Experiment with New Forms of Controls

New in Wolfram Mathematica 6: Symbolic Interface Construction

Mathematica 6 provides an unprecedentedly flexible interface experimentation system, allowing not only traditional controls, but arbitrary graphics, layout and actions, as well as connection to arbitrary human interface devices.

In[1]:=

CircularWinder[Dynamic[\[Theta]_]] := 

 DynamicModule[{}, 

  Deploy[EventHandler[

    Graphics[{GrayLevel[0.97], Disk[{0, 0}, 1], GrayLevel[0.5], 

      Circle[{0, 0}, 1], GrayLevel[0.8], Circle[{0, 0}, 0.98], Black, 

      Disk[{0, 0}, 0.01], Arrowheads[0.1], 

      Arrow[{{0, 0}, Dynamic[{Cos[\[Theta]], Sin[\[Theta]]}]}], 

      Darker[Cyan, 0.5], 

      Dynamic[First[

        ParametricPlot[

         Evaluate[((Sign[\[Theta]] t)/50)*{Cos[t], Sin[t]}], {t, 

          0, \[Theta] + 0.001}]]]}, ImageSize -> 200, 

     PlotRange -> 1.1], 

    "MouseDragged" :> 

     Module[{\[Alpha], dir, 

       r = MousePosition["Graphics"], \[Beta] = 

        ArcTan[Cos[\[Theta]], Sin[\[Theta]]] + 

         If[Sin[\[Theta]] < 0, 2 \[Pi], 0]}, 

      If[r == {0, 0}, r = {1, 0}];

            

      If[! VectorQ[r, NumericQ], r = {Cos[\[Theta]], Sin[\[Theta]]}];

            \[Alpha] = ArcTan @@ r + If[r[[2]] < 0, 2 \[Pi], 0];

            dir = Mod[\[Alpha] - \[Beta], 2 \[Pi]];

            \[Theta] += 

       If[dir < 5, dir, -Mod[-\[Alpha] + \[Beta], 2 \[Pi]]];]]], 

  Initialization :> If[! NumericQ[\[Theta]], \[Theta] = 0]]

In[2]:=

DynamicModule[{a = 0, b = 0}, 

 Column[{{CircularWinder[Dynamic[a]], CircularWinder[Dynamic[b]]}, 

   Framed[Dynamic[{a, b, a - b, a + b}], Background -> LightYellow]}, 

  Center]]

Out[2]=