Bézier spline
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In the mathematical field of numerical analysis and in computer graphics a Bézier spline is a spline curve where each polynomial of the spline is in Bézier form.
[edit] Definition
Given a spline S of degree n with k knots xi we can write the spline as a Bézier spline as: ![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.](../../../../math/a/e/d/aed618e06f8f78567291370c3e739853.png)
