\version "2.19.57"

\paper {
    indent = 0
}

#(define draw-nc-position #f)
#(define draw-starter-border #t)
#(define draw-x-offset-ref #t)
#(define draw-accs-box #t)
#(define draw-intended-space #f)
#(define draw-clef-acc-dist #f)

#(define assumed-padding 2)
#(define intended-space 4)

#(set-object-property! 'seen 'backend-type? boolean?)

#(define (distance-info tie)
   (let*
    (;; our helper grobs
      (sys (ly:grob-system tie))
      (left-nh (ly:grob-parent tie X))
      (nc (ly:grob-parent left-nh Y))
      ; NOTE: For simplicity we don't handle missing accidentals
      (accs (ly:note-column-accidentals nc)))
    (if (not (ly:grob-property nc 'seen))
        (let*
         ;;;; some lengths and props
         ((acc-x-extent (ly:grob-property accs 'X-extent))
          (acc-width (- (cdr acc-x-extent) (car acc-x-extent)))
          (left-acc-x-extent (car acc-x-extent))
          ;; first NonMusicalPaperColumn, includes clef, key and timesignature
          (staff-starter (first (ly:grob-array->list (ly:grob-object sys 'elements)))) 
          (staff-starter-width
           (let ((ext (ly:grob-property
                       staff-starter
                       'X-extent)))
             (- (cdr ext) (car ext))))
          (staff-starter-x-pos (ly:grob-relative-coordinate staff-starter sys X))
          ;; position of note column, relative to system (blue vertical line)
          (nc-x-pos (ly:grob-relative-coordinate nc sys X))
          (nc-x-offset
           (let ((off (ly:grob-property nc 'X-offset)))
             (if (null? off) 0 off)))
          
          (nc-acc-dist (- nc-x-offset left-acc-x-extent))

          ;(staff-starter-nc-dist (- nc-x-pos staff-starter-width))

          (clef-acc-dist (- nc-x-pos staff-starter-width nc-acc-dist))
          
          (missing-length
           (let ((mw (- intended-space clef-acc-dist)))
             (if (> mw 0) mw #f)))
          
          (to-offset 
           (+ 
            nc-acc-dist
            intended-space 
            (* -1 assumed-padding)))
          )
         ;        (ly:message "\nNote column X position: ~a" nc-x-pos)
         ;        (ly:message "Accidentals X position: ~a" acc-x-pos)
         ;        (ly:message "Width of staff starters: ~a" staff-starter-width)
         ;        (ly:message "Space between clef and notes: ~a" staff-starter-nc-dist)
         ;        (ly:message "Accidentals Width: ~a" acc-x-extent)
         ;        (ly:message "nc-acc-dist: ~a" nc-acc-dist)

         (ly:message "\n")
         (ly:message "Staff start padding: ~a" (ly:grob-property staff-starter 'padding))
         (if missing-length
             (ly:message "missing space: ~a" missing-length))
         (ly:message "Set X-offset to ~a\n\n" to-offset)
        
         (ly:grob-set-property! nc 'seen #t)

         (ly:stencil-add

          ;; the space we want to have
          (if draw-intended-space
              (ly:stencil-translate
               (stencil-with-color
                (ly:make-stencil
                 `(path 0.1
                    `(moveto 0 -3 rlineto 0 6 rlineto ,,intended-space 0 rlineto 0 -6 rlineto -4 0)))
                red)
               (cons
                (- staff-starter-width nc-x-pos)
                0))
              empty-stencil)

          ;; where is the "origin" of the note column?
          (if draw-nc-position
              (stencil-with-color
               (ly:make-stencil `(path 0.1 `(moveto 0 -3 rlineto 0 6))) blue)
              empty-stencil)
         
          (if draw-starter-border
              (ly:stencil-translate
               (stencil-with-color
                (ly:make-stencil
                 `(path 0.1
                    `(moveto 0 -3.5
                       rlineto 0 7)))
                blue)
               (cons
                (+
                 staff-starter-x-pos
                 (- staff-starter-width nc-x-pos))
                0))
              empty-stencil)
         
          (if draw-x-offset-ref
              (ly:stencil-translate
               (stencil-with-color
                (ly:make-stencil
                 `(path 0.1
                    `(moveto 0 -4.5
                       rlineto 0 9)))
                magenta)
               (cons
                (* -1 nc-x-offset)
                0))
              empty-stencil)
         
          ;; origin and extent of accidentals
          (if draw-accs-box
              (ly:stencil-translate
               (stencil-with-color
                (ly:make-stencil
                 `(path 0.1
                    `(moveto ,,(car acc-x-extent) -2.5
                       rlineto 0 5
                       rlineto ,,acc-width 0
                       rlineto 0 -5
                       rlineto ,,(* -1 acc-width) 0
                       )))
                magenta)
               (cons
                (* -1 nc-x-offset)
                0))
              empty-stencil)

          ;; Available distance between clef and accidentals
          (if draw-clef-acc-dist
              (ly:stencil-translate
               (stencil-with-color
                (ly:make-stencil
                 `(path 0.2
                    `(moveto 0 1 rlineto 0 -2 moveto 0 0
                       rlineto ,,clef-acc-dist 0 rmoveto 0 1 rlineto 0 -2)))
                green)
               (cons
                (- staff-starter-width nc-x-pos)
                0))
              empty-stencil)

          (ly:tie::print tie)
          ))

        (ly:tie::print tie)
        )))

music = { <c' eis' gis' ais' cis''>1 ~ q }

\markup "Default result (no X-offset):"

{  
  \music
}

\markup "X-offset: 2"

{  
  \once \override NoteColumn.X-offset = 2
  \music
}

\markup "X-offset: 3"

{  
  \once \override NoteColumn.X-offset = 3
  \music
}

\markup "X-offset: 4"

{  
  \once \override NoteColumn.X-offset = 4
  \music
}

\markup "X-offset: 4.875"

{  
  \once \override NoteColumn.X-offset = 4.875
  \music
}

\markup "X-offset: 5.875"

{  
  \once \override NoteColumn.X-offset = 5.875
  \music
}

\markup "Intended result:"
\markup #(format "X-offset: ~a" 6.875)

{  
  \once \override NoteColumn.X-offset = 6.875
  \music
}

\markup "Default spacing without accidentals"

{
  <c' e' g' c''>1
}

\layout {
  \context {
    \Score
    \override Tie.stencil = #distance-info
    \override NoteColumn.seen = ##f
  }
  \context {
    \Score
  }
}