Bezier Curves

Bezier curves are smooth curves that are frequently linked together to create paths in computer graphics. It is possible to create degree \(n\) curves, but quadratic and cubic are the most common. A Bezier curve between points \(A\) and \(B\) with degree \(n\) will have \(n-1\) control points \(C_0, C_1, C_2, \ldots \) between \(A\) and \(B\). A quadratic Bezier curve from \(A\) to \(B\) is traced by the function \[ P(t) = (1-t^2)A+2(1-t)tC_0+t^2B \] as \(t\) ranges from 0 to 1. Similarly, a cubic Bezier curve from \(A\) to \(B\) is traced by the function \[ P(t) = (1-t)^3A+3(1-t)^2tC_0++3(1-t)^2tC_1 + t^3B \]