![[bezier.gif|invert_Sepia]] A type of [[Parametric Spline]], a [[Polynomial]] curve / [[Hermite Interpolation]]. This a For a bezier curve, not only are their 'anchor' [[Point|points]] restricting the position of the curve at certain values, there are also 'anchor points' which determine how the curve 'aproaches' to each anchor. Typically bezier curves are [[Cubic]]. Given two anchor points $(x_{i},y_{i}), (x_{i+1},y_{i+1})$ and two control points (modeled as [[Vector|vectors]] with a root at a control point) $\vec v_{i}, \vec u_{i+1}$. $\huge \begin{align} \vec S_{i}(t) &= (t-1)(2t+1)\vec x_{i} \\ &+ t^{2}(2t-3)\vec x_{i+1} \\ &+ t(t-1)\vec v_{i} \\ &- t^{2}(t-1)\vec u_{i+1} \end{align} $ theres a cool shortcut to get the control points based on the derivative bezier from $\vec A$ to $\vec B$ with derivatives needing to be $\vec A'$ and $\vec B'$ the control points would be $\set{A,B, A+\frac{A'}{3}, B-\frac{B'}{3}}$