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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)

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    As a general rule, if a Google search for a term doesn't yield a Wikipedia or MathWorld or PlanetMath article as one of the first hits, and instead your own question appears as one of the first hits, it's a good idea to include a definition of that term in the question.2012-11-30
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    Even if the definition is googleable, it is a good idea to make it easy for people to answer the question by providing the definition.2012-11-30
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    Two links added for more information on Clothoid and Splines.2012-11-30
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    In many practical applications, you only use rather short or rather straight parts of a clothoid, such that any local distance minimum would be a global minimum as well. Is this the case for the individual pieces of your spline as well? If so, you could compute the distance with respect to every piece using some iterative solution, like bisection in the simplest of cases. Otherwise you'd probably need to find the correct “layer” first.2012-11-30
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    This is true for my problem: we use rather short and straight parts of the clothoid. The problem domain is road and rail geometry; a road/rail is built of straight lines, arcs and "non-aggressive" clothoids. We need this to be solved as a part of an extensive optimization algorithm, hence the method need to be as fast as possible. **Analytic solution is preferrable if such exists?** Bisection seems to be slow, but may be used to generate a starting guess for a faster algorithm.2012-11-30

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