# 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 $P(t) = (1-t)^3A+3(1-t)^2tC_0++3(1-t)^2tC_1 + t^3B$