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Re:Bezier Curves and Type Design: A Tutorial by jacobolus on Monday May 12, 2014 @06:31AM (#7731964)
Yes, the article is wrong. It’s possible to exactly convert a quadratic curve to a cubic curve, but going the other way the best possible is just an approximation. (Though the integer control point locations required by font descriptions can make it not quite exact.)

Also, this conversion doesn’t seem like something anyone should do by hand (e.g. adding extra control points which don’t change the curve): some algorithm is going to be able to optimize curves to minimize points, convert between curve types, etc. much better than a human is, and much much faster. [Though for all I know some existing software has crappy implementations]

Personally, I’d recommend people use Raph Levien’s Spiro curves to design their fonts (and not use Béziers directly); they make it much much easier to make whatever shape the designer is actually trying to make. (Folks on Hacker News interested in the mathematics of curve drawing should also definitely check out his PhD thesis.) http://www.levien.com/spiro/

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