I can't answer your question directly, but maybe this could be used as an option if u and v are intended to be constants.
restart:
assume(u::complexcons, v::complexcons);
Re(u) + Re(v) - Re(u+v);
Re(u) + Re(v) - Re(u + v)
evalc(%);
0

If you are thanking me there is no need. Any useful information I provided was purely accidental, a direct result of my lack of understanding (see comments below). So if any thanks are in order they are from me to you, Robert, DJ, and John, since I understand things a little better now.
Also, I have a mac so I have never seen classic. I know that the experienced users seem to prefer it. I wish there were a mac version.
Thanks again,
Thomas

If you are thanking me there is no need. Any useful information I provided was purely accidental, a direct result of my lack of understanding (see comments below). So if any thanks are in order they are from me to you, Robert, DJ, and John, since I understand things a little better now.
Also, I have a mac so I have never seen classic. I know that the experienced users seem to prefer it. I wish there were a mac version.
Thanks again,
Thomas

Now I see it. Just more evidence that I should read more and post less. Sorry for the mess. Thanks!

Now I see it. Just more evidence that I should read more and post less. Sorry for the mess. Thanks!

Ok, now I really don't know what is going on. Look at this
restart:
p1,p2 := , :
r := t->piecewise(t<0, p1, p2):
r(1);
the output from r(1) is
versus
restart:
r:= t-> piecewise( t<0, , <0,t,0>):
r(1);
the output from r(1) is <0,1,0>
Why did Maple pass the argument to the component functions in the second case and not in the first? I guess my assessment above was premature. I am still thinking piecewise was not intended for vectors, but I don't know. I will leave it to the experts.

Ok, now I really don't know what is going on. Look at this
restart:
p1,p2 := , :
r := t->piecewise(t<0, p1, p2):
r(1);
the output from r(1) is
versus
restart:
r:= t-> piecewise( t<0, , <0,t,0>):
r(1);
the output from r(1) is <0,1,0>
Why did Maple pass the argument to the component functions in the second case and not in the first? I guess my assessment above was premature. I am still thinking piecewise was not intended for vectors, but I don't know. I will leave it to the experts.

BTW this is what I get with cut and paste and tags
Vector(3, {(1) = t, (2) = 0, (3) = t^3})
with lprint
Vector[column](3, {(1) = t, (3) = t^3}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

BTW this is what I get with cut and paste and tags
Vector(3, {(1) = t, (2) = 0, (3) = t^3})
with lprint
Vector[column](3, {(1) = t, (3) = t^3}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

I didn't mean to imply that piecewise was a problem. I was only pointing out that the construction
p1,p2 := , :
r :=t-> piecewise( t<0, p1, p2);
does not produce a vector valued function in the usual sense. It produces a function that maps the entire set of nonnegative reals onto the object , and the entire set of negative reals onto the object .
r(1) evaluates to rather than <1, 1, 0>.
It was not clear to me from your post whether or not this was the point you were making. I assumed you were wondering why it did not give <0,0,0> as the limit. Sorry for the confusion.

I didn't mean to imply that piecewise was a problem. I was only pointing out that the construction
p1,p2 := , :
r :=t-> piecewise( t<0, p1, p2);
does not produce a vector valued function in the usual sense. It produces a function that maps the entire set of nonnegative reals onto the object , and the entire set of negative reals onto the object .
r(1) evaluates to rather than <1, 1, 0>.
It was not clear to me from your post whether or not this was the point you were making. I assumed you were wondering why it did not give <0,0,0> as the limit. Sorry for the confusion.

I am not sure what you are after, since I cannot see the points on the plot from this example. However, from the title of your post it seems that animate may be of use to you. Here is a 2D example, from the help page, of a ball moving on a sine wave.
ball := proc(x,y) plots[pointplot]([[x,y]],color=blue,symbol=solidcircle,symbolsize=40) end proc:
animate(ball, [0,sin(t)], t=0..4*Pi, scaling=constrained, frames=100);
sinewave := plot( sin(x), x=0..4*Pi ):
animate( ball, [t,sin(t)], t=0..4*Pi, frames=50,
background=sinewave, scaling=constrained );
(You have to click on the plot and then click play)
Hope this helps.

I am not sure what you are after, since I cannot see the points on the plot from this example. However, from the title of your post it seems that animate may be of use to you. Here is a 2D example, from the help page, of a ball moving on a sine wave.
ball := proc(x,y) plots[pointplot]([[x,y]],color=blue,symbol=solidcircle,symbolsize=40) end proc:
animate(ball, [0,sin(t)], t=0..4*Pi, scaling=constrained, frames=100);
sinewave := plot( sin(x), x=0..4*Pi ):
animate( ball, [t,sin(t)], t=0..4*Pi, frames=50,
background=sinewave, scaling=constrained );
(You have to click on the plot and then click play)
Hope this helps.

You may be interested in looking at

carl-madigan/multivariable-calculus as a resource. I think it might offer you some ideas on how to use Maple to do some of the things you are using it for. I have looked at some of it and have found it to be very useful.

Robert,
Thanks, and my apologies to ichyfat and Acer for the misleading post above. It occurs to me that graph is the same in either case I stated above. This is simply more evidence that the we just can't get by without mathematicians:)
Thomas