Restarting an Animate animation after variable in Manipulate changes

Question

I've been trying to restart an animation after variables change from Manipulate PopUpMenus. My animation takes the form:

Animate[expr, {u, umin, umax, du}]. 

I can change u, after variations to Manipulate, back to an initial value momentarily, but from there u jumps back to its previous position (or farther forward) as if its continued running. I would be content with simply restarting the entire animation after changing the Manipulate variables.

My code for Animate[] is in the following simplified form (I hope to make the i slider bar return back to the left and the red dot to begin being plotted at x=-10 each time the function is changed):

gPrev[x_] := Sin[x];
Manipulate[
 Switch[functionNumb, 
   0, g[x_] := Sin[x], 
   1, g[x_] := Cos[x], 
   2, g[x_] := ArcTan[x]], 
 {functionNumb, 0, 2, 1}]

Animate[
 Plot[{g[x]}, {x, -10, 10}, 
   Epilog -> {Red, PointSize[0.015], Point@{i, g[i]}}], {i, -10, 10, 1}, 
   DisplayAllSteps -> True, AnimationRunning -> False]

Answer 1

Not a complete answer yet: I've built the functionality using DynamicModule and Animator, thinking that it will be possible to manually set the index i when using the second argument of Dynamic. Sadly this only works if the animation is not running. So if the animation is not running i is reset correctly. Still, here is the code

EDIT Stealing from Kuba, I'm 80% there. The animation is restarted, but the old animation state is lost. In other words, changing the function will always run the animation.

DynamicModule[{i = -10, f = Sin, run = False}, 
 Column@{SetterBar[
    Dynamic[f, (i = -10; run = False; FinishDynamic[]; run = True; 
       Print@i; f = #) &], {Sin, Cos, ArcTan}], 
   Dynamic@Animator[Dynamic[i], {-10, 10, 0.1}, 
     ContinuousAction -> True, AnimationRunning -> run], 
   Dynamic@Plot[{f[x]}, {x, -10, 10}, ImageSize -> Medium, 
     Epilog -> {Red, PointSize[0.015], Point@{i, f[i]}}]}]

Answer 2

First I've give one way that fits with the setup in your question, and then I'll give the way I would do it myself, in case that helps.

---

Wrap Animate in Dynamic and make it track g; also keep the Manipulate from tracking g. Wrapping Animate will make it reset whenever g is changed.

gPrev[x_] := Sin[x];
Manipulate[
 Switch[functionNumb, 0, g[x_] := Sin[x], 1, g[x_] := Cos[x], 2, 
  g[x_] := ArcTan[x]]; g[x], {functionNumb, 0, 2, 1}, 
 TrackedSymbols :> {functionNumb}]

Dynamic@Animate[
  Plot[{g[x]}, {x, -10, 10}, 
   Epilog -> {Red, PointSize[0.015], 
     Dynamic@Point@N@{i, g[i]}}], {i, -10, 10, 1}, 
  DisplayAllSteps -> True, AnimationRunning -> False, 
  TrackedSymbols -> {g}]

---

Here's a single Manipulate that has the same functionality, as I see it, and a more integrated look.

Manipulate[
 Column[{
   i = -10; 
   Animator[Dynamic[i], {-10, 10, 1}, AnimationRunning -> False],
   Plot[function, {x, -10, 10}, 
    Epilog -> {Red, PointSize[0.015], Dynamic@Point@N@{i, function /. x -> i}},
    ImageSize -> Medium]
   }],
 {function, {Sin[x], Cos[x], 2 ArcTan[x]}},
 {i, -10, 10, 1, ControlType -> None},
 TrackedSymbols :> {function}]

Putting the Animator in the control area is a bit trickier, it seems. It can be done, but my solution is a bit too kludgy to post.