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Re: What to do wanting a 4th order Bézier?
From: |
Andrew Bernard |
Subject: |
Re: What to do wanting a 4th order Bézier? |
Date: |
Sun, 18 Sep 2016 21:54:31 +1000 |
User-agent: |
Microsoft-MacOutlook/f.1a.1.160916 |
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?
Just because this is so well written and one of the best elementary expositions
of Bezier curve maths I have come across, here’s a useful link:
http://pomax.github.io/bezierinfo/
Andrew
On 18/09/2016, 4:27 AM, "lilypond-user on behalf of Simon Albrecht"
<address@hidden on behalf of address@hidden> wrote:
Hello folks,
I’m attaching an excerpt from my current project, where I’d actually
really need a 4th order Bézier slur – but that’s impossible with Lily
now. Unfortunately I also lack an idea what else to do in this situation
– I’d like to avoid an extra staff…
Any ideas?
Best, Simon
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- OT: What to do wanting a 4th order Bézier?, (continued)
- OT: What to do wanting a 4th order Bézier?, Karlin High, 2016/09/21
- Re: What to do wanting a 4th order Bézier?, Carl Sorensen, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Thomas Morley, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Simon Albrecht, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, Kieren MacMillan, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Kieren MacMillan, 2016/09/18
Re: What to do wanting a 4th order Bézier?,
Andrew Bernard <=
- Re: What to do wanting a 4th order Bézier?, Simon Albrecht, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Hans Åberg, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, David Kastrup, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, Hans Åberg, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, David Kastrup, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, Hans Åberg, 2016/09/19
[OT] Re: What to do wanting a 4th order Bézier?, Kieren MacMillan, 2016/09/18
Re: What to do wanting a 4th order Bézier?, Simon Albrecht, 2016/09/23