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I'm doing research for Bézier curves for school, and I don't really understand how to fill in a point in an equation. I mean, I'd like to represent this on an x,y (or t,y) curve, but what do I need to fill in to calculate, say, B(1) or B(2)? I can't just fill in x and y coordinates.

$B(t) = (1-t)\cdot P_0+ t \cdot P_1$

hansottowirtz
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1 Answers1

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The points are bold because they are representing vectors. So, the equation you are looking at actually represents a $B_x(t)$ and $B_y(t)$. You then need to graph these parametrically. So, for $B_x(t)$, take the x-coordinates of the points on your control polygon and plug it in for $P_x$ and then $B_y(t)$ is merely the same equation with the y-coordinates. Then, graph these as a $(B_x(t),B_y(t))$ curve, where $t \in [0,1]$.

Rellek
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  • Thanks, but how can I convert this $(Bx(t),By(t))$ to an $y = f(x)$ function? – hansottowirtz May 13 '15 at 12:54
  • Well, it really depends on the function itself. If you have something like a loop, then it is clear that you will not be able to put this in a simple function since it fails the fundamental vertical line test. If you DO have a function that passes the vertical line test, then you can set these two functions up such that they share a common parameter, namely $t$. If you are studying Bezier curves, I imagine that you know the methods to solve parametrized curves in terms of each other. If you do not, I suggest looking into that! – Rellek May 13 '15 at 13:41