Bézier spline
(Redirected from Bezigon)
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.
Definition
Given a spline S of degree n with k knots xi we can write the spline as a Bézier spline as:<math>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.</math>
See also
Categories
Splines