Re: Understanding the eps bounding box (rounding)

[Alexander Kobel]

Hi Urs,

some educated guessing (and hopefully another suggestion):

On 03/01/2018 11:11 PM, Urs Liska wrote:
> Hi all,
>
> can anyone tell me *exactly* how the bounding box values are generated 
> and especially rounded in LilyPond? What are they exactly referring to, 
> the content *with* or *without* a border (of the bounding box)?
> [...]
> Does the -80 mean:
>
>   * any value between -79 and -80
>   * any value between -79.5 and -80.4999999
>   * or is it even an *outer* box? I mean, the "1" as the Y value of the
>     upper right corner looks suspiciously like  "exclusive" value,
>     doesn't it?

Without knowing the code that generates these numbers:
I'd assume it *should* mean the first (any value between -79 and -80), 
that is, the rounding is on the conservative side.

(Precise) bounding box evaluation is highly non-trivial as soon as 
curves are involved - you need to determine the x- and y-extrema of any 
such curve.
IIUC, GhostScript "simply" renders the page with some resolution to 
determine the bounding box. To get 1bp-accuracy, use 72ppi, ignore 
coloring, "just" remember the page area where something has been drawn; 
then compute an axis-aligned bbox for all those values.
To get higher accuracy (see below), the procedure is repeated with 
higher resolution (and, for efficiency's sake, only for those graphic 
elements that potentially contribute to the bounding box).

I *guess* that to decide on the layout, Lily has to do something 
similar, and it flushes those bbox values to the EPS.

> I'd be glad about any concrete information or other suggestions.

Both slightly more concrete and another suggestion: wouldn't you be 
better off with using the high-resolution bounding box determined by GS 
from an actual rendering of the page? E.g.,

  gs -sDEVICE=bbox -q -dBATCH -dNOPAUSE bbox.pdf

gives

  %%BoundingBox: 0 0 480 136
  %%HiResBoundingBox: 0.486000 0.432000 479.510774 135.017433

for your attached file. These numbers are as accurate as they can 
reasonably expected to be: GS promises that the numbers are 
conservatively rounded and accurate to 1 unit in the last place. 
(Subject to theoretical limitations on Turing-complete page description 
languages, I guess...)

Note that AFAICS the EPS generated by Lilypond has a white background on 
the integer coordinates, so the values reported by GS will match the 
numbers in the file. But since you use LuaLaTeX apparently, I assume you 
include PDFs rather than EPSs, right? No need to work with both formats, 
then.


HTH and doesn't add a whole lot of confusion,
Alex

smime.p7s
Description: S/MIME Cryptographic Signature