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I am plotting a Bezier curve in a computer program I've written. The curve is created using four control points to generate the coefficients to the following equations:

x = ax*t^3 + bx*t^2 + cx * t + dx

y = ay*t^3 + by*t^2 + cy * t + dy

Where t a value between 0 - 1 to evaluate along the Bezier curve.

However, I need to know what the differential of this curve is, not with respect to t, but with respect to x. i.e. dy/dx at a value of x that you choose.

The reason for this is that I'm plotting a Bezier through some experiemental data and I need a mathematical representation of that data so I can get a smooth differential and double differential. But I've now come across this problem.

The only way I've thought of to do this so far is to, at your given x value, involves solving the cubic for t, which is quite expensive and diffucult.

Any suggestions?

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# Differential of Bezier curve

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