Question: How to color an odeplot given a function of some dependent variable?

restart

with(plots):

sys := {
   diff(x(t), t) = v(t)
  ,diff(v(t), t) = cos(t)
  ,x(0) = -1
  ,v(0) = 0

  ,px(t) = piecewise(x(t) >=0, 1, -1)
  ,pv(t) = piecewise(v(t) >=0, 1, -1)
}:

sol := dsolve(sys, numeric):

 

odeplot(sol, [t, x(t), v(t)], t=0..4*Pi)
 

# I would like to color this space curve depending on the signs of x(t) and y(t)
#
# for instance, f being a "color function"
f := proc(s)
  local a, b:
  if s::numeric then
    a := round(eval(px(t), sol(s))):
    b := round(eval(pv(t), sol(s))):
    return piecewise(a+b = 2, "Green", a = 1, "Red", b = 1, "Blue", "Gold")
  end if:
end proc:

SOL := proc(s)
  if s::numeric then
    eval([t, x(t), v(t)], sol(s))
  end if:
end proc:


# I would like to make something like this to work

plot3d(SOL(s), s=0..4*Pi, colorfunc=f(s)):  #... which generates a void plot


 

# In some sense a continuous version of this

opts := symbol=solidbox, symbolsize=20:
display( seq(pointplot3d({SOL(s)}, opts, color=f(s)), s in [seq](0..6, 0.1)) );