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

[Jean Abou Samra]

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.