CODEWITHSUNDEEP
audiobeziersamplingpcmcubic-bezier
user7950306
user7950306

Reputation:

Is it possible to get the y value of a cubic bezier curve based on the x value?

I am working with bezier curves to represent wave data for audio. I want to then sample the wave at an x coordinate and get the y coordinate so that I can then convert it to PCM data. Now since bezier curve are represented with a parametric equation this could pose problems as there could be multiple y values an x value, but with the curves I would sampling I can guarantee that they meet the criteria of a function only they are still represented para-metrically. So my question is, is there a way to directly sample the y value based on an x value? If not what would be the best way to go about doing this? My best idea right now is move along the curve until I reach the desired x-value and then use that y value, but this feels slow and inefficient. Thank you.

Upvotes: 1

Views: 2092

Answers (1)

GCB613
GCB613

Reputation: 184

Yes, it is possible but it is somewhat complex. You must solve for t at a given x and then calculate y from t. This can be approximated with the newton-raphson method. This link does a much better job explaining how to implement it: http://greweb.me/2012/02/bezier-curve-based-easing-functions-from-concept-to-implementation/

Another option is to use a an explicit bezier curve, not a parametric bezier curve. Explicit meaning that y is a function of x (i.e. y=f(x)). As opposed to a parametric equation where both x and y are functions of t (i.e. x=f(t) and y=f(t)). As long as the x values of the control points are evenly spaced the curve is explicit and you can assume that x=t.

EDIT: I should point out that my statement of equally spaced x coordinates means x=t is an over-simplification. That would be true if the x coordinates were evenly spaced between 0 and 1. Otherwise you need to convert the x coordinate to a value between 0 and 1. For example if the x coordinates were evenly spaced and located at 3,4,5,6 then t = (x - 3) / (6 - 3).

Upvotes: 1

Related Questions