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DynamicModule, Speed, and locally static variables.

• To: mathgroup at smc.vnet.net
• Subject: [mg82003] DynamicModule, Speed, and