Knuth on TrueType vs Metafont

[Shyjan Mahamud]

don't know if you folks have seen this on

        http://www.advogato.org/article/28.htm

here's the relevant excerpt (see his last sentence if you are short on 
time) :

Interviewer: Another similar issue is  TrueType fonts.  TrueType fonts
have   this  property  of   including instructions,  computer programs
effectively, in the font, to do hinting.

Knuth: Well, I never met Elias or whatever.

Interviewer: Sampo Kaasila? 

Knuth: I don't know.  I know enough about TrueType to know that it's a
very  intelligent design, that is  similar to  Metafont except that it
strips out everything that's slow. So  the way the  hinting is done is
by program, certainly.  Of  course, it came  out maybe ten years after
Metafont, so probably something got through somehow.

     There was  the F3 font that  Folio was making,  if I can remember
the name, what the  people in industry  called it. Some of  the people
that I had worked with on Metafont went into  making font designs that
were similar to TrueType, but have not been successful.

Interviewer:  There's a fairly  major  controversy with TrueType right
now, that there a number of patents that are owned now by Apple.  It's
kind of interesting  to me that that is  the case even though it's for
the most part derivative work of what was in Metafont.

Knuth:  I've been very unhappy  with the way  patents are handled. But
the more I look at it, the more I decide that it's a  waste of time. I
mean, my  life is  too short  to fight with  that,  so I've just  been
staying away.  But  I know that the   ideas for rendering...  The main
thing is  that  TrueType uses  only quadratic splines,  and that Type1
fonts use  cubic splines, which  allow you to  get by with a lot fewer
points where you have to specify things.

     The quadratic has  the great advantage that  there's a real cheap
way to render them. You  can make hardware to  draw a quadratic spline
lickety-split. It's all Greek mathematics, the conic sections. You can
describe a quadratic spline by a quadratic equation (x, y) so that the
value of f(x, y) is positive on one side of the  curve and negative on
the other side. And then you can just follow along pixel by pixel, and
when x changes by one and y changes by  one, you can  see which way to
move to draw the curve   in the optimal   way. And the mathematics  is
really simple for a quadratic. The corresponding thing  for a cubic is
six times as complicated, and it has  extra very strange effects in it
because cubic curves can have cusps in  them that are hidden. They can
have places  where  the function will  be  plus on both   sides of the
cubic, instead of plus on one side and minus on the other.

     The   algorithm that's like  the quadratic  one,  but for cubics,
turns   out that you    can be in  something   that looks like  a very
innocuous   curve,   but  mathematically you're   passing   a singular
point. That's sort of  like a dividing by zero  even though it doesn't
look like there's any reason  to do so. The   bottom line is that  the
quadratic   curves that TrueType  uses   allow extremely fast hardware
implementations, in parallel.

Interviewer: The question is whether that matters  of course, now that
CPU's are a zillion times faster.

Knuth: But  for rendering, Metafont was  very very slow by comparison,
although I'm amazed at  how fast it goes now.   Still, it has to be an
order of magnitude better, and certainly that  was a factor in getting
TrueType adopted  at the  time that  it was,  because machines weren't
that  fast then. So TrueType  was an intelligently  chosen subset, but
certainly  all  the ideas I've  ever  heard of about  TrueType were, I
believe, well known in the early '60s.