Is there any way to analytically decide the shortest distance between a spline of clothoids and a point? Both lies in XY-plane. The clothoid spline has G2 continuity. The result should be used in geometric optimzation, so squared distance (xp - xc)2 + (yp - yc)2 may be used.
If there is no analytic solution, can anyone give a good suggestion to an iterative solution.
Definition of clothoid and splines:
Clothoid is also called Cornu spiral or Euler spiral.
http://mathworld.wolfram.com/CornuSpiral.html
A spline is a piecewise-defined function:
http://en.wikipedia.org/wiki/Spline_(mathematics)