An easy way to look at the problem might be to use a simple spiral with the
radius as a direct function of the turned angle. Dead simple to calculate.

Ralf Muschall <rmu### [at] t-onlinede> wrote in message
news:388### [at] t-onlinede...
> 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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