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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.

BuzierBezier
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  • Firstly, the wikipedia page given by @ad2004 is great. I used the "Explicit Definition" section to write a bezier function that's working exactly as intended. But secondly, for what I'm inferring from your question are your purposes... you realize that $B(t), 0\leq t\leq 1$ will only go through your first and last control points, right? That is, $B(0), B(1)$ will evaluate to your first and last control points, respectively. But there's typically no $t$ for which $B(t)$ exactly passes through any other control point (unless they all happen to lie on a straight line, or other special case). – John Forkosh Jun 19 '20 at 03:37
  • Yes indeed, The page is great and is exactly what I was looking for – BuzierBezier Jun 19 '20 at 04:35

1 Answers1

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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.

ad2004
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