Reprise

It hasn't been easy getting back to work on PhD thesis, after the long leave I had taken. (Where 'long', or rather 'too long', could actually be referred to any amount of time, given the approaching deadlines, and 'leave' doesn't refer to a discussion but to time dedicated to studying other subjects, getting ready for the post-doc.)

The hard part has been, as always, getting started. Opening up the source files containing the code for the library I've been working on. Once they were opened the first time, and despite the long wait, it was almost immediate to spot a bug and to add the new features I needed for my tests.

Well, immediate ... even here, we're talking about three days. Not because the actual coding was slow, but because I only set up to work between midnight and 2am ... not the best time to get some work done, one would think, but anyway, to day it seemd to have worked ok.

The aim of my PhD thesis is to analyse known and new methods to transform fonts from the model used in METAFONT to the one used in PostScript Type1. Both models describe fonts mathematically, taking advantage of the flexibility of Bézier cubics, but whereas METAFONT uses these curves to describe paths stroked by pens (of circular or other convex shape), Type1 fonts use Bézier cubics to describe the outline of the glyphs.

Therefore, mathematically the problem to tackle is one of using Bézier cubics to describe the envelope of a set of circles centered on given Bézier cubic. Since this is not possible to achieve in general, the problem is actually one of finding the best approximation.

The advantage of dealing with Bézier cubics is that it's possible to split and splice them preserving graphical continuity, so when any approximation sought isn't good enough one can split the initial curve, approximate the parts (likely to give better results, since splitting curves tends to straight lines) and the splice the approximations.

How to avoid splitting, where to split, and other relevant questions are the topic of discussion in my thesis.

Which I'll have to write, sooner or later ...