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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 Spline (mathematics) ： ウィキペディア英語版 Spline (mathematics) In mathematics, a spline is a numeric function that is piecewise-defined by polynomial functions, and which possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as ''knots''). In interpolating problems, ''spline interpolation'' is often preferred to polynomial interpolation because it yields similar results to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon. In computer graphics, parametric curves whose coordinates are given by splines are popular because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The most commonly used splines are cubic spline, i.e., of order 3—in particular, cubic B-spline, which is equivalent to C2 continuous composite Bézier curves. They are common, in particular, in spline interpolation simulating the function of flat splines. The term ''spline'' is adopted from the name of a flexible strip of metal commonly used by drafters to assist in drawing curved lines. == Examples == A simple example of a quadratic spline (a spline of degree 2) is :$$ S(t) = \begin (t+1)^2-1 & -2 \le t < 0\\ 1-(t-1)^2 & 0 \le t \le 2 \end for which $S\text{'}(0)=2$. A simple example of a cubic spline is :$S(t)\; =\; \backslash left|t\backslash right|^3$ as :$$ S(t) = \begin t^3 & t \ge 0\\ -t^3 & t < 0 \end and :$S\text{'}(0)\; =\backslash \; 0$ :$S\text{'}\text{'}(0)\; =\backslash \; 0$ An example of using a cubic spline to create a bell shaped curve is the Irwin-Hall distribution polynomials: :$$ f_X(x)= \begin \frac(x+2)^3 & -2\le x \le -1\\ \frac\left(3|x|^3 - 6x^2 +4 \right)& -1\le x \le 1\\ \frac(2-x)^3 & 1\le x \le 2 \end 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「Spline (mathematics)」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.