaces are an analogue of ruled surfaces. In the case of circular surfaces the generators are circles; called the generating circles. In the case of ruled surface the generators are straight lines; called rulings. == References == 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「Circular surface」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.