Kdtyjb

I have a very strange effect while debugging yhmath math fonts items. I am generating cmex10.tfm from cmex10.mf, and convert the tfm to pl file.

Then I rename only rename the driver file to yrcmex10.mf, and add the following new glyph definitions in bigdel.mf, without changing anything in the rest of the files:

cmchar "big left parenthesis";

beginchar(oct"200",8u#,rule_thickness#,2.5dh#-rule_thickness#);

adjust_fit(1.75u#,-.25u#); left_paren(hair,stem); endchar;



cmchar "big left parenthesis";

beginchar(oct"201",10u#,rule_thickness#,3.5dh#-rule_thickness#);

adjust_fit(2.25u#,-.25u#); left_paren(hair,stem); endchar;





cmchar "big left parenthesis";

beginchar(oct"202",12u#,rule_thickness#,4.5dh#-rule_thickness#);

adjust_fit(2.75u#,-.25u#); left_paren(hair,stem); endchar;



cmchar "big left parenthesis";

beginchar(oct"203",13u#,rule_thickness#,5dh#-rule_thickness#);

adjust_fit(3u#,-.25u#); left_paren(hair,stem); endchar;





cmchar "big left parenthesis";

beginchar(oct"204",15u#,rule_thickness#,6dh#-rule_thickness#);

adjust_fit(3.5u#,-.25u#); left_paren(hair,stem); endchar;



cmchar "big left parenthesis";

beginchar(oct"205",17u#,rule_thickness#,7dh#-rule_thickness#);

adjust_fit(4u#,-.25u#); left_paren(hair,stem); endchar;



cmchar "big left parenthesis";

beginchar(oct"206",19u#,rule_thickness#,8dh#-rule_thickness#);

adjust_fit(4.5u#,-.25u#); left_paren(hair,stem); endchar;

So the only diff between the cmex10 font and yrcmex10 font is the addition of the above characters.

Converting both tfm to pl, and making a diff I see changes in unrelated glpyphs, in particular the DP parameter changes:

--- cmex10.pl   2019-03-07 09:30:01.263513678 +0900

+++ yrcmex10.pl 2019-03-07 09:52:25.578670436 +0900

@@ -1,7 +1,7 @@

 (DESIGNSIZE R 10.0)

 (COMMENT DESIGNSIZE IS IN POINTS)

 (COMMENT OTHER SIZES ARE MULTIPLES OF DESIGNSIZE)

-(CHECKSUM O 37254272422)

+(CHECKSUM O 35311171576)

 (FONTDIMEN

    (SLANT R 0.0)

    (SPACE R 0.0)

@@ -20,85 +20,85 @@

 (CHARACTER O 0

    (CHARWD R 0.458336)

    (CHARHT R 0.039999)

-   (CHARDP R 1.160013)

+   (CHARDP R 1.135567)

    (NEXTLARGER O 20)

    )

 (CHARACTER O 1

    (CHARWD R 0.458336)

    (CHARHT R 0.039999)

-   (CHARDP R 1.160013)

+   (CHARDP R 1.135567)

    (NEXTLARGER O 21)

    )

...

This is very surprising, I would have guessed that the glyph dimensions of other non-changed glphs do not change. Furthermore, this changes become bigger the more additional glyphs I add.

Anyone having an explanation for this?

According to MetaFont, The Program:

Since it is quite common for many characters
to have the same height, depth, or italic correction, the TFM format
imposes a limit of 16 different heights, 16 different depths, and
64 different italic corrections.

Incidentally, the relation width[0]=height[0]=depth[0]=
italic[0]=0 should always hold, so that an index of zero implies a
value of zero.

So there can be at most 15 different depth values beside 0 in a single TFM file.
Now let's look at the depth values in your yrcmex10.pl:

     1     (CHARDP R 0.300003)

     2     (CHARDP R 0.580007)

     3     (CHARDP R 0.900009)

     4     (CHARDP R 1.000013)

     5     (CHARDP R 1.135567)

     6     (CHARDP R 1.480014)

     7     (CHARDP R 1.780019)

     8     (CHARDP R 2.060022)

     9     (CHARDP R 2.222246)

    10     (CHARDP R 2.360025)

    11     (CHARDP R 2.660028)

    12     (CHARDP R 2.9600315)

    13     (CHARDP R 3.560038)

    14     (CHARDP R 4.160044)

    15     (CHARDP R 4.76005)

(List generated using grep 'CHARDP' yrcmex10.pl|sort|uniq|nl)

So your font already contains the maximal number of distinct depths, which explains the changes:
The depth of 0 was 1.160013, but this value is not a part of the list above. So it would have to be added, but then there would be too many distinct depths. So when MetaFont read the additional characters, it realized that it could not store all the depths in the TFM file. So some values had to be rounded, and 1.135567 and 1.160013 are very close, making them ideal candidates.

This also explains why the change becomes bigger the more additional glyphs you add: If the new glyphs again have different depths, there are even more distinct depths MetaFont has to reduce to 15. This requires being more aggressive about "value unification", resulting in bigger changes.