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Bzier SplineIn the mathematical subfield of numerical analysis and in computer graphics a Bzier spline is a spline curve where each polynomial of the spline is in Bzier form. A Bzier spline is sometimes called bezigon as Bzier splines are like polygons but instead of straight lines they consist of Bzier curves. Bezigons can be made big or small or rotated with no "jaggies". Adobe PostScript fonts are made up of bezigons. Bezigons can be used to create scalable shapes directly. Definition Given a spline S of degree n with k knots xi we can write the spline as a Bzier 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.
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