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They aren't beautiful if you have a picture in your mind that you want to realize.

It hit me one day that some of the best character designers in the world didn't know any better than I did how to draw anime characters with Bezier curves.

That sounds like a case of using the wrong tool for a job. That's like saying that Computer Aided Design is inelegant because it's hard to get the shading right on your life-drawings.

I wrote programs that tool arbitrarily long path lists and connected them with Bezier curves - not because they lend themselves to creating art but because I had constraints on the smoothness, curvature and number of inflection points of the compound path.