algorithm for Bezier curve with eleven control points

Question

I would like to know the algorithm/ polynomial equation for a Bezier curve with eleven control points. Thanks in advance.

Answer 1

The curve of degree $m$ with control points $P_0, \ldots, P_m$ has the equation: $$ C(t) = \sum_{i=0}^m \varphi_i^m(t)P_i \quad\quad (0 \le t \le 1) $$ where $$ \varphi_i^m(t) = \displaystyle \binom{m}{i}(1 - t)^{m-i} t^{i} \quad\quad (0 \le t \le 1) $$ is the $i$-th Bernstein polynomial of degree $m$.

For $m=11$, the Bernstein polynomials are: $$ \varphi_0(t) = (1 - t)^{11} \\ \varphi_1(t) = 11t(1 - t)^{10} \\ \varphi_2(t) = 55t^2(1 - t)^{9} \\ \vdots \\ \varphi_{11}(t) = t^{11} $$ You can calculate points on the curve using the well-known deCasteljau algorithm.