How does pdf export compute the size of the bounding box of Inset?

Question

It does not seem to be using Rasterize[Text[...], "RasterSize"] nor ImageDimensions[ImageCrop[Graphics[Text[...]]]] nor Rasterize[Text[...], "BoundingBox"] (and indeed seems to do the computation differently than png export, which leads me to suspect this might be a bug).

Consider

Rasterize[p1 = With[{nmax = 10},
   Graphics[
    Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]}, 
      Inset[Text[v], 
       Offset[ImageDimensions[ImageCrop[Graphics[Text[v]]]]/2 + {3, 
          0}, {0, n/nmax}], {0, 0}]], {n, 1, nmax}]
    ]]]
Rasterize[p2 = With[{nmax = 10},
   Graphics[
    Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]}, 
      Inset[Text[v], 
       Offset[Rasterize[Text[v], "RasterSize"]/2 + {3, 0}, {0, 
         n/nmax}], {0, 0}]], {n, 1, nmax}]
    ]]]
Rasterize[p3 = With[{nmax = 10},
   Graphics[
    Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]}, 
      Inset[Text[v], 
       Offset[Rasterize[Text[v], "BoundingBox"][[1 ;; 2]]/2 + {3, 
          0}, {0, n/nmax}], {0, 0}]], {n, 1, nmax}]
    ]]]
Export[FileNameJoin[{NotebookDirectory[], "foop1.pdf"}], p1]
Export[FileNameJoin[{NotebookDirectory[], "foop2.pdf"}], p2]
Export[FileNameJoin[{NotebookDirectory[], "foop3.pdf"}], p3]

In Mathematica, only the first one is correctly aligned:

p2 looks like this:

And p3 is similar but not identical. However, when I export to pdf, foop1.pdf looks like this (screenshot):

and foop2.pdf and foop3.pdf look similar. What's going on?

Answer 1

I don't think you're using Inset properly. Look at the documentation:

?Inset

(*
Inset[obj] represents an object obj inset in a graphic. 
Inset[obj,pos] specifies that the inset should be placed at position pos in the graphic. 
Inset[obj,pos,opos] aligns the inset so that position opos in the object lies at position pos in the enclosing graphic. 
Inset[obj,pos,opos,size] specifies the size of the inset in the coordinate system of the enclosing graphic. 
Inset[obj,pos,opos,size,dirs] specifies that the axes of the inset should be oriented in directions dirs.  >>
*)

Notice that the second usage statement says that the inset is placed at position pos in the graphic. Yet you are using different values for pos for even and odd lines. Secondly, when using a Text object in an inset, using {0, 0} for the opos value means that the center of the Text object is placed at pos. You should instead use {-1, 0} for the opos value so that the left end of the Text object starts at pos. So, using the same pos value for each row, and {-1, 0} for the opos value would produce left-aligned output. For example:

nmax=10;
Graphics[
    Table[
        With[{v=StringJoin@@Table["a",Mod[n,2,1]*10]},
            Inset[Text[v], Offset[{0, 0}, {0, n/nmax}], {-1,0}]
        ],
        {n,1,nmax}
    ]
]

Addendum

If you must use {0, 0} for $\operatorname{opos}$, then to get the raster size right you should include an explicit FontSize setting:

Graphics[
    Table[
        With[{v = StringJoin @@ Table["a",Mod[n,2,1]*10]},
            Inset[
                Text[Style[v,16]],
                Offset[
                    Rasterize[Text[Style[v,16]],"RasterSize"]/2+{3,0},
                    {0,n/nmax}
                ],
                {0,0}
            ]
        ],
        {n,1,nmax}
    ]
]