4 ms·

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 f

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 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.

trelbutate 6mo ago
I was also confused about that because they did mention clothoids in their first post: https://sandboxspirit.com/blog/art-of-roads-in-games 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
- ajs1998 6mo ago
  :( but the math is fun And they went through all this effort anyways, and to blog about it.
amelius 6mo ago
Here's a nice article on it: https://www.dgp.toronto.edu/~mccrae/projects/clothoid/sbim2008mccrae.pdf https://www.dgp.toronto.edu/~mccrae/projects/clothoid/sbim20...
Ef996 6mo ago
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.

trelbutate 6mo ago

I was also confused about that because they did mention clothoids in their first post: https://sandboxspirit.com/blog/art-of-roads-in-games 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

ajs1998 6mo ago
:( but the math is fun And they went through all this effort anyways, and to blog about it.

amelius 6mo ago

Here's a nice article on it: https://www.dgp.toronto.edu/~mccrae/projects/clothoid/sbim2008mccrae.pdf https://www.dgp.toronto.edu/~mccrae/projects/clothoid/sbim20...

Ef996 6mo ago

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.