Obtaining curve equation

[nahroge]

Hi @ChevronOne and/or other folks who are using this repo,

I would like to have the equation of the created curve. However, I got a bit confused. Could you show me how I can get the equation?

I hope you will see my question and thanks in advance.

[ChevronOne]

Hi, the fitting function fits cubic-Bézier curves, it returns four control points (P0 to P3) for each curve and by which the equation of the curve C is then defined as follows:
https://bit.ly/39LnG93 "C(t) = \sum_{i=0}^{n}\binom{n}{i} (1-t)^{n-i}t^{i}P_i"
where and the curve is defined only in . For cubic curves n=3.
This can simplified further to https://bit.ly/3wFIBBZ "C(t)=(1-t)^{3}P_{0}+3(1-t)^{2}tP_{1}+3(1-t)t^{2}P_{2}+t^{3}P_{3}, 0\leq t\leq 1"
"if the equations above did not render properly, you can copy-paste them in a proper latex renderer".
Also if you're not familiar with Bézier or parametric curves in general, here's a quick introduction. The Wikipedia article on the subject is pretty explanatory too.

You can get the four control points of a single curve by writing something like this: auto stat = ppl::LERPer::fitSingle(data, control_points, tolerance);. The control points will then be stored in the vector control_points. You may also need to check the error of the fitting process, which will be given by stat.ERR, and see if your application can tolerate it.

More about it in README.md

[nahroge]

Hi again @ChevronOne, thanks a lot for your explanation and prompt answer!