The simple geometry behind any road

(sandboxspirit.com)

82 points | by azhenley 2 days ago

7 comments

  • jstanley 7 hours ago
    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.

  • OgsyedIE 1 hour ago
    The wikipedia page on some of the considerations is a good introduction on where the real world goes beyond this:

    https://en.wikipedia.org/wiki/Geometric_design_of_roads

    It's tempting to think that the cross-section geometry of a road only applies in three dimensions and can be elided for 2D overheads, but the parabolas that smoothly connect straights and curves in the overhead perspective are often subtly warped to permit any requirements of cant and superelevation.

  • kalmar 2 hours ago
    The care taken here to achieve aesthetically pleasing results reminds me of this post about creating nice transit maps in the Transit App: https://blog.transitapp.com/how-we-built-the-worlds-pretties...
  • red_admiral 6 hours ago
    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
  • lencastre 4 hours ago
    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
  • 21asdffdsa12 5 hours ago
    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.
  • dilberx 6 hours ago
    many are yet to catchup