Circular/Angular slider

Question

A recent SO question reminded me of some code I tried to write a while back. The aim is to make a CircularSlider[] object that can be used for angle-like variab

Answer 1

As for problem#1, I wouldn't consider the use of the second argument to Dynamic as a kludge -- that is what the second argument is for. Therefore, I don't have an alternative solution for that one.

Problem #2 can be avoided if you refrain from assigning t in the first argument to Dynamic.

With this in mind, here is another implementation:

CircularSlider2[Dynamic[t_], r:{min_, max_}:{0, 1}] :=
  DynamicModule[{scale, toXY, fromXY},
      scale = (max - min) / (2. Pi);
      toXY[a_?NumberQ] := Through@{Cos, Sin}[a / scale];
      toXY[a_] := {1, 0};
      fromXY[{x_, y_}] := Mod[Arg[x + I y] scale, max, min];
      LocatorPane[
        Dynamic[toXY[t], (t = fromXY[#])&],
        Graphics[{
            AbsoluteThickness[1.5], Circle[],
            Dynamic[{Text[NumberForm[t, {3,2}], {0, 0}]}]
          }],
        ImageSize -> Small
      ]
  ]

The only material difference between this version and the original version is that the first argument to Dynamic is an expresssion that is free of side-effects.

---

Edit

I just stumbled across this undocumented experimental feature in Mathematica 8:

DynamicModule[{x = RandomReal[{0, 50}]},
  {Experimental`AngularSlider[Dynamic@x], Dynamic@x}
]