Re: What to do wanting a 4th order Bézier?

[Simon Albrecht]

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