The Bézier curve $B_{P_1\cdot \cdot \cdot P_n}$ determined by $n$ ordered points is a weighted average of the curves through the first $n-1$ points and the last $n-1$ points, where the weight depends on the parameter of the curve. A precise recursive definition is as follows:

or, more explicitly:

$B_{P_1\cdot \cdot \cdot P_n}\left(t\right) \= \sum _{i\=0}^n\left(\genfrac{}{}{0ex}{}{n}{i}\right)\cdot {\left(1-t\right)}^{n-i}\cdot t^i\cdot P_i$

The Bézier curve is the graph of this parametric equation for $t$ from 0 to 1.