Question: Controlling animations better

Dear Maple users

I like to use animations in Maple for different educational purposes. The other day I tried making an animation simulating a simplified Epicycle, which is a small circle with its centre running on a larger circle. The smaller one has a ball running on it with a constant velocity. I used the following code:

> with(plots);
> with(plottools);
> omega := 1; k := 5; R := 5; r := 2;
> plot1 := plot([R*cos(omega*t), R*sin(omega*t), t = 0 .. 2*Pi]);
> Epi := proc (t) display(circle([R*cos(omega*t), R*sin(omega*t)], r, color = red), disk([R*cos(omega*t)+r*cos(k*t), R*sin(omega*t)+r*sin(k*t)], .2, color = blue)) end proc;
print(`output redirected...`); # input placeholder
> animate(Epi, [t], t = 0 .. 2*Pi, background = plot1, frames = 50, trace = 0, scaling = constrained);

My problem: I want to have the curve travelled by the ball displayed in the animation. To do so I set trace to trace=50, but then I also get a trace of the smaller circle, which is not my intention. I don't see any solution to this problem, but I guess it can be done. How?

Another thing: It seems that animations take up a lot of space. Why aren't those animations made on a vector basis, but (as it seems) as bitmaps? Using vector graphics means a large save in space, time and quality as long as the objects can be mathematically represented. The free program "Geogebra" seems to do this job much better. Couldn't Maple do a better job here?



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