Re: Slur with left and/or right arrow head

[Thomas Morley]

Am Mi., 17. Apr. 2019 um 21:30 Uhr schrieb David Kastrup <address@hidden>:
>
> Thomas Morley <address@hidden> writes:
>
> > Hi Aaron,
> >
> > thanks a lot for this.
> > I was aware of not going for the bezier-curve itself, but only for the
> > control-points was a raw approximation.
> > Yours is far better.
> > Mostly I did so for reasons of lacking knowledge of beziers, both the
> > math and how to compute them.
> > Now there is a fine tool-set available, many thanks again.
> > I tried to understand what you coded (not finished yet), but while
> > playing around with code I always think making it visible will help.
> > Thus the attached file and image.
> > One question I really couldn't answer is:
> > What kind of value is `t´ in (define (bezier-angle control-points t) ...)
> > Seems not to be a x- or y-value, not an arc-length-value .., but what
> > else?
>
> "time".

Well, actually I read that in some papers trying to explain beziers, already.
But what means "time"?
I'm arranging pixels on a screen, or tell a printer what to print
where or draw points and lines with a pencil on a sheet of paper.
This may be "time"-consuming lol
But what does "time" means here in the mathematical sense, this part I
didn't get yet.

> For t=0, you get the starting point, for t=1 you get the end
> point.  For values in between, you get points in between.  The starting
> direction is from starting point (control point 0) to control point 1
> (which is not usually touched at all).  Similarly the ending direction
> is from control point 2 to the end point (control point 3).

I think (hope) I understand this part.

Thanks,
  Harm