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-1}(x) := & \sum_{\nu=0}^{n} \beta_{\nu,k-1} b_{\nu,n}(x - x_{k -1}) & x \in [x_{k-1}, x_k) \\ \end{matrix}\right.

[edit] See also

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