Cubics & Quadratics - Approximation results

I spent a few hours going through the Font Forge files to get a grip on how much work it would be to use it in Cello. My suspicion is that the code in Font Forge will produce better results in converting Cubics to Quadratics for fonts, simply because Fount Forge is dedicated to this kind of work and George Williams (the author) has obviously put a lot of work and consideration into the approximation - which specifically looks for various things like points of inflection when breaking the curve, and detecting Cubics that have been converted from Quadratics - something which happens with fonts.

Looking through the Font Forge code it does seem possible to map CGPaths onto the Splines and SplineSets - but it will be a bit of a fiddle to get it all working. On he other hand getting the existing Cello classes to work with CGPaths is actually quite straight forward. These classes are all written in C++ and the conversion is fairly trivial.

There is a huge amount to do so I am going with the path of least resistance. As the project progresses I can always open the Font Forge option again. It is something I would like to revisit as there is a huge amount of interesting stuff dedicated to the manipulation of splines in Font Forge.

I would personally recommend checking out the Font Forge FAQ for some great answers to questions. I particularly liked Why isn't Font Forge written in C++ - George Williams has written a great piece of software, is giving it away lock, stock and build instructions to whoever wants it for whatever purpose - it is there enjoy it.

To test the conversion of Cubics into Quadratics I took the Apple PathDemo sample code, that is in the installed with xcode in the developer folder, and made some changes. This sample code will, amongst other things, draw random paths - so the changes are quite small. I also added some code that will draw the on-curve points so that I can get an idea of the complexity of the new paths. Probably the biggest thing is Cello has it's own definitions points, lines, splines etc - and you need to satisfy the a reasonable spread of dependencies before you can use the magic ShapeVectorApproximator class.

Here are a couple of screen-shots from the test program. The grey thick line is the Cubic and the thin green one is the Quadratic.
The Quadratic on curve points are drawn in blue and the Cubic in red - so you can eaisly see that there are quite a few more cubic segments in the approximation.

If you look carefully in the image below you can see areas where the approximation breaks down and the green line strays outside of the grey - it should be in the exact centre.