Glyphs to Paths - Cubics & Quadratics in CoreText

Sometimes the world is a bit more upside down than you might initially perceive - Cello's output file format requires its curves to be described as Quadratics rather than Cubics. So I need to convert any Cubic paths that I get from CoreText to Quadratics.

Converting from Quadratics to Cubics is far less straight forward than the other way around. Cubics can only be approximated by Quadratics they can not be exactly converted. This sort of conversion is something that I have had to deal with in the past - it is not the sort of maths that I can pull off from first principles - so I have been working out with Google.

The best explanation of Cubics & Quadratic conversion that I have found is in the Font Forge (an open source font editor) website and can be found here. The section Converting Postscript to TrueType explains very clearly the issues that are involved in the conversion - check it out!

In doing the actual conversion after grubbing arround it would seem that I have a few options.

1. Font Forge - As a font editor Font Forge does this conversion. Looking through the sources this happens in a file called SplineOrder2.c. Of the implementations of the conversion this is by far the biggest and I conjecture might be the one best suited to converting fonts. The license for the software is a modified BSD license (a very permissive license) so I could use it. Font Forge has its own representation for curves so my CGPath would need to be converted.
   
2. Cello - Elsewhere Cello converts Cubics to Quadratics. The curves are in it's own internal path representation.
3. GXLibrary - When QuickDraw GX was released the SDK had a library (supplied as source code) that includes a conversion from Cubics to Quadratics. The source can be found in CubicLibrary.c. The conversion is all based on GX data stuctures and fixed point maths.