I wanted to write a private message to you but I couldn't due to reputation points.
Above, I promised to inform you when I achieved some results in my project. Unfortunately I didn't manage to build the projective plane yet, but I wrote a little article explaining the whole project here
http://matheplanet.com/default3.html?article=1533
It's in german only because it's a german website, sorry for that. But I gave credit to you regarding the maple project and I attached the plots for building the projective plane.

I wanted to write a private message to you but I couldn't due to reputation points.
Above, I promised to inform you when I achieved some results in my project. Unfortunately I didn't manage to build the projective plane yet, but I wrote a little article explaining the whole project here
http://matheplanet.com/default3.html?article=1533
It's in german only because it's a german website, sorry for that. But I gave credit to you regarding the maple project and I attached the plots for building the projective plane.

@Preben Alsholm 

Yeah I like this solution better, thanks! Now I'll start another try plotting...

@Preben Alsholm 

Yeah I like this solution better, thanks! Now I'll start another try plotting...

I found a little issue now. Your first code for the radial curves doesn't work so well with special values of alpha=Pi/10. See here (the code works for other alpha, I just modified the layout and the output routines)

ProjRad.mw

So I took your last code (my version only with minor changes: ProjConc.mw) and tried to change the type of curve to radial which seemed easy enough, but this resulted in an error

Error, (in f) unable to store 'HFloat(HFloat(undefined))+HFloat(HFloat(undefined))*I' when datatype=float[8]

in the dsolve command. Heres the code:

ProjRadX.mw

Could you have a look at it please?

EDIT: Ok I have found the problem in ProjRadX.mw. I now changed the "start" value in dsolve to a near zero value 0.0000000001. Is this a dirty solution?? But it works also for Pi/10 and is faster than ProjRad.mw.

I found a little issue now. Your first code for the radial curves doesn't work so well with special values of alpha=Pi/10. See here (the code works for other alpha, I just modified the layout and the output routines)

ProjRad.mw

So I took your last code (my version only with minor changes: ProjConc.mw) and tried to change the type of curve to radial which seemed easy enough, but this resulted in an error

Error, (in f) unable to store 'HFloat(HFloat(undefined))+HFloat(HFloat(undefined))*I' when datatype=float[8]

in the dsolve command. Heres the code:

ProjRadX.mw

Could you have a look at it please?

EDIT: Ok I have found the problem in ProjRadX.mw. I now changed the "start" value in dsolve to a near zero value 0.0000000001. Is this a dirty solution?? But it works also for Pi/10 and is faster than ProjRad.mw.

@Preben Alsholm Oh you must be right, I probably screwed your first code, your last worksheet seems to work perfectly. I don't know how you managed this yet, but I will have a closer look at it, then modify it to make hi-res plots of a suitable collection of curves. After that I'll have to photoshop the plots (thickening to stripes, cutting into pieces,...) print them and build them together. I'll let you know when i have managed this. Thank you for the help so far!

@Preben Alsholm Oh you must be right, I probably screwed your first code, your last worksheet seems to work perfectly. I don't know how you managed this yet, but I will have a closer look at it, then modify it to make hi-res plots of a suitable collection of curves. After that I'll have to photoshop the plots (thickening to stripes, cutting into pieces,...) print them and build them together. I'll let you know when i have managed this. Thank you for the help so far!

Hello Preben and Georgios, thank you for your answers.

The problem is, that calls like res(0.5) or ans(0.5) are expensive and should be avoided. So you say that I cannot extract e.g. x(0.5) from the odeplot result? How can I make the res(0.5) calls faster, or, how can I tell odeplot to calculate also the values at 0.5,0.6,etc. It seems that odeplot calculates the values much faster than res(0.5).

Hello Preben and Georgios, thank you for your answers.

The problem is, that calls like res(0.5) or ans(0.5) are expensive and should be avoided. So you say that I cannot extract e.g. x(0.5) from the odeplot result? How can I make the res(0.5) calls faster, or, how can I tell odeplot to calculate also the values at 0.5,0.6,etc. It seems that odeplot calculates the values much faster than res(0.5).

Ok, i checked your code now. unfortunately i have to compute other types of curves c, too. Instead of linear i have to compute the same thing for circle curves c(t)=a*exp(2*Pi*I*t) which is even more complex. Meanwhile i have modified my own code. The calculation takes 15min and memory stays at 75M. With your code, the maple server eats my complete 4gigs of ram, so i don't think the calculation can be done in a reasonable amount of time. Ok now, i have to plot 20 curves of this type, this is ok with 15mins per plot. The problem is that i still have to plot markings at specific parameter values (the blue points in your code), 40 per plot. This is done by calling subs(p(t),b(s)) 40 times, where p is the dsolve result. This takes even more time than the odeplot call?!? So i have posted another Q for this:

http://www.mapleprimes.com/questions/137618-Extracting-Values-From-Odeplot

Heres the code with the circle curves:

concentric.mw

Of course I'm still interested in code which is faster than mine. ;)

Ok, i checked your code now. unfortunately i have to compute other types of curves c, too. Instead of linear i have to compute the same thing for circle curves c(t)=a*exp(2*Pi*I*t) which is even more complex. Meanwhile i have modified my own code. The calculation takes 15min and memory stays at 75M. With your code, the maple server eats my complete 4gigs of ram, so i don't think the calculation can be done in a reasonable amount of time. Ok now, i have to plot 20 curves of this type, this is ok with 15mins per plot. The problem is that i still have to plot markings at specific parameter values (the blue points in your code), 40 per plot. This is done by calling subs(p(t),b(s)) 40 times, where p is the dsolve result. This takes even more time than the odeplot call?!? So i have posted another Q for this:

http://www.mapleprimes.com/questions/137618-Extracting-Values-From-Odeplot

Heres the code with the circle curves:

concentric.mw

Of course I'm still interested in code which is faster than mine. ;)

uhh, this is a rich answer, that will take some time to get through. Thank you. :)

uhh, this is a rich answer, that will take some time to get through. Thank you. :)

I guess you use too much symbolics.

Yeah, I thought the same too, bit how can I do it differently? How to avoid symbolic calculation?