Bug in Computer Modern Roman

The bulbs in "a","c", and "ae" depend on resolution (device, mode)

"a" and "c" in cmr10.mf are not correct?!


During tests of LM and comparisons with bitmapped CS and CM I observed a strange differences in Computer Modern Roman and Computer Modern Slanted Roman glyphs "a","c" and "ae".
I have prepared some test with examples.

README

Bug in Computer Modern Roman: the bulbs in "a","c", and "ae" depend on resolution (device, mode).
The METAFONT sources for "a","c","ae" in cmr(10,12,17,5,6,7,8,9), cmsl(10,12,8,9), and cmdunh10 produce different results at different resolutions in the bitmapped images in the GF/PK format.

Examples

unzip cmr_a.zip
# A short overview in PDF (compiled manually)
acroread cmac.pdf
# Acrobat Reader version 7 or newer is needed!

# Run a test:
# Modify UNIX/Linux procedures (pkcomp and pkcomp.sh)
# if necessary, then run the script
./pkcomp.sh # two images in PDF (1200dpi and 2602dpi)
# are subsequently mixed into one figure,
# mixpk.pdf should be the result of this test;
# cyan:1200pk, red:2602pk, light red:common area.

Comments

Of course, the figures are scaled.
The following table could give an additional explanations concerning
Figure 1: cmr10:a 1200pk 2602pk in cmac.pdf

resolution MF parameters
1200 2602 cmr10.mf
13 25 stem#:=25/36pt#; % lowercase stem breadth
16 33 flare#:=33/36pt#; % diameter of bulbs
5 9 hair#:=9/36pt#; % lowercase hairline breadth
5 8 vair#:=8/36pt#; % vertical diameter of hairlines

At these resolutions (1200dpi and 2602dpi) the gap = the distance between the bulb and the curve below is more than 10 pixels.

Comparison with "2"

22 Feb 2007
I add an illustration with numeral "2" from cmr10 for better understanding and for the people who do not know fonts in details.
The numeral "two" can be rasterized (a little) differently at various resolutions but the positioning of the bulb is stable (invariant) and no fluctuation (movement, shift) is observed. The differences between resolutions are adequate and fully correspond to my expectations; i.e. "2" is O.K. as should be.
The effects at a lower resolution (300 dpi) shown in fig. 4 demonstrate other dependences on resolution. Of course, that kind of dependence on resolution was not the subject of my report; and any comments on the low resolution are irrelevant to the problem.
In the comparison of the 2600 dpi bitmap (red) with other resolutions (cyan)
(page/figure 1. 2400 dpi, 2. 1200 dpi, 3. 600 dpi, 4. 300 dpi, 5. 5333 dpi)
we can observe cases of discrepancy, i.e. the differences between "2" (correct) and "a","c","ae".

Comparison with Type 1

24 Feb 2007
The next example cmr10: PK v.s. Type 1 (PDF) demonstrates the close agreement of the PostScript/Type 1 version [converted by BlueSkyResearch and Y&Y and copyrighted by AMS] with 2602dpi(1) and 2400dpi(2) --- and different positioning of the bulb at 1200dpi(3) and 600dpi(4).

Appendix

E-mails to tex-fonts -- TeX fonts discussion list

1. 19 Feb 2007
2. 21 Feb 2007 (partial study of calculating y1)

Created: 18 Feb 2007
Last modified: 24 Feb 2007