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I have a Bezier curve with following points
$x_0,y_0 = 0.03,0.03$(start point)
$x_1,y_1 = 0.335,0.6$
$x_2,y_2 = 0.667,0.9$
$x_3,y_3 = 1,1$(end point)
What is the equation for the curve in terms of $x$ and $y$ only? So that i can find the value of $y$ when I have $x$ where $(x,y)$ is a point on the curve.

bubba
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Nakul Wenger Ramakumar
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  • Welcome to Math Stack Exchange. In clear, you want a cartesian equation $y=f(x)$, knowing parametric equations x=x(t), y=y(t) (if possible, in fact, in some cases, you will need 2, or even 3 cartesian equations). But have you already computed the parametric equations ? It is important for us to know what you have done already and where you are blocked. – Jean Marie Apr 13 '17 at 08:16
  • This same question has been asked (and answered) many times. The latest occurrence is here: http://math.stackexchange.com/questions/2127059/finding-y-coordinate-given-x-coordinate-of-cubic-bezier-curve-under-restrict?rq=1. Or just look at the "related" links on the right-hand side of the page. – bubba Apr 13 '17 at 08:42

1 Answers1

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As the answers to the related questions point out, you can't really get $y$ as a function of $x$, in general.

But your particular case is (almost) a special one that's easy to handle. If you had $x_0 = 0$, $x_1 = \tfrac13$, $x_2 = \tfrac23$, $x_3 = 1$, then the equation would be: $$ y = (1-x)^3 y_0 + 3x(1-x)^2y_1 + 3x^2(1-x)y_2 + x^3y_3 $$ If you don't need high accuracy, then maybe you can use this equation, or adjust it a little to meet your needs.

bubba
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