[Cin] DAR, PAR and SAR, again

[Andrea paz]

I am opening a new post because the previous one, for me, was becoming
too confusing.

I quote Terje's latest email:

==============================================================

Well, I have prioritized more to understand what happends than
interprete the somewhat ambiguous definitions.
(the order of the factors is indifferent).
https://stackoverflow.com/questions/18877243/why-ffmpeg-print-sar-instead-of-par

I think of SAR in the FFmpeg output as a correction factor for the
recordered picture frame format resolution (Wp), to get the desired
output display resolution (expanded Wd with square px) at a given DAR,
(or in opposite order).

I found a useful table at ffmpeg-user that contains information for
practically all SD and HD video formats.
Maybe something for the manual?
https://www.mail-archive.com/ffmpeg-user@ffmpeg.org/msg27522.html


               display     DAR       picture     PAR      SAR = DAR/PAR
             ===========  ====     ===========  ====     =====
16:9-2160:  3840 x 2160  16:9  :  3840 x 2160  16:9  :   1:1
  4:3-2160:  2880 x 2160   4:3  :  2880 x 2160   4:3  :   1:1
16:9-1080:  1920 x 1080  16:9  :  1920 x 1080  16:9  :   1:1
  4:3-1080:  1440 x 1080   4:3  :  1440 x 1080   4:3  :   1:1
  16:9-576:  1024 x 576   16:9  :   720 x 576    5:4  :  64:45
   4:3-576:   768 x 576    4:3  :   720 x 576    5:4  :  16:15
  16:9-480:   853 x 480   16:9  :   720 x 480    3:2  :  32:27
   4:3-480:   640 x 480    4:3  :   720 x 480    3:2  :   8:9
[...]

===========================================================

My God, I feel like giving up....
The following is my opinion (indeed, my delirium!).
The table is wrong (for ffmpeg!) because it uses PAR. As is also
stated in the thread you cited:

"> PAR (picture aspect ratio [1]) [noun]: 1, The horizontal-to-vertical
 > size [3] ratio (H:V, e.g. 5:4, 3:2) for pictures.
get rid of this one altogether, because nothing in FFmpeg use it, and
rightly, because nobody should use it."

Instead of calling it PAR, it should be considered simply the aspect
ratio of W x H of the input. That is, the W/H of the formula DAR=W/H x
SAR (and not DAR=PAR x SAR). PAR and SAR cannot be different since
they are the same thing (i.e. the shape of a single pixel, as seen
from the image https://stackoverflow.com/questions/18877243/why-ffmpeg-print-sar-instead-of-par
that you mentioned). In practice, in my opinion, the PAR in the table
is nothing more than the SAR meant as Storage aspect ratio; in fact,
the author of the table defines it as a Picture aspect ratio, which is
a frame aspect ratio and not a pixel aspect ratio. It seems to me that
in an effort to be precise, it creates even more confusion. Instead,
the SAR in the table is nothing more than the S(ample)AR ( =
P(ixel)AR). If you think I am crazy to keep up with these definitions,
you are right!

The formula DAR = PAR x SAR was convenient and simple, however, ffmpeg
decided to use "samples" instead of pixels and so PAR should no longer
be used. That is why I was thinking of removing all reference to PAR.
The trouble is that if one searches around one always finds PAR and
never SAR meant as "sample a.r."; including many tutorials on ffmpeg.

The sample concept is derived from analog video signals and is encoded
in the standards BT. 601 and Digital. It refers to horizontal scan
lines (in MHz) and not simply pixels. From Wikipedia: "analog video
does not have pixels, but rather a raster scan, and thus has a
well-defined vertical resolution (the lines of the raster), but not a
well-defined horizontal resolution, since each line is an analog
signal." S(ample)AR was created precisely to adapt the analog concept
to the digital world.

To further explore the concept of sample:
https://web.archive.org/web/20140816103129/http://lipas.uwasa.fi/~f76998/video/conversion/

Your definition of SAR as a correction factor is right and I will use
it in txt. Thank you for the cue.

To summarize: in the digital domain we can use the concept of
S(ample)AR when we are dealing with digital anamorphic formats (for
example, when transcoding to a format that has different aspect
ratio). But the most frequent use is in "standard-definition
television or with DV, HDV and a few other formats. SAR is used via
the formula DAR = SAR x (W/H), where SAR is the conversion factor
between anamorphic Input and Output.

Perhaps the clearest treatment is as follows:
https://encodingwissen.de/hintergrund/videobild/anamorph/itu-r-bt601/

It is in German and therefore needs to be translated (the Italian
translation is not very good...). They seem to me to be similar
concepts to Raffaella Traniello's guide.

As an additional (my) confusion, in CinGG we also have the W/H Ratio
parameters, which are simple multipliers but, if set only one of them
(with values of the classic aspect ratios, 4:3; 16:9, etc.) and
leaving the other one at 1, they act as a real SAR even though they
are not...

@Andrew
In CinGG/Info-->Detail is the data reported taken using ffmpeg?
In other words: does CinGG use SAR like ffmpeg or does it have an even
different way?
PS: In my opinion, it would be better to change W/H Ratio to "W/H multiplier"