Bezier curve, get consistent points on axis?

Question

So I have a bezier curve >

Now, I would like to get a y point, value every says, 0.01 value on x-axis. As far as I know, there is no method to "find Y given X" using bezier. So I have to subdivide it into flat straight chunks and then get... "somehow" nearest chunk value as an approximation?

So my question is, how can I... "equally" subdivide the bezier curve so that chunk distance is more equal on... x-axis? Right now the chunk distancing that I get is quite... "random" using https://en.wikipedia.org/wiki/B%C3%A9zier_curve as my current algo.

Regards Dariusz

Answer 1

As far as I know, there is no method to "find Y given X" using bezier.

Then you probably need to look for "finding Y given X" a bit more =) https://pomax.github.io/bezierinfo/#yforx

As for the result you want, with regularly spaced intervals based on distance along the curve is the general problem of reparameterizing the curve for distance rather than time., and it's a hard problem for quadratic, and literally impossible problem for higher order Beziers.

So instead of trying to do that, what we typically do is just build a lookup table by sampling the curve, storing those "t maps to x/y and distance d along the curve", and then we use that combined with interpolation to get good-enough approximate coordinates (e.g. sub-sub-pixel accurate) rather than mathematically perfect coordinates. https://pomax.github.io/bezierinfo/#tracing