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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 Schwarz–Christoffel mapping ： ウィキペディア英語版 Schwarz–Christoffel mapping In complex analysis, a Schwarz–Christoffel mapping is a conformal transformation of the upper half-plane onto the interior of a simple polygon. Schwarz–Christoffel mappings are used in potential theory and some of its applications, including minimal surfaces and fluid dynamics. They are named after Elwin Bruno Christoffel and Hermann Amandus Schwarz. ==Definition== Consider a polygon in the complex plane. The Riemann mapping theorem implies that there is a bijective biholomorphic mapping ''f'' from the upper half-plane :$\backslash \backslash ,\backslash zeta\; >\; 0\; \backslash \}$ to the interior of the polygon. The function ''f'' maps the real axis to the edges of the polygon. If the polygon has interior angles $\backslash alpha,\backslash beta,\backslash gamma,\; \backslash ldots$, then this mapping is given by :$$ f(\zeta) = \int^\zeta \frac(w-c)^ \cdots} \,\mboxw where $K$ is a constant, and are the values, along the real axis of the $\backslash zeta$ plane, of points corresponding to the vertices of the polygon in the $z$ plane. A transformation of this form is called a ''Schwarz–Christoffel mapping''. It is often convenient to consider the case in which the point at infinity of the $\backslash zeta$ plane maps to one of the vertices of the $z$ plane polygon (conventionally the vertex with angle $\backslash alpha$). If this is done, the first factor in the formula is effectively a constant and may be regarded as being absorbed into the constant $K$. 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「Schwarz–Christoffel mapping」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.