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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 Bézier triangle ： ウィキペディア英語版 Bézier triangle A Bézier triangle is a special type of Bézier surface, which is created by (linear, quadratic, cubic or higher degree) interpolation of control points. ==Cubic Bézier triangle== A cubic Bézier triangle is a surface with the equation :$\backslash begin$ p(s, t, u) = (\alpha s+\beta t+\gamma u)^3 =& \beta^3\ t^3 + 3\ \alpha\beta^2\ st^2 + 3\ \beta^2\gamma\ t^2 u + \\ &3\ \alpha^2\beta\ s^2 t + 6\ \alpha\beta\gamma\ stu + 3\ \beta\gamma^2\ tu^2 + \\ &\alpha^3\ s^3+ 3\ \alpha^2\gamma\ s^2 u + 3\ \alpha\gamma^2\ su^2 + \gamma^3\ u^3 \end where α3, β3, γ3, α2β, αβ2, β2γ, βγ2, αγ2, α2γ and αβγ are the control points of the triangle and s, t, u (with 0 ≤ s, t, u ≤ 1 and s+t+u=1) the barycentric coordinates inside the triangle. The corners of the triangle are the points α3, β3 and γ3. The edges of the triangle are themselves Bézier curves, with the same control points as the Bézier triangle. By removing the γu term, a regular Bézier curve results. Also, while not very useful for display on a physical computer screen, by adding extra terms, a Bézier tetrahedron or Bézier polytope results. Due to the nature of the equation, the entire triangle will be contained within the volume surrounded by the control points, and affine transformations of the control points will correctly transform the whole triangle in the same way. 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「Bézier 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.