Re: programming error for thickness/control-points of Slur

[Thomas Morley]

Am Fr., 27. Mai 2022 um 14:59 Uhr schrieb Jean Abou Samra <jean@abou-samra.fr>:
>
>
>
> Le 27/05/2022 à 13:28, Thomas Morley a écrit :
> > I decided to go for a better approximation of the bow-length, but
> > dropped some comments what to do, if execution time gets worse.
> > https://lsr.di.unimi.it/LSR/Item?u=1&id=1028
>
> Here's an experiment:
>
> \version "2.23.9"
>
> #(define (bezier-curve control-points t)
> "Given a Bezier curve of arbitrary degree specified by @var{control-points},
> compute the point at the specified position @var{t}."
>    (if (< 1 (length control-points))
>        (let ((q0 (bezier-curve (drop-right control-points 1) t))
>              (q1 (bezier-curve (drop control-points 1) t)))
>          (cons
>            (+ (* (car q0) (- 1 t)) (* (car q1) t))
>            (+ (* (cdr q0) (- 1 t)) (* (cdr q1) t))))
>        (car control-points)))
>
> #(define (bezier-approx-length control-points from to steps)
> "Given a Bezier curve of arbitrary degree specified by @var{control-points},
> compute its approximate arc length between the positions @var{from} and
> @var{to}."
>    (let* ((params (iota steps from (/ (- to from) (1- steps))))
>           (points (map (lambda (x) (bezier-curve control-points x)) params))
>           (length
>             (fold
>               (lambda (a b prev)
>                 (+ prev (ly:length (- (car a) (car b)) (- (cdr a) (cdr
> b)))))
>               0
>               (drop points 1)
>               (drop-right points 1))))
>      ; Need to support negative length when the range is inverted.
>      (if (< from to) length (- length))))
>
>
> #(let ((bezier '((0 . 0) (1 . 1) (2 . 1) (3 . 0))))
>     (for-each
>      (lambda (n)
>        (ly:message "bezier-approx-length with ~a segments: ~a"
>                    n
>                    (bezier-approx-length bezier 0 1 n)))
>      '(10 50 100 500 1000 5000 10000)))
>
>
> =>
>
>
> bezier-approx-length with 10 segments: 3.439011160316537
>
> bezier-approx-length with 50 segments: 3.44323346616539
>
> bezier-approx-length with 100 segments: 3.4433446505712593
>
> bezier-approx-length with 500 segments: 3.4433793042010272
>
> bezier-approx-length with 1000 segments: 3.443380369827364
>
> bezier-approx-length with 5000 segments: 3.4433807099411706
>
> bezier-approx-length with 10000 segments: 3.443380720552721
>
> I don't think doing many iterations is worth it here.
>

Using your test-code I did own experiments with more crazy
control-points like '((17 . 0) (8 . 10) (22 . 10) (13 . 0)).
While I got differences up to ~0.15, those beziers will not occur in
real music, afact.
Thus I'll reduce the steps in said snippt to 10, usually very nice already.

Thanks,
  Harm