[FFmpeg-user] Glossary: DAR, PAR, and SAR

[Mark Filipak (ffmpeg)]

Revision: Shorter sentences, better consistency, no extra 'lesson' about how to minimize ratios.\
Formatted for email, plain text.

DAR (display aspect ratio [1]) [noun]: 1, The width-to-height ratio
   (W:H, e.g. 16:9, 4:3) for the intended display. DAR is distingushed
   by metadata: 'aspect_ratio_information', (also see "SAR", note [2]).
   2, H.262 §3.44: "The ratio of height divided by width (in spatial
   measurement units such as centimetres) of the intended display."
   [2].
   [1] It's mistakenly asserted by some that "DAR" is an acronym for
       "data aspect ratio" or "disc aspect ratio".
   [2] Criticism: H.262 claims that DAR is a "ratio", then wrongly
       defines it as a quotient (which it turns upside down): "height
       divided by width"; also H.262 §6.3.3 (i.e. "3 ÷ 4", "9 ÷ 16").

PAR (picture aspect ratio [1]) [noun]: 1, The horizontal-to-vertical
   size [3] ratio (H:V, e.g. 5:4, 3:2) for pictures. PAR is
   distingushed by metadata: 'horizontal_size' & 'vertical_size', [2]
   [4] (also see "SAR", note [2]).
   [1] It's mistakenly asserted by some that "PAR" is an acronym for
       "pixel aspect ratio".
   [2] PAR can also be calculated from DAR & SAR thusly: PAR = DAR/SAR.
   [3] Note that PAR is virtual (i.e. defined by dataset indexes, not
       by physical dimensions).
   [4] Criticism: H.262 doesn't define PAR, however, it does define a
       quotent that correlates with PAR, to wit: H.262 §6.3.3,
       aspect_ratio_information:
         "SAR = DAR × horizontal_size/vertical_size".
       The foregoing implies that H.262 would have defined PAR as
       vertical_size/horizontal_size. Opinion: By defining DAR & SAR as
       quotients (which it turns upside down), and by implying that
       metadata: 'aspect_ratio_information', is also such a quotient
       (which it also turns upside down), H.262 causes much confusion
       that helps explain why so many Internet sites get DAR, PAR, and
       SAR wrong.

SAR (sample aspect ratio [1]) [noun]: 1, The physical horizontal-to-
   vertical spacing ratio (H:V) for samples [2][3]. SAR is
   distinguished as a computed value: DAR/SAR. 2, H.262 §3.114: "This
   specifies the relative distance between samples. It is defined (for
   the purposes of Rec. ITU-T H.262 | ISO/IEC 13818-2), as the vertical
   displacement of the lines of luminance samples in a frame divided by
   the horizontal displacement of the luminance samples [2]. Thus, its
   units are (metres per line) ÷ (metres per sample)." [7].
   [1] It's mistakenly asserted by some that "SAR" is an acronym for
       "storage aspect ratio".
   [2] A standardized set of picture sizes & aspects has been
       established:
                  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  [4]
   [3] Ideally, SAR would also be the width-to-height ratio of the
       sampling aperture, but that is not mandatory.
   [4] Example: If a 35mm film area (0.906 x 0.680 inches) is to
       produce 345,600 samples (visual density) with 480 rows (vertical
       resolution), then each row must have 720 samples (horizontal
       resolution) [5] and sample spacing should be 32 µm horizontally
       by 36 µm vertically [6].
   [5] (345,600 samples)/(480 rows).
   [6] (0.906 in)(25400 µm/in)/720 by (0.680 in)(25400 µm/in)/480 = 32
       by 36 µm = 32:36 = 8:9 aspect ratio.
   [7] Criticism: H.262 claims that SAR is a "ratio", then, as it does
       with DAR, wrongly defines it as a quotient (which it turns
       upside down).

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