New package for drawing direction fields with gnuplot

Valery Pipin <pip at iszf.irk.ru> writes:
>> > For a brief demonstration of drawdf's capabilities, please see:
>> >    http://www.netris.org/~mhw/maxima/drawdf-demo.html
>> > 
> I wonder if the things that shown in the demo would be possible to extend
> for 3d field.

I see no great difficulty in converting drawdf to use 3d.  However, it
would require a large number of changes throughout the code, and would
reduce its efficiency in the 2d case.  As Mario suggested, a 3d version
of drawdf should probably be based on model3d instead of draw3d.

I won't have time to make these changes anytime soon, but if you'd like
to work on this, I'd be glad to give some hints to get you started, and
to answer any questions you might have.

> The complication is that field components are not given in analytical
> form they are results of simulation

This is not a serious problem, as long as it is possible to obtain first
derivatives at any point in the field.  Second derivatives are also
required to plot quadratic splines (field_degree=2).

You should also be able to plug in your own integrator if needed, but if
you'd like to draw a field of many small numerical solutions
(field_degree='solns), your integrator must be able to automatically
stop at the edge of a given box, specified as intervals of x,y,z.

Only saddles_at() does non-trivial symbolic manipulation, requiring both
second derivatives and the eigenvalues and eigenvectors of the
linearized system, but this feature for convenience only, and can always
be replaced by solns_at().

     Best,
      Mark