On Tue, Jan 11, 2022 at 9:11 PM Bakul Shah <bakul@iitbombay.org> wrote:
> Don = Knuth talks at length about how TeX & MetaFont came about etc. in his W= eb of Stories interview in parts 50 through 70. In Part 56 he does say he l= ooked at "the system developed at Bell Labs", presumably troff.
Among the Bell Labs technical reports I read when I was younger, a tr= ilogy by MD McIlroy on the challenges drawing ellipses stand out: https://citeseerx.ist.psu.edu/viewdoc/download?= doi=3D10.1.1.49.3440&rep=3Drep1&type=3Dpdf

These stuck i= n my mind and some relatively short time later, I read how the analogous pr= oblem was approached in TeX. The solution there was to treat the shape as i= f it were drawn using a pen with a diamond-shaped nib. From the MetaFont bo= ok:

= Similarly, some diagonal lines of slope~1 digitize to be twice as dark as o= thers, when a truly
circular pen is considered. But the diamond-shaped n= ib that \MF\ uses
for a pencircle of diameter~1 does not have this defec= t; all straight
lines of the same slope will digitize to lines of unifor= m darkness.
Moreover, curved lines drawn with the diamond nib always yie= ld one pixel per
column when they move more-or-less horizontally (with s= lopes between \$+1\$
and \$-1\$), and they always yield one pixel per row wh= en they move vertically.
By contrast, the outlines of curves drawn with = circular pens produce
occasional ``blots.'' Circles and ellipses= of all diameters can profitably
be replaced by polygons whose sub-pixel= corrections to the ideal shape
will produce better digitizations; \MF\ = does this in accordance with the
interesting theory developed by John~D.= ^{Hobby} in his Ph.D.
dissertation (Stanford University, 1985).
If I can be so bold as to offer an interpretation: Doug's appr= oximations treat ellipses as mathematical objects and algorithmically deter= mine what pixels are closest to points on the infinitesimally-thin=C2=A0cur= ves, while Knuth's (or one his students') method acknowledges that = the curve has a width defined by the nib; any "pixel" the nib tou= ches becomes part of the figure. Perhaps I'm wrong on the details, but = it hardly matters; my point is that there was clearly interesting work done= in the area in both places. I find it impossible that neither Knuth nor Ho= bby were unaware of McIlroy's work and vice-versa; of course he would h= ave known about and examined troff just as the Bell Labs folks knew=C2=A0ab= out TeX. These were hot areas of practical research! This is also a good re= minder that not only was Unix itself a subject of research, but it supporte= d a lot of other research at Bell Labs and elsewhere. On this list, we tend= to focus on the tool, but that tool was put to use building many more thin= gs as well.

> [snip]
> I must say I am a fan of TeX/LaTeX a= nd not a fan of nroff/troff -- I don't like the troff look and I don= 9;t like the markup.

I've always admired the look of= troff. I wonder if, in retrospect, that is due to me mentally tying the pr= esentation with so many formative documents that were strong early influenc= es. Similarly, I love the look of Tex (even the CM fonts). They are of cour= se different, but I find each beautiful in different ways.

> The nice thing is we can choose whatever typesetting tools we want!=

This!

=C2=A0 =C2=A0 =C2= =A0 =C2=A0 - Dan C.

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