Sorry, Nathan. I will try to make my point clearer. 

*Firstly*, I got the code developed earlier in this thread and altered the
numbers of handles of path-gliss to four -- the original version came with
the values (list 'curveto 0 0 (first handle) (second handle)).

Here's my version of the code:

\version "2.18.2"

glissWidth = #0.175 %<< global variable for glissando width

#(define (path-gliss handle)
  (lambda (grob)
    (if (ly:stencil? (ly:line-spanner::print grob))
        (let* ((stencil (ly:line-spanner::print grob))
              (X-ext (ly:stencil-extent stencil X))
              (Y-ext (ly:stencil-extent stencil Y))
              (width (interval-length X-ext))
              (height (interval-length Y-ext))
              (lefty (cdr (assoc 'Y (ly:grob-property grob 'left-bound-info))))
              (righty (cdr (assoc 'Y (ly:grob-property grob 
'right-bound-info))))
              (deltay (- righty lefty))
              (dir (if (> deltay 0) 1 -1))
              
             
              
              )


          (ly:stencil-translate
            (grob-interpret-markup grob
              (markup
                    ;(#: tiny (format "~a" (ly:grob-properties grob)))
                            ;(format "~a" (cdr (assoc 'Y (ly:grob-property grob
'left-bound-info))))
                            ;(#: tiny (format "~a" handle))
                (#:path glissWidth
                  (list (list 'moveto 0 0)
                        (list 'curveto (first handle) (second handle) (third 
handle) (fourth
handle) width (* height dir)))))) 
            
            (if (> dir 0)
                   (cons (interval-start X-ext) (+ (interval-start Y-ext) 0.1))
                   (cons (interval-start X-ext) (+ (interval-start Y-ext) 
height)))))#f)))


#(define (add-gliss m)
   (case (ly:music-property m 'name)
     ((NoteEvent) (set! (ly:music-property m 'articulations)
                      (append (ly:music-property m 'articulations)
                         (list (make-music (quote GlissandoEvent)))))
                   m)
     (else #f)))

addGliss = #(define-music-function (parser location music)
                 (ly:music?)
           (map-some-music add-gliss music))


\relative c' {
  \numericTimeSignature
  \tempo 4=52
\override NoteHead.font-size = #-1.5

$(add-grace-property 'Voice 'NoteHead 'font-size -4.5)


\time 5/8 
  
   
   \override Score.GraceSpacing.spacing-increment = #7
   
       \once \override Glissando #'bound-details = 
                         #'((right (attach-dir . -2) (end-on-accidental .
#f) (padding . 1)) 
                            (left (attach-dir . 0) (padding . 0.)))  
       
       \addGliss {
       \once \override Glissando #'stencil = #(path-gliss '(7 1 0 4))
   \grace b16
   a''4.~->} 
   \tuplet 5/4 { a16 gis fis, e'-> a,~ } 
  
\time 3/8                                                   
 
}

With that, i am able to get that (missing only the arrowhead to get what I
want):

<http://lilypond.1069038.n5.nabble.com/file/n177488/example1.png> 

---

Then, I got your useful version and was able to get that:

\version "2.18.2"


arc = #(list 0 0) %<< global variable to bezier curve handle 
glissWidth = #0.2 %<< global variable for glissando width 

#(define (set-arc x y) 
        (set! arc (list x y))) 

#(define (get-arc) 
        arc) 

#(define (radians->degrees theta)
   (* theta (/ 180 PI)))

#(define (path-gliss grob) 
                  
        (if (ly:stencil? (ly:line-spanner::print grob)) 
    (let* ((stencil (ly:line-spanner::print grob)) 
                        (X-ext (ly:stencil-extent stencil X)) 
            (Y-ext (ly:stencil-extent stencil Y)) 
            (width (interval-length X-ext)) 
            (height (interval-length Y-ext)) 
            (lefty (cdr (assoc 'Y (ly:grob-property grob
'left-bound-info))))    
                (righty (cdr (assoc 'Y (ly:grob-property grob
'right-bound-info)))) 
                        (deltay (- righty lefty)) 
                        (dir (if (> deltay 0) 1 -1)) 
                        (handle (get-arc))) ;<<------------- getting the
handle value here       
                                
       (ly:stencil-translate
         (ly:stencil-add
           (grob-interpret-markup grob 
             (markup 
                 ;(#: tiny (format "~a" (ly:grob-properties grob))) 
                 ;(format "~a" (cdr (assoc 'Y (ly:grob-property grob
'left-bound-info)))) 
                           ;(#: tiny (format "~a" handle))
               (#:path glissWidth 
                 (list (list 'moveto 0 0) 
                                           (list 'curveto 0 0 (first handle)
(second handle) width (* height dir))))))
           (ly:stencil-translate
             ; the \rotate markup command doesn't let us pick a rotation
center, so we resort to the stencil command
             (ly:stencil-rotate
               (grob-interpret-markup grob
                 (markup #:arrow-head X RIGHT #t))
               (radians->degrees
                 ($atan2
                   (- (* height dir) (second handle))
                   (- width (first handle)))) 1 0)
             (cons width (* height dir))))
         (if (> dir 0) 
                (cons (interval-start X-ext) (+ (interval-start Y-ext) 0.1)) 
                (cons (interval-start X-ext) (+ (interval-start Y-ext) 
height))))) 
      #f))


\relative c' {
  \numericTimeSignature
  \tempo 4=52
\override NoteHead.font-size = #-1.5

$(add-grace-property 'Voice 'NoteHead 'font-size -4.5)


\time 5/8 
  
   
   \override Score.GraceSpacing.spacing-increment = #7
   
        \once \override Glissando #'bound-details = 
        #'((right (attach-dir . 0) (end-on-accidental . #f) (padding . 2.)) 
           (left (attach-dir . 1) (padding . 0.))) 
        
