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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 De Casteljau's algorithm ： ウィキペディア英語版 De Casteljau's algorithm In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value. Although the algorithm is slower for most architectures when compared with the direct approach, it is more numerically stable. ==Definition== A Bézier curve ''B'' (of degree ''n'', with control points $\backslash beta\_0,\; \backslash ldots,\; \backslash beta\_n$) can be written in Bernstein form as follows :$B(t)\; =\; \backslash sum\_^\backslash beta\_b\_(t)$, where ''b'' is a Bernstein basis polynomial :$b\_(t)\; =\; (1-t)^t^i$. The curve at point ''t''0 can be evaluated with the recurrence relation :$\backslash beta\_i^\; :=\; \backslash beta\_i\; \backslash mbox\; i=0,\backslash ldots,n$ :$\backslash beta\_i^\; :=\; \backslash beta\_i^\; (1-t\_0)\; +\; \backslash beta\_^\; t\_0\; \backslash mbox\; i\; =\; 0,\backslash ldots,n-j\; \backslash mbox\; j=\; 1,\backslash ldots,n$ Then, the evaluation of $B$ at point $t\_0$ can be evaluated in $n$ steps of the algorithm. The result $B(t\_0)$ is given by : :$B(t\_0)=\backslash beta\_0^.$ Moreover, the Bézier curve $B$ can be split at point $t\_0$ into two curves with respective control points : :$\backslash beta\_0^,\backslash beta\_0^,\backslash ldots,\backslash beta\_0^$ :$\backslash beta\_0^,\backslash beta\_1^,\backslash ldots,\backslash beta\_n^$ 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「De Casteljau's algorithm」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.