You're missing one very important type of curve: a clothoid (or "Euler spiral") is a curve of continuously-varying radius, these are encountered on roads very frequently. And especially on race circuits.
A clothoid is used to connect two lines the same way your fillet is, except instead of just 1 radius it has a radius configured for each end and smoothly changes in between.
They are also used in railways, because on a railway you don't have the freedom of moving the car's position across the road, so a transition from a straight track to a constant radius would imply an instantaneous step change in centrifugal force, or infinite jerk. Using a clothoid to smooth the change between the straight track and the constant-radius turn means the lateral acceleration increases smoothly instead of instantaneously.
vehicular speed is very important as a consideration in any road curvature, as well as “pitch and yaw” when changing slope and direction at speed, so… simple it is not, and if we are mostly “offsetting” straight lines and arcs, we are doing it wrong
Expected it to at least mention the slant imposed on any road surface so water does not pool. Disappointed to tears and thus salt-water-aquaplaning in all games build upon this.
You're missing one very important type of curve: a clothoid (or "Euler spiral") is a curve of continuously-varying radius, these are encountered on roads very frequently. And especially on race circuits.
A clothoid is used to connect two lines the same way your fillet is, except instead of just 1 radius it has a radius configured for each end and smoothly changes in between.
https://en.wikipedia.org/wiki/Euler_spiral
They are also used in railways, because on a railway you don't have the freedom of moving the car's position across the road, so a transition from a straight track to a constant radius would imply an instantaneous step change in centrifugal force, or infinite jerk. Using a clothoid to smooth the change between the straight track and the constant-radius turn means the lateral acceleration increases smoothly instead of instantaneously.
I was also confused about that because they did mention clothoids in their first post: https://sandboxspirit.com/blog/art-of-roads-in-games
Although re-reading that it seems they just don't want to deal with the math involved
Here's a nice article on it:
https://www.dgp.toronto.edu/~mccrae/projects/clothoid/sbim20...
vehicular speed is very important as a consideration in any road curvature, as well as “pitch and yaw” when changing slope and direction at speed, so… simple it is not, and if we are mostly “offsetting” straight lines and arcs, we are doing it wrong
And then you have various types of hairpin bend where you actually vary the width of the lanes with the radius: https://www.google.com/maps/@46.8360535,9.6369913,68m
Expected it to at least mention the slant imposed on any road surface so water does not pool. Disappointed to tears and thus salt-water-aquaplaning in all games build upon this.
many are yet to catchup