Fwd: [UAFDKOML] Technical issues in using decimal coordinates in PostScript fonts.

FYI
---------- Forwarded message ----------
From: <[email protected]>
Date: 3 September 2015 at 16:11
Subject: [UAFDKOML] Technical issues in using decimal coordinates in
PostScript fonts.
To: UAFDKOML <[email protected]>


The latest version of the FDK supports decimal coordinates in Type1/CFF
fonts.


We did run into one issue which is a problem with the font format, that
would benefit from some discussion among the font tool developers. Type 2
fonts (OpenType/CFF) store decimal coordinate values as a Fixed 16.16
number. This means that it is stored as two parts: an integer number which
represents the integer part of the decimal value, with a range of −32K to
+32K. The second part is the decimal fraction, and this is stored as an
integer number which is a multiple of 1/64K. The fractional values that can
be represented are thus a multiple of 1/64K, aka a multiple of
0.0000152879. This means that many decimal values cannot be exactly
represented in the Fixed 16.16 value. For example, if you convert the
coordinate value 41.37 into a Fixed value, and then convert this back into
a decimal value, you get 41.3699951. This has never been a problem before,
as the decimal values used in hints have typically been 0.5 or 0.25, and
and all fractions that are 1/(2n) can be exactly represented in both Fixed
and decimal values. Now that we are beginning to explore arbitrary decimal
values, it is a problem. If you round-trip between a CFF font and a UFO
font, and truncate rather than round, the fractional errors for the
relative coordinates can add up to several design units over a long path
with hundreds of points. Also, closed paths can become an almost closed
path, adding an extra on-curve point, and you get an implied line-to at the
end of the path that is a small decimal fraction in length.


What I did in the AFDKO tools was to round coordinate values (away from
zero) to 4 significant places when converting from decimal values in a UFO
font, and to round (away from zero) to the nearest Fixed 16.16 when
converting to Fixed 16.16. With this in place, there can still be
cumulative errors from the truncation of sequential relative coordinate
values, but it would take a lot of coordinate values to add up to one
design unit. I would like to see this approach adopted by other developers
as well. The degree of rounding precision is arguable. I chose four decimal
places, since this is the most than can be supported when converting
between Fixed 16.16 and decimal values, but I think it would make sense to
have fewer. I also think that it would be useful to have font tool
developers agree on a convention for rounding decimal values.


An oddity which is specific to the AFDKO tools is that that the font
development workflow will support only 2 decimal places. This is because of
the autohint tool, which originally supported only a Fixed 25.7 format for
coordinate values (in other words, the fractional part is a multiple of
1/128). I changed this to Fixed 24.8, which will support two decimal
places, but not more. I would obviously have liked to support a larger
fractional part, or switch to using real decimal values, but we needed to
be able to produce the same output before and after with the same original
input. If I had disturbed the code with a larger change, the output but
would not be exactly comparable, and we did not have time to do a large QA
effort (as in man-months) to evaluate new autohint output.

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-- 
Cheers
Dave

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