The Euler spiral seems very similar to a curve I was generating in a stepwise manner while doing self driving car work. I was trying to generate the path the v

The Euler spiral seems very similar to a curve I was generating in a stepwise manner while doing self driving car work. I was trying to generate the path the vehicle would follow if you were driving at a constant speed, and start turning the steering wheel at a constant rate. The full curve would then see you holding that angle, then returning the wheel to center. After brute forcing this curved portion, I was able to solve a linear algebra problem to determine how far to drive during these straight segments to smoothly enter a parking spot with exactly 3 turns: 2 arbitrary turns, and a 3rd that brings the vehicle to the correct angle. After brute forcing each combo of the first 2 turns, throwing the path through a weighted fitness function that minimised travel, and penalized reverse moves, while at the same time checking for collisions, it would spit out a very simple and elegant parking plan.