cc wrote:

> I don't know anything about Bessel functions.  What are they?  And btw, no
> I'm not sure about anything regarding this :)

They are a sort of special functions. One obtains them either as
solutions of the wave equation in polar coordinates or as integrals
(hard ones, which cannot expressed by using only those functions
which are taught at school).

> When I was searching for the integrals, (and I'm not very exprienced) I
> tried simplifying the integral into something I knew how to deal with.   I

This can't work -- if it were possible, there were no need to
invent special functions.

> The other thing I wanted to ask you is where can I get information about
> Gradstein/Ryshik and Abramowitz/Stegun and Runge Kutta?  I'm very much a

The first is probably the most famous table of integrals and related
stuff, the other a collection of mainly definitions with an emphasis
on correctness (the less-used special functions are sometimes defined
by different specialists with different factors in front of them,
A/S tries to straighten this out). Both are probably useless unless
one is a mathematician, engineer or scientist.

I still believe that differentiation is better suited to your
problem than integration for the following reasons:

1. Even if you manage the integrals, you would have to compute
   the Bessel functions (or whatever) numerically. This either
   requires hacking the whole Netlib into POV (which would be a
   nice idea, btw. -- it would give a cool gnuplot replacement :-)
   ) or doing them slowly using #macro.
2. If you do it by integration, you input a strategy (steering
   and speed) and get some curve of the car. Since you probably
   want the curve to be where the street is, you have to use
   trial and error. The other way around, you just describe the
   street by a mathematical expression, and get the steering
   by some derivatives.

Ralf

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