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Re: Slur with left and/or right arrow head


From: David Kastrup
Subject: Re: Slur with left and/or right arrow head
Date: Wed, 17 Apr 2019 21:52:37 +0200
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/27.0.50 (gnu/linux)

Thomas Morley <address@hidden> writes:

> 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

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.

>> 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.

-- 
David Kastrup



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