        \once \override Glissando #'stencil = #path-gliss 
        
        #(set-arc 0 -4)
   
   \grace b16\glissando
   a''4.~->
   \tuplet 5/4 { a16 gis fis, e'-> a,~ } 
  
\time 3/8                                                   
 
}

<http://lilypond.1069038.n5.nabble.com/file/n177488/example2.png> 

...which is very ok! But I would like (probably in other points of the score
I am working on) to have more flexibility to draw the four variables of the
curveto list, as I had with the arrowhead-less solution. 

This let me to try making similar changes I did in the first version of the
code, adding third and fourth handles to the curveto list and deleting the
double zero of that line:

\version "2.18.2"


arc = #(list 0 0) %<< global variable to bezier curve handle 
glissWidth = #0.2 %<< global variable for glissando width 

#(define (set-arc x y) 
        (set! arc (list x y))) 

#(define (get-arc) 
        arc) 

#(define (radians->degrees theta)
   (* theta (/ 180 PI)))

#(define (path-gliss grob) 
                  
        (if (ly:stencil? (ly:line-spanner::print grob)) 
    (let* ((stencil (ly:line-spanner::print grob)) 
                        (X-ext (ly:stencil-extent stencil X)) 
            (Y-ext (ly:stencil-extent stencil Y)) 
            (width (interval-length X-ext)) 
            (height (interval-length Y-ext)) 
            (lefty (cdr (assoc 'Y (ly:grob-property grob
'left-bound-info))))    
                (righty (cdr (assoc 'Y (ly:grob-property grob
'right-bound-info)))) 
                        (deltay (- righty lefty)) 
                        (dir (if (> deltay 0) 1 -1)) 
                        (handle (get-arc))) ;<<------------- getting the
handle value here       
                                
       (ly:stencil-translate
         (ly:stencil-add
           (grob-interpret-markup grob 
             (markup 
                 ;(#: tiny (format "~a" (ly:grob-properties grob))) 
                 ;(format "~a" (cdr (assoc 'Y (ly:grob-property grob
'left-bound-info)))) 
                           ;(#: tiny (format "~a" handle))
               (#:path glissWidth 
                 (list (list 'moveto 0 0) 
                                           (list 'curveto (first handle)
(second handle) (third handle) (fourth handle) width (* height dir))))))
           (ly:stencil-translate
             ; the \rotate markup command doesn't let us pick a rotation
center, so we resort to the stencil command
             (ly:stencil-rotate
               (grob-interpret-markup grob
                 (markup #:arrow-head X RIGHT #t))
               (radians->degrees
                 ($atan2
                   (- (* height dir) (fourth handle))
                   (- width (third handle)))) 1 0)
             (cons width (* height dir))))
         (if (> dir 0) 
                (cons (interval-start X-ext) (+ (interval-start Y-ext) 0.1)) 
                (cons (interval-start X-ext) (+ (interval-start Y-ext) 
height))))) 
      #f))


\relative c' {
  \numericTimeSignature
  \tempo 4=52
\override NoteHead.font-size = #-1.5

$(add-grace-property 'Voice 'NoteHead 'font-size -4.5)


\time 5/8 
  
   
   \override Score.GraceSpacing.spacing-increment = #7
   
        \once \override Glissando #'bound-details = 
        #'((right (attach-dir . 0) (end-on-accidental . #f) (padding . 2.)) 
           (left (attach-dir . 1) (padding . 0.))) 
        
        \once \override Glissando #'stencil = #path-gliss 
        
        #(set-arc 7 1 0 -4)
   
   \grace b16\glissando
   a''4.~->
   \tuplet 5/4 { a16 gis fis, e'-> a,~ } 
  
\time 3/8                                                   
 
}

This gave me the Error Log copied below:

*
Starting lilypond 2.18.2 [Untitled (2)]...*
Processing
`/var/folders/93/2hc4wy_x7ygf7rb7q181xfgm0000gn/T/frescobaldi-4di9Vd/tmpcv2O7y/document.ly'
Parsing...
/var/folders/93/2hc4wy_x7ygf7rb7q181xfgm0000gn/T/frescobaldi-4di9Vd/tmpcv2O7y/document.ly:75:10:
error: GUILE signaled an error for the expression beginning here
        #
         (set-arc 7 1 0 -4)
Interpreting music...
Preprocessing graphical objects...
Finding the ideal number of pages...
Fitting music on 1 page...
Drawing systems...Wrong number of arguments to #<procedure set-arc (x y)>
/var/folders/93/2hc4wy_x7ygf7rb7q181xfgm0000gn/T/frescobaldi-4di9Vd/tmpcv2O7y/document.ly:39:90:
In procedure caddr in expression (third handle):
/var/folders/93/2hc4wy_x7ygf7rb7q181xfgm0000gn/T/frescobaldi-4di9Vd/tmpcv2O7y/document.ly:39:90:
Wrong type (expecting pair): ()
*Exited with return code 1.*

It's clear for me that the  







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