Tweak beam slashes for small staves

[Edward Neeman]

Hello,

This snippet produces very nice slashed grace note beams: 
http://lsr.di.unimi.it/LSR/Snippet?id=721

However the slashes don’t adjust properly for smaller staves that are tweaked 
with the \magnifyStaff function. In the example below, the slash on the second 
(smaller) staff is too high and too long. How might I change the function to 
accommodate the \magnifyStaff value?

Thanks,
Edward

\version "2.19.80"

slash =
#(define-music-function (ang stem-fraction protrusion)
   (number? number? number?)
   (remove-grace-property 'Voice 'Stem 'direction) ; necessary?
   #{
     \once \override Stem #'stencil =
     #(lambda (grob)
       (let* ((X-parent (ly:grob-parent grob X))
              (is-rest? (ly:grob? (ly:grob-object X-parent 'rest))))
         (if is-rest?
             empty-stencil
             (let* ((ang (degrees->radians ang))
                    ; We need the beam and its slope so that slash will
                    ; extend uniformly past the stem and the beam
                    (beam (ly:grob-object grob 'beam))
                    (beam-X-pos (ly:grob-property beam 'X-positions))
                    (beam-Y-pos (ly:grob-property beam 'positions))
                    (beam-slope (/ (- (cdr beam-Y-pos) (car beam-Y-pos))
                                   (- (cdr beam-X-pos) (car beam-X-pos))))
                    (beam-angle (atan beam-slope))
                    (stem-Y-ext (ly:grob-extent grob grob Y))
                    ; Stem.length is expressed in half staff-spaces
                    (stem-length (/ (ly:grob-property grob 'length) 2.0))
                    (dir (ly:grob-property grob 'direction))
                    ; if stem points up. car represents segment of stem
                    ; closest to notehead; if down, cdr does
                    (stem-ref (if (= dir 1) (car stem-Y-ext) (cdr stem-Y-ext)))
                    (stem-segment (* stem-length stem-fraction))
                    ; Where does slash cross the stem?
                    (slash-stem-Y (+ stem-ref (* dir stem-segment)))
                    ; These are values for the portion of the slash that
                    ; intersects the beamed group.
                    (dx (/ (- stem-length stem-segment)
                           (- (tan ang) (* dir beam-slope))))
                    (dy (* (tan ang) dx))
                    ; Now, we add in the wings
                    (protrusion-dx (* (cos ang) protrusion))
                    (protrusion-dy (* (sin ang) protrusion))
                    (x1 (- protrusion-dx))
                    (y1 (- slash-stem-Y (* dir protrusion-dy)))
                    (x2 (+ dx protrusion-dx))
                    (y2 (+ slash-stem-Y
                           (* dir (+ dy protrusion-dy))))
                    (th (ly:staff-symbol-line-thickness grob))
                    (stil (ly:stem::print grob)))

              (ly:stencil-add
                stil
                (make-line-stencil th x1 y1 x2 y2))))))
   #})

slashI = {
  \slash 50 0.6 1.0
}

  <<
   \new Staff { \grace { \slashI b''8[ c'''] } c'' }
   \new Staff \with { \magnifyStaff #2/3 } { \grace { \slashI b''8[ c'''] } c'' 
}
  >>

---
Dr. Edward Neeman
www.neemanpianoduo.com