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For a cubic Bezier curve, I have this formula:

$$\mathrm{B}(t)=\mathrm{P}_0(1-t)^3+3\mathrm{P}_1t(1-t)^2+3\mathrm{P}_2t^2(1-t)+\mathrm{P}_3t^3,\ t\in[0,1]$$

Now about $t$ I only know that is should be between $0$ and $1$, but which value should I choose? And how does the value that I choose influence the curve?

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Every $t$ gives you a point of the curve, so you need all of them to get the whole curve. See this graph. –  Glen The Udderboat Feb 10 '13 at 17:43
    
Thanks, very clear now. –  Ramy Al Zuhouri Feb 10 '13 at 17:46

1 Answer 1

up vote 3 down vote accepted

Choosing a single value of $t$ doesn't give you a curve at all.

For every value of $t$ between $0$ and $1$ you get one point in the plane. All those points for different $t$s taken together make up the curve.

In practice, to draw the curve, you could apply the formula to (say) 1001 different $t$s: $$ t = 0,\ 0.001,\ 0.002,\ 0.003, \ldots,\ 0.998,\ 0.999,\ 1 $$ and then connect the points you get out with straight line segments. If some of the corners in the polyline bend too sharply for your taste, increase the number of $t$s until the result looks nice and smooth.

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