On 18.09.2016 13:54, Andrew Bernard wrote:
Hello Simon,

Others have of course already replied, but when I look at your attached sample 
I only see a slightly curved slur. What makes you say you want a quartic bezier 
curve? I can’t quite see it.

Are you sure that’s what you want in any case? Quickly scanning through some of 
the maths of bezier curves and splines, it seems that people are pretty much in 
agreement that curves higher than cubic are problematical in many ways, and 
that the way to deal with non cubic representable curves is to piecewise 
approximate them with cubic beziers. This is from the point of view of maths, 
and all the answers here give the practical way of doing that in lilypond.

What is it exactly that you are expecting a quartic to give you?

Oh, I think you’re quite overestimating the amount of in-depth mathematical background I had – I just thought: ‘A 3rd order Bézier curve can have one turning point, but I need two turning points, so I’d need a 4th order Bézier’. Which I now see is wrong, after some experimenting with the interactive fields in that article you linked: it requires a 5th order Bézier for that, and then it already gets quite unhandy. But now I know that the goal is much better achieved by linking two cubic ones. As is said in the article: ‘you can link up multiple Bézier curves so that the combination looks like a single curve.’ So – problem solved (if also the control points have to be specified manually…).

Best, Simon

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