Older blog entries for haruspex (starting at number 110)

Cubic Beziers are actually pretty good at making an S curve, in my opinion. Certainly, it's not uncommon in professional fonts to see a single Bezier traverse from a vertical tangent in the upper left corner to another vertical tangent in the lower right.

I agree Beziers are efficient, but I don't think this should seduce us into concluding they are natural.

If you draw the main slope of the S with, say, eight arcs, then the centers should describe a fairly continuous path in and of themselves. ... But if you don't do a good job visualizing the radii of curvature, and put the tool in novice hands, my guess is that you'll see bad curves.

That's a good point. But rather than having the user think about the circles, I wonder if they could use the abstraction of a digital spline and ducks (the non-mathematical meaning of spline). I suspect this is what Dr Karow had in mind when he came up with IKARUS' curve model.

it's probably not anywhere nearly as painful as you might think to work directly in the space of the Cornu parameters

That sounds interesting.

having an uneven baseline or x-height line is a pretty serious artifact

Surely only subpixel placement can help with non-integral lineskips? But it seems to me that (at a cost of performance, i.e. glyph caching), FontFocus could be adapted to subpixel positioning? (In the vertical, to solve the baseline problem.)

The CoolType samples in your paper do not work. In my opinion the subpixel rendering on OS X and XP (and Adobe Reader 6) does a fine job; the screen dump can only work in exceedingly rare circumstances (1:1, digital LCD of correct triplet ordering, etc) and should be deleted from the paper as a misleading comparison.

yeupou:

she said windows, not Microsoft Windows. Well, as I understand it, the company does not own the word windows, but the trade mark Microsoft Windows.

You missed Michael's point. Regardless of what M$ "owns", in common usage, the word "windows" has gained another (less useful) meaning. In real life this overloading easily results in the kind of ambiguity that his anecdote illustrated.

AlanHorkan, you might enjoy this great tune from Monty Python's irrepressible Eric Idle.

tk:

<small>people who succumb to the threat of the Ivan hurricane and run away are sending the wrong signal to Ivan. We must stand strong in the face of Ivan. We must not allow Ivan to disrupt our way of life and attack our cherished institutions. </small>

Hilarious, thanks :)

PS. Advogato, why can't me have <small>? (Thanks for allowing <cite>)

raph, circle segments are indeed the primitive used by IKARUS, as I've mentioned here before. This is clear from the exposition in Dr Karow's book (op cit.) and the source code therein. Also, I relate them to METAFONT deliberately, as this was explicitly the ideal around which Hobby's Bezier generation was designed. Again, this is derived from the technical descriptions given in The METAFONTbook. Of course, I know METAFONT's underlying representation and rendering engine works with Beziers, but concerning the higher level user abstraction, I stand by what I have asserted. I understand where Hobby departs from pure circles. In fact METAFONT's overall approach seems to solve most of the difficulty.

circular arcs do not have this property. You need quite a few of them to closely fit an ellipse, say.

Yes, I agree with what you write here, but I am not sure it matters. The fact is, any geometrical figure - ellipse, circle, parabola - is irrelevant to the problem of fitting a natural, drawn curve. Pure geometric shapes (with the exception of straight lines) rarely occur in a letter outline, so I disregard them as modelling test cases. Instead, I ask, how well can this primitive deal with a pre-mathematical, natural curve, as might have come from the designer's hand? How awkward is the translation? (Your curve continuity arguments are relevant theoretical ammunition here I think, although my assessments are usually subjective, not objective.)

My counter-assertion would be, for a natural curve, Beziers are not necessarily better than circle segments and further that counting control points does not prove this either way. My gut tells me that Beziers are excellent for rendering purposes but horrible for curve modelling. I certainly see advantages for Cornu over both these representations, and you've given some interesting reasons.

I have studied many IKARUS markups and not found them excessively overspecified. (It would be nice to hear from an IKARUS veteran on this.) One very intriguing thing about IKARUS is that most markups I've seen were made by non-technical draughtsmen, usually type designers themselves - Zapf, Frutiger, Spiekermann. Whereas no-one can do good Bezier drawings without a lot of training - and such drudgery would waste the time of a designer of this calibre. It took me a few years to learn how to "trick" Beziers into looking natural - and it's always a compromise.

In sum, my subjective assessments generally lead me to feel that IKARUS splines - or let's say, a mechanical spline and ducks - are quite natural to the draftsman and designer; and Beziers could not be more artificial and difficult.

We are coming at this from different angles, however. You're the mathematician, and I am just a typographer who isn't happy with the compromises that plague digital type.

raph:

I've also been playing with the Cornu spline...as a primitive for curve design, and am now absolutely convinced that it's better than Bezier curves.

I think it's long been clear that Beziers are not a good user abstraction for curve editing - but what's wrong with circle segments between on-curve knots, as chosen by IKARUS, METAFONT, et al? I am not sure anything could be more natural. I suppose the Cornu could be seen as a French-curve style extension of circles. I think I need to write that experimental path editor I always planned, to play with these alternatives :)

My hot metal friend Nick Summers is not out of the game. He wrote me recently with very exciting news:

I should finally be printing - letterpress, of course - by the end of this month ... I hope to be assembling the fabled Benton Engraving Machine some time soon as well. And restoring my Linotype. And casting on the Monotypes...

nymia: I wrote a Photoshop plugin that's downloaded 100 times a day. It's free. If I had put even a very modest sticker price on it, I'd be lucky to get one download a day. I decided that a comparatively large benefit to "the all" was preferable to a small benefit to me.

(update) nymia: The benefit I receive is the traffic. There are a couple of commercial and donation-ware plugins available from the same page, which should account for a small trickle of compensation flowing back from the free-loaders? It will never pay my mortgage, but it is -something-. After all, I only wrote the software once, if I get paid 100,000 times that might not be ethical. I don't want the bad Karma of uber-thief Gates and his kind.

TheMuso:

If you are aware of Australian internet access, it is quite different to the rest of the world, particularly broadband. I am sitting here on a 512/128K ADSL internet connection,

I am not sure what you mean, "different", unless you mean very very expensive. My Melbourne ADSL costs A$170 per month for 512kbps and an embarrassingly small download inclusion. I presume you're luckier to be paying less than this extortionate rate.

Gah. Couldn't figure out why OS X's integrated WebDAV handling wasn't working (WebDAV servers are first class file systems on OS X). Eventually figured out the problem was my squid proxy server - which at 2.2.5-4 is too old (old Debian 2.2 install on Alphaserver).

movement: hey, thanks for pointing out the idiotic Olympic linking policy. Taken with their ridiculous stance on blogging it makes them look like a bunch of dumb shits.