Re: Slur with left and/or right arrow head

[Thomas Morley]

Am Mi., 17. Apr. 2019 um 21:52 Uhr schrieb David Kastrup <address@hidden>:
>
> Thomas Morley <address@hidden> writes:
>
> > Am Mi., 17. Apr. 2019 um 21:30 Uhr schrieb David Kastrup <address@hidden>:
> >>
> >> Thomas Morley <address@hidden> writes:

> >> > 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
>
> Lol to you: it's the drawing time of drawing the curve, so yes, this is
> exactly the meaning assigned to t.  It is normalised from 0 to 1 instead
> of measuring it in pencil-seconds.
>
> > But what does "time" means here in the mathematical sense, this part I
> > didn't get yet.
>
> How far you have progressed with drawing the curve.

Well, as already said, making things visible may help.
If I look at the dotted bezier of my recently posted pdf (the dots are
made by splitting t from 0 to 1 in sixty pieces) then it seems drawing
more or less straight lines takes less effort, i.e. is less
time-consuming than to draw curves, more steeper curves means more
work, i.e. more time.

Though, I'm used to think of mathematical functions assigning one
x-value to one (or more) y-values, at least if we keep thinking in two
dimensions.
Thus I still have problems to accept this thinking.

Thanks,
  Harm