accurate bezier curve fitting

[vince touache]

hello,

I was looking for an algorithm to predict the best Bezier curve, given a vector of points. I ended up implementing  "An Algorithm for Automatically Fitting Digitized Curves" from Graphics Gems vol.1, but I'm not 100% happy with the result.

Out of curiosity, I compared it against the fitBspline node in Maya, which seems to give a better result.

Does anyone know what algorithm the fitBspline node is using internally? And/or does anyone know other bezier curve fitting algorithms?

TLDR:

what I don't like with the Graphics Gems approach is that it assumes the tangent is the unit vector P1-P0 / ||P1-P0||, which is always wrong. Close to be right, but not right. So I'd like something that can retrieve the tangents more accurately

Thank you

[Alok Gandhi]

This might be a useful read maybe?

https://raphlinus.github.io/curves/2021/03/11/bezier-fitting.html

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[Marcus Ottosson]

Would it be possible to post the results you weren't happy with, along with the results in Maya you thought gave better results?

To view this discussion on the web visit https://groups.google.com/d/msgid/python_inside_maya/CAPaTLMTx4yJjYMk4wDd6o3CwZ3PoHbaVAkc59xtp2m-P7zzu7A%40mail.gmail.com.

[vince touache]

@Marcus: as you can see, fitBspline (green) produces a better result than my version (red). Moreover, it requires way too many controls. My original curve is 4 CVs, so I would expect a solution close to 4 CVs as well. You can see the difference b/w mine and the maya one on fitting_curve1.jpg and fitting_curve2.jpg (closeup)

@Alok: the problem with what's exposed here is the same (I believe) as the one coming with the Graphics Gems solution. I didn't find an implementation, so I may be wrong, but seems that at no point the partial derivative is actually discussed. Instead, they just take P1-P0 (in yellow on fitting_curve3.jpg) to be the tangent (from P0->Pn, with n input points), but the "true" tangent is different (in red on fitting_curve3.jpg). Of course, the algorithm has no idea of this true tangent, since all it gets is a vector of input points.

Hope it makes sense

Thank you