\version "2.19.25"

#(define (lyric-text::interpolate-alignment grob)
   "Calculates values for 'self-alignment-X using the width = X-extent of the syllable. Values are zero up to @var{lower-threshold}, @var{maximum} above @{upper-threshold}, with a smooth interpolation inbetween."
   (let*
    ((width (cdr (ly:grob-property grob 'X-extent)))

     (lower-threshold 3)
     (upper-threshold 11)
     (maximum (- 4/5))
     
     ;; calculate parameters for use in the ‘sigmoid’ cubic function with
     ;; (sigmoid lower-threshold) --> 0
     ;; (sigmoid upper-threshold) --> maximum
     ;; and zero ‘slope’ in both these points
     
     (a (/ (* 2 maximum)
          (+ (- (expt upper-threshold 3))
            (* 3 upper-threshold upper-threshold lower-threshold)
            (* -3 upper-threshold lower-threshold lower-threshold)
            (expt lower-threshold 3))))
     (b (/ (- maximum (* a (+ (expt upper-threshold 3)
                             (* 2 (expt lower-threshold 3))
                             (* -3 upper-threshold (expt lower-threshold 2)))))
          (expt (- upper-threshold lower-threshold) 2)))
     (c (/ (- maximum
              (* b (- (expt upper-threshold 2) (expt lower-threshold 2)))
              (* a (- (expt upper-threshold 3) (expt lower-threshold 3))))
           (- upper-threshold lower-threshold)))
     (d (- maximum
          (* upper-threshold c)
          (* (expt upper-threshold 2) b)
          (* (expt upper-threshold 3) a)))

     (sigmoid (lambda (x) (+ (* a x x x) (* b x x) (* c x) d))))

    ;(format #t "The four parameters have been determined as: \n a ~a \n b ~a \n c ~a \n d ~a\n" a b c d)

    (cond
     ((<= width lower-threshold) 0)
     ((< lower-threshold width upper-threshold)
      (sigmoid width))
     ((>= width upper-threshold) maximum))))

\layout {
  \context {
    \Lyrics
    \override LyricText.self-alignment-X = #lyric-text::interpolate-alignment
    \override LyricText.before-line-breaking =
    #(lambda (grob)
       (let
        ((extent (ly:grob-property grob 'X-extent))
         (txt (ly:grob-property grob 'text)))
        (format #t "For ~a, X-extent is ~a\n" txt extent)))
  }
}

<<
  {
    \repeat unfold 8 g'8\noBeam
  }
  \addlyrics {
    llll lllll llllll lllllll llllllll lllllllll llllllllll llllllllllll
  }
>>