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Author here. Engineers use clothoids as the primary geometry for high-speed roads by offsetting a centerline clothoid. However, the offset of a clothoid is not itself a clothoid, so the left and right edges are not mathematically clothoids.

A clothoid is simply a mathematically ideal way to achieve continuously increasing curvature along a path. In practice, it can be approximated by chaining multiple circular arcs with decreasing radii.

Nope. But I mean aren't functions of circles essentially some kind of SDFs in 2d? Or at least those of disks.

I will definitely explore this in the future as architecture is probably my next passion after roads :D

This is amazing. Some objective would be great

Author here: i agree the article oversimplified here and in practice vehicle tracks can sometimes be non concentric. But it has nothing to do with differentials. Differentials just allow wheels to rotate at different speeds (as perimeter of a smaller radius circle is smaller the outer one). Non parallelism usually comes from the Ackerman steering or slipping. But rear tracks of a vehicle going slowly through sand will always be concentric. Parallelism is important for engineers because it also allows multiple vehicles to go in parallel on a multi lane road. You can see how that is failing with bezier paths in the CS2 ss in the article. Also hairpin turns are usually designed with arcs in mind as well

Thanks for references! I initially considered bevy for this but I was a bit scared it was not mature enough. How do you find it now?

True. I mostly meant not personal vehicles, so jut buses, trams etc. I supposed emergency services will use those dedicated lanes. or maybe civilization is so advanced those will be served via flying only. Idk just since fiction thinking.

Yep, good point. I am myself a huge fan of livable oriented infrastructure (bike lanes, pedestrian paths, public transportation) but the hard truth is that roads were initially designed for carriages and later for cars. A though I recurrently have is how would a city designed from scratch by a civilization that uses only bikes and walking look like?

I am a huge fan of satisfactory as well (probably no surprise for anyone)