Thomas Morley <thomasmorle...@gmail.com> writes: > Am Mi., 17. Apr. 2019 um 21:30 Uhr schrieb David Kastrup <d...@gnu.org>: >> >> Thomas Morley <thomasmorle...@gmail.com> 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 _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
