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Re: What to do wanting a 4th order Bézier?
From: |
David Kastrup |
Subject: |
Re: What to do wanting a 4th order Bézier? |
Date: |
Mon, 19 Sep 2016 00:32:56 +0200 |
User-agent: |
Gnus/5.13 (Gnus v5.13) Emacs/25.1.50 (gnu/linux) |
Urs Liska <address@hidden> writes:
> Am 18.09.2016 um 20:54 schrieb David Kastrup:
>>
>> Do you know how to split a bezier at a given ratio into equivalent
>> beziers? It's a comparatively simple operation and I think it's already
>> somewhere in the C++ code though without access from Scheme.
>
> No, but I should be able to figure it out (if noone sends a pointer
> before I manage to do so).
Well, METAFONT uses the notation
a[z1, z2]
for z1 + a*[z2-z1], mapping a range of 0..1 for a linearly between z1
and z2.
If we have points z1, z2, z3, z4 defining a Bezier, then the two split
beziers are defined with the points
z1, a[z1, z2], a[a[z1, z2], a[z2, z3]], a[a[a[z1, z2], a[z2, z3]],
a[a[z2, z3], a[z3, z4]]
and
a[a[a[z1, z2], a[z2, z3]], a[a[z2, z3], a[z3, z4]]],
a[a[z2, z3], a[z3, z4]], a[z3, z4], z4
Basically, calculation of a point a on an n-grade Bezier is done using a
recursive formula to depth n, and keeping the intermediate results will
give you the control points for the Bezier curves split at that point.
--
David Kastrup
- Re: What to do wanting a 4th order Bézier?, (continued)
- 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, 2016/09/18
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 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?, 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?, David Kastrup, 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?, David Kastrup, 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?,
David Kastrup <=
- 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?, David Kastrup, 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?, Urs Liska, 2016/09/19
- Re: What to do wanting a 4th order Bézier?, Simon Albrecht, 2016/09/20
- Re: What to do wanting a 4th order Bézier?, Trevor Daniels, 2016/09/20
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/20
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/21
- Re: What to do wanting a 4th order Bézier?, Urs Liska, 2016/09/21