The corner in that picture looks absolutely disgusting, you can see the discontinuity. I would rather have a square corner if you are not going to bother to rou

The corner in that picture looks absolutely disgusting, you can see the discontinuity. I would rather have a square corner if you are not going to bother to round them properly. The way to actually produce rounded squares is to fix the curvature, and then solve for a corresponding curve. You want at least a differentiable function for the curvature. Something with a bit of a spike (think of a Gaussian, but make it level off to flat after the spikes). From the curvature you can use something like the Frenet–Serret formula, integrate and find a formula for a curve. You then approximate it with a bunch of bezier curves. Should get something nice and smooth.