[TheRealPomax]

And they don't have to. The approximation of a circle with a bunch of cubic curves is so accurate [1] that you'd need to print a huge circle and then sit there with a measuring tape to be able to even tell it's not a perfect circle. Which is why "you can't draw a circle with Bezier curves" is only a mathematical "problem", it's not an actual problem.

[1] https://pomax.github.io/bezierinfo/#circles_cubic

[ad8e]

It's a UI problem, not a mathematical problem. No set of curves can represent everything exactly, but they all can get close. The goal is just to make it easy to get close.

The computer can produce a near-perfect circle with Béziers for each 1/4 arc, and near-perfect circles are usually good enough. It's just inconvenient. It's also hard to manipulate the generated circle; the user might have a clear image of his head of the changed circle he wants, but pushing the control points to get there is not easy.

The mathematical "axioms" in the article are only attempting to provide a clean interface, so that the user can easily translate what is in his head to what the program creates. The circle axiom says, "The user often wants a circle, and also expects a circle, so let's produce the expected circle." There's no other mathematical purity involved.