贝济埃样条 在数学的数值分析和计算机图形学中，贝济埃样条是条样的每个多项式都是伯恩斯坦多项式的样条。 定义 给定有k个结点xi的n次样条S，可以如下这样使这个样条为贝济埃样条： S ( x ) := { S 0 ( x ) := ∑ ν = 0 n β ν , 0 b ν , n ( x ) x ∈ [ x 0 , x 1 ) S 1 ( x ) := ∑ ν = 0 n β ν , 1 b ν , n ( x − x 1 ) x ∈ [ x 1 , x 2 ) ⋮ ⋮ S k − 2 ( x ) := ∑ ν = 0 n β ν , k − 2 b ν , n ( x − x k − 2 ) x ∈ [ x k − 2 , x k − 1 ] {\displaystyle S(x):=\left\{{\begin{matrix}S_{0}(x):=&\sum _{\nu =0}^{n}\beta _{\nu ,0}b_{\nu ,n}(x)&x\in [x_{0},x_{1})\\S_{1}(x):=&\sum _{\nu =0}^{n}\beta _{\nu ,1}b_{\nu ,n}(x-x_{1})&x\in [x_{1},x_{2})\\\vdots &\vdots \\S_{k-2}(x):=&\sum _{\nu =0}^{n}\beta _{\nu ,k-2}b_{\nu ,n}(x-x_{k-2})&x\in [x_{k-2},x_{k-1}]\\\end{matrix}}\right.} 参见 贝济埃曲线
![S(x) := \left\{
\begin{matrix}
S_0(x) := & \sum_{\nu=0}^{n} \beta_{\nu,0} b_{\nu,n}(x) & x \in [x_0, x_1) \\
S_1(x) := & \sum_{\nu=0}^{n} \beta_{\nu,1} b_{\nu,n}(x - x_1) & x \in [x_1, x_2) \\
\vdots & \vdots \\
S_{k-2}(x) := & \sum_{\nu=0}^{n} \beta_{\nu,k-2} b_{\nu,n}(x - x_{k -2}) & x \in [x_{k-2}, x_{k-1}] \\
\end{matrix}\right.](/media/math_img/81996/2567d3290ff78ec985e04bf43e42aa6a33719b0c.svg)