## Tiffany Wardle Memorial Liveblogging™ of a presentation at TypeTech, ATypI Brighton 2007 (q.v.)

(I missed some of the historical discussion.) Not much later, we have a radically different approach: In Bauhaus, they really fancied the circle. It depicts other things, not just an abstract piece of art. It was really used in a dogmatic way (shows hemispheric teapot). In the ’60s, we began to have these really free-form shapes, and that’s where Bézier curves come in. Also in architecture. Just the fact that the curves were popular then is a matter of the style of the period. Car design (shows a Citroën DS): Ærodynamics, but also clearly a design decision here. They are very clean, but they are not constructed like the Bauhaus.

So these curves actually come from France: Pierre Bézier, 1962. Both font formats use Bézier curves, except that PostScript uses third-order or cubic and TrueType uses second-order or quadratic. A spline is always an addition of several curves. B-splines are not Bézier splines but base splines and are not used in fonts, so become a bit suspicious if anyone tells you they are. They might not be a real expert.

A Bézier curve is a voyage along four points. It starts at P0. He’s attracted by P1 (the first curve direction), but you slowly change your mind toward P2 and P3 (the terminus). But he’s still a bit attracted to P1. In the end, he reaches P3.

(Discusses history of Bézier curves at Apple and Adobe.) Essentially, Adobe’s PostScript won the race, and that is why I am standing here today talking about cubic Bézier curves. (Shows URW method of using only splines and letting the computer find the smoothest path between them. Also Spiro, which uses only curved points.) The only problem with everything that isn’t Bézier curves is that they have to be converted, which leads to quite a few points, which leads to rounding errors and not a nice shape, or you have to manually edit them again. Who knows, it might be developed into a proper editor.

How to control the curves: How do they react as I change the control points? Let’s look at categories: `S`-curves are the only ones that can be handled intuitively. If you move one point, the curve changes in proportion to the degree of change. But you can look at it two ways: Making it narrower or wider or shifting the whole curve. In the first case, you change both handles equally; in the latter case, you make one longer than the other. That’s two degrees of freedom.

A semi-`S`: A bit like a mountain. If you change one handle, you change the height, and the position of the summit (left to right) hardly shifts. Change the other handle, and you move the summit without changing the height.

(Lists several more. Scribe stopped writing partway through. Pleasant and informed speaker, but too hard to encapsulate with his visual demos.)