I can only respond with a quote from the ImageMagick manual:
"It is not recommended that you use more or less than 4 points per
'bezier' curve segment, to keep things simple."

On Thu, 17 Sep 2020 at 15:00, Marc Nieper-Wißkirchen
<xxxxxx@nieper-wisskirchen.de> wrote:
>
> A Bézier curve is defined through its control *points*. Don't call
> them vectors, please. The canvas is an affine space (with a Euclidean
> metric), not a vector space.
>
> Two points shall yield a linear curve, which is perfectly valid.
> Three points shall yield a quadratic curve.
> Four points shall yield a cubic curve.
>
> I don't understand why the N >= 5 point case is discouraged? There is
> a well-defined notion of a Bézier curve of degree N - 1.
>
> Marc
>
> Am Do., 17. Sept. 2020 um 08:04 Uhr schrieb Vladimir Nikishkin
> <xxxxxx@gmail.com>:
> >
> > >which it isn't--(draw-bezier vec1 vec2) is a valid call)
> >
> > It is required, or at least I meant it to be required. For simple
> > straight lines, (draw-line) is a reasonable choice.
> > I think Bezier curves can be reduced to straight lines in the
> > two-point case, but I am not exactly sure of the math.
> > So at least three points, two knots and a control point are required.
> > Moreover, adding additional points (as in 5 arguments) does not turn a
> > cubic Bezier into a quartic Bezier in the sample implementation, but
> > does some evil image-magick trickery (ImageMagick explicitly warns
> > against using 5 points).
> >
> > >(draw-bezier vec1 vecI ... vecN)
> >
> > I wanted to use an ellipsis, but ellipsis seems to have some special
> > meaning in Scheme (at least in the macro definitions), which I am not
> > as familiar as I should be. If it is fine, I will replace the bracket
> > notation with the ellipsis.
> > The brackets I took from man pages, where it usually denotes
> > "optional", and the asterisk means "0 or more times" almost
> > everywhere.
> >
> > On Thu, 17 Sep 2020 at 13:49, Wolfgang Corcoran-Mathe <xxxxxx@sigwinch.xyz> wrote:
> > >
> > > On 2020-09-17 12:00 +0800, Vladimir Nikishkin wrote:
> > > > Is it fine to use the [vecI]* notation, or there is a more common one in Scheme?
> > >
> > > The [vecI]* notation is unfamiliar to me.  Is it used in other SRFIs,
> > > or elsewhere?
> > >
> > > The new version,
> > >
> > >     (draw-bezier vec1 vec2 [vecI]* vecN),
> > >
> > > seems a little misleading, since vecN appears to be required (which it
> > > isn't--(draw-bezier vec1 vec2) is a valid call).  If the double-bracket
> > > version mentioned earlier seems ugly, I recommend:
> > >
> > >     (draw-bezier vec1 vecI ... vecN)
> > >
> > > --
> > > Wolfgang Corcoran-Mathe  <xxxxxx@sigwinch.xyz>
> > >
> > > "A LISP programmer knows the value of everything, but the cost
> > > of nothing." --Alan J. Perlis
> >
> >
> >
> > --
> > Yours sincerely, Vladimir Nikishkin

--
Yours sincerely, Vladimir Nikishkin