Hi, all I just wanted to see if anyone knows the formula for a quintic bezier curve

Question

If possible I'd like to find out the formula for a quintic bezier curve. I have a set of 6 static points that I need to turn into a parametric equation and would like to be able to do it a simpler way than going through each individual step

Thanks.

Answer 1

I believe this might be what you are looking for. For $n=5$

\begin{align} \mathbf{B}(t) &= (1 - t)^5\mathbf{P}_0 + 5t(1 - t)^4\mathbf{P}_1 + 10t^2(1 - t)^3 \mathbf{P}_2 + 10t^3 (1-t)^2 \mathbf{P}_3 + 5t^4(1-t) \mathbf{P}_4 + t^5 \mathbf{P}_5 && 0 \leqslant t \leqslant 1 \end{align}

It was an example from the Bezier wiki: https://en.wikipedia.org/wiki/B%C3%A9zier_curve in the section named "Explicit definition".

I hope this helps.