Manipulate for variable number of sliders

Question

I'm trying to use Manipulate for plotting multidimensional data, where higher dimensions are defined as sliders.

First, this simple example works:

myfun[v1_Real, v2_Real, v3_Real, v4_Real, v5_Real] := 
 Sin[v1]*Cos[v2]*v3 + v4*v5

Manipulate[
 Plot3D[myfun[v1, v2, v3, v4, v5], {v1, 0, 2}, {v3, 0, 2}], {{v5, 
   0.5}, 0., 1.}, {{v2, 0.5}, 0., 1.},(*{{v3,0.5},0.,1.},*){{v4, 0.5},
   0., 1.}]

But when the dimensions for plotting and for controls are configured to change dynamically, then Mathematica gets stuck:

Manipulate[
 With[{myaxis = Sequence @@ {{v[ax1], 0, 2}, {v[ax2], 0, 2}}, 
   mycontrols = 
    Sequence @@ {{{v[sl1], 0.5}, 0., 1.}, {{v[sl2], 0.5}, 0., 
       1.}, {{v[sl3], 0.5}, 0., 1.}}}, 
  Manipulate[Plot3D[myfun[v[1], v[2], v[3], v[4], v[5]], myaxis], 
   mycontrols]], {ax1, Range[1, 4, 1], ControlType -> Setter}, {ax2, 
  Range[ax1 + 1, 5, 1], ControlType -> Setter}, {sl1, 
  Complement[Range@5, {ax1, ax2}], ControlType -> Setter}, {sl2, 
  Complement[Range@5, {ax1, ax2, sl1}], ControlType -> Setter}, {sl3, 
  Complement[Range@5, {ax1, ax2, sl1, sl2}], ControlType -> Setter}]

How can I make the last piece of code to evaluate correctly?

Answer 1

This isn't quite what you asked, but it is hopefully giving the required result. The whole nested Manipulate with changing controls seemed like a can of worms to me.

Manipulate[
 If[oldax1 != ax1 || oldax2 != ax2,
  If[ax1 == ax2, ax2 = Mod[ax1, 5] + 1];
  oldax1 = ax1; oldax2 = ax2;
  set[ax1, ax2]];
 Plot3D[f[{a, b, c, v1, v2}], {v1, 0, 2}, {v2, 0, 2}],

 {{ax1, 1, ""}, {1, 2, 3, 4, 5}}, {{oldax1, 1}, None},
 {{ax2, 2, ""}, {1, 2, 3, 4, 5}}, {{oldax2, 1}, None},
 {{a, 0.5}, 0., 1.}, {{b, 0.5}, 0., 1.}, {{c, 0.5}, 0., 1.},
 {{sl1, 3}, None}, {{sl2, 3}, None}, {{sl3, 3}, None},
 Dynamic@f[{a, b, c, v1, v2}],
 Initialization -> {
   Clear[set, f];
   set[a1_, a2_] :=
     (ax1 = a1; ax2 = a2;
      With[{other = Complement[Range@5, {ax1, ax2}]}, 
       sl1 = other[[1]]; sl2 = other[[2]]; sl3 = other[[3]]];
      f[v_] := myfun[Permute[v, {sl1, sl2, sl3, ax1, ax2}]]
      );
   }]

There is no longer any changing controls, instead we just select which of the variables we plot against. These are fed into myfun by permuting the order of the variables (now passed a list instead of a sequence).

There are a few other tricks in here, which I might explain later if there is any interest.