????? #143 ?????? ???????? ???????? CyrTeX-en@vsu.ru
??: Vladimir Volovich <vvv@vsu.ru>
?????: Re: CM-Super font package v0.3.0 released
?????: Fri, 12 Oct 2001 17:27:29 +0400
???: Berthold K.P. Horn <bkph@ai.mit.edu>
???? ?????? ???: <CyrTeX-en@vsu.ru>, <CyrTeX-ru@vsu.ru>, <tex-fonts@math.utah.edu>, <tetex@informatik.uni-hannover.de>
"BKPH" == Berthold K P Horn writes:

 >> * Generated precise (non-integer) widths for all glyphs in PFB
 >> files to match TFM widths (using continuous fraction
 >> approximation).  Corrected width of space glyph to match default
 >> TeX font space width.

 BKPH> It's nice to see this rather subtle and unappreciated bit of
 BKPH> cleverness from the original BSR/Y&Y CM fonts replicated :-)

thank you. :-)

 BKPH> Using continued fractions you can get about n + m bits worth of
 BKPH> accuracy when the numerator and denominator have n and m bits
 BKPH> respectively.  Much better then the obvious way of dividing by
 BKPH> some fixed quantity like 1000, where you only get about n bits
 BKPH> worth... And of course much better than the junk fonts that
 BKPH> just round to the nearest integer.

i've added the following paragraph into the README file:

It should also be noted that the fonts use precise (non-integer) glyph
widths which better match the TFM widths. These widths are generated
using the best approximation (based on continuous fractions) with the
denominator not exceeding 107 to fit in 1 byte in CharString.
Apparently, such subtle technique was used first in BSR/Y&Y CM fonts.

Best,
v.

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