function evaluations in graphic structures

[rcasini]

Greetings. I'm new to Maxima so it's possible the issue I'm having is just the result of my inexperience and incomprehension of how Maxima works.

My general problem can be stated this way: I need to plot parametric curves of the form

[ x(f(t; a,b,...)), y(f(t; a,b,...)) ]

where t is the true curve parameter, while a,b,... are parameters that identify different realizations within the same family of curves. The function f(t; a,b,...) can be a complicated one, but this doesn't seem to be relevant for the issue I'm having...

I want to plot a continuous parametric curve using

parametric( x(f(t; a,b,...)), y(f(t; a,b,...)), t, t_min, t_max )

say with nticks=100, and then put isolated points as markers at specific points along the curve, something that I do with

ptsarr: makelist( [ x(f(t; a,b,...)), y(f(t; a,b,...)) ], t, t_min, t_max, t_step )

It appears that while the parametric calculation runs like a breeze, even if f(t; a,b,...) is computing heavy, the creation of the point array becomes a frustrating time sink, even if the array has many fewer points than the nticks specified for the parametric curve.
What am I doing wrong? Or is this expected?

The funny thing is that this whole issue could be avoided if only parametric() allowed to plot the array as disconnected points (e.g., using the same point type specifications available in gr2d) rather than always as a continuous curve, in which case I'd use parametric() also for creating the point array rather than makelist(). Perhaps this could be an idea for upgrading parametric() in the future.

Thank you very much for any help you can provide!
Roberto

P.S. If interested, I'd be willing to share the actual wxMaxima notebook that I'm trying to "debug".