Euler Spiral

Also known as clothoids, spiros or Cornu spirals
They are curves whose curvature changes linearly with curve length (curvature of
a circular circle is the reciprocal of it's radius)
eg: Railway tracks where the curve changes into a straight track

Derived using Fresnel Integrals

Usages

Track Transition Curves
Used in Optics to describe diffraction patterns
Rollercoaster clothoids
Velodromes (bicycle curves) - for rapid entry and gradual exit

Tags:
Jerk
clothoids