Calculate BarLine 'kern to fit with a given stencil-x-extent

[Thomas Morley]

Hi,

for some custom-function I need to know how to calculate the 'kern of
a BarLine from a given stencil-x-extent, so that their visual
length/amont is equal.

As a test-case I constructed a draw-line-markup, which should fit
between the two lines of \bar "||"


\version "2.17.21"

\paper { ragged-right = ##f }

% Better viewing
\layout {
        \override Score.RehearsalMark #'color = #red
        \override Score.RehearsalMark #'layer = #10
        \override Score.RehearsalMark #'extra-offset = #'(0 . -2.5)
}

{
        R1
        %%{
        \mark \markup \draw-line #'(1 . 0)
        \override Staff.BarLine.kern = #9.7
        %}
        %{
        \mark \markup \draw-line #'(2 . 0)
        \override Staff.BarLine.kern = #18.3
        %}
        %{
        \mark \markup \draw-line #'(10 . 0)
        \override Staff.BarLine.kern = #87
        \bar "||"
        %}
        %{
        \mark \markup \draw-line #'(20 . 0)
        \override Staff.BarLine.kern = #173
        %}
        \bar "||"
        R1
}

As you can see
a line with x-length  1 leads to a 'kern of   9.7
a line with x-length  2 leads to a 'kern of  18.3
a line with x-length 10 leads to a 'kern of  87
a line with x-length 29 leads to a 'kern of 173

I failed to detect a correct calculation-method.
Is it a matter of units?
Or perhaps I'm missing some factors.

How to  do?
Any help would be appreciated.

Cheers,
  Harm