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

[David Kastrup]

Simon Albrecht <address@hidden> writes:

> May I incorporate that into the LSR version?
>
>
> On 18.09.2016 16:04, Urs Liska wrote:
>>
>> Am 18.09.2016 um 16:01 schrieb Urs Liska:
>>>                            (cps (ly:slur::calc-control-points grob))
>>>                            (cps1 (first contr-pts))
>>>                            (cps2 (second contr-pts))
>>>                            (cp2-2 (mirror-point (fourth cps1) (third cps1)))
>>>                            (cps2 `(,(fourth cps1) ,cp2-2 ,@cps2))
>> This should actually read
>>
>>                            (cps (ly:slur::calc-control-points grob))
>>                            (cps1 (first contr-pts))
>>                            (cp2-2 (mirror-point (fourth cps1) (third cps1)))
>>                            (cps2 `(,(fourth cps1) ,cp2-2 ,@(second
>> contr-pts)))

I think this may actually be overdoing the symmetry since it forces the
control points around the inflection point to not just have the same
tangent but also the same distance (resulting, if I judge correctly, in
the same curvature).  That is actually providing more continuity than
warranted: the whole point of having multiple slur pieces is that a
single consistent bezier is not enough to reflect the problem space.

So maybe it would be warranted to express the usefully available degrees
of freedom differently than by control points?

-- 
David Kastrup