arrows in the middle of bezier curves

[Paulo Abreu]

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Hi, all!

This is my first message to this list.

I consider PsTricks a wonderfull package for (La)TeX.

I am typesetting a book about differential equations,
with lots of curves and arrows, and graphs and
shadded regions, and pstricks is a great help. Just
creating each graphic with CorelDraw or
Mathematica wasn't enough for the high quality
output needed. Pstricks is the package for the job.

There is, however, a small feature that I miss a lot:
the ability to put an arrow automaticaly in the middle
of a curve.

I am able to create that arrow when I
can draw the curve parametricaly: I simply draw part of
the curve with the arrow I need, and then another
part, and so on, until the curve is complete. Some times
I need to go back a little to draw over the tip of
the last arrow, but that's not really a problem.
E.g., here's how I draw a circle with radius R
with two arrows in it:
\psset{arrows=->}
\parametricplot{0}{182}{%
   R t cos mul R t sin mul}
\parametricplot{180}{362}{%
   R t cos mul R t sin mul}

(note: (R*cos(t), R*sin(t)) with  0 < t <= 360 is a circle)

The thing is more complicated when I want to have
arrows somewhere in the middle of a bezier curve.
The only solution I found for that is to print the curve,
measure on the paper where I want to put the arrows and
where will they point to, and then draw a \psline with
[linestyle=none] and with {->} or whatever arrow, so that
the arrow falls in the curve and points the right direction.
This methode is cumbersome, slow and needs lots of adjustments.

Has anyone got a better suggestion? 

I have also tried to split the bezier curve in the point
where I want the arrow to appear, but this involves two
problems: 
1. more calculations to fit two curves to the path of one
(anyone has an algorithm to find the points of two
bezier curves that fit into the path of a third one,
given the points of the third curve?)
2. even when the two curves fit, it is usually necessary
to overlap them a bit, so that the tip of the arrow
is inside of a curve.

I am also aware of the \arrows{...} command, but I think
that it isn't the solution (or I am missing something there?)

I hope I wasn't to unclear stating the problem. It is
always hard to describe a graphic, and the task is even
harder when it is not in your language.

Thanks to everybody that helped making PsTricks the
good and powerful package I enjoy so much!

Paulo


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