Hi Harm,

I think I've got it...

You are perfectly right, there is a slight inconsistency in
lily/stencil-integral.cc
C++ code.
(I just have to get it completely right, still experimenting a bit...):

The C++ code obviously confuses line thickness and blot diameter and and
"corrects" (i.e. enlarges) the frame by half the line thickness (in reality:
half the corner-radius).
I'll have to check the complete chain of calls of calls of calls, but when
simply removing the extra shift of the cornering points p0 (left, bottom)
and p1 (right, top), that's what comes out using our original example (with
TextScript.outside-staff-padding set to 0):

{
  \override TextScript #'outside-staff-padding = 0
  f''2^\markup \box "1" ^\markup \box "2"
  f''2^\markup \rounded-box "1" ^\markup \rounded-box "2"
}

<http://lilypond.1069038.n5.nabble.com/file/t3887/rounded-box-2.png> 

All the best,
Torsten





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