Jason (jcreed) wrote,
Jason
jcreed

Wicked awesome font nerd (and fellow googler!) Raph Levien was visiting today and stopped by for a chat. I learned a new (albeit rather elementary) fact, which is that G1 continuity of splines is not preserved by linear interpolation!

In plain english, if you have a regular font, and a bold font, and you want to make a semi-bold by taking the average of all the control points in them, you may find extra ugly kinks on the curves that were present on neither original font. (Figure 10.12 on p. 159 of his PhD thesis)

What is the property G1? It's the "geometric" version of continuously-differentiable --- that is, the C1 that you're more likely to have heard of. Both curves in figure 10.12 are G1 but not C1 at their middle on-curve point. G1 says that requires exists some reparametrization of the curve that is C1. If you have an on-curve point such that its nearby off-curve handles are collinear, then it's G1 there, and looks visually smooth. But it's only actually C1 if the nearby off-curve handles are equidistant from the on-curve point as well.
Tags: fonts, math
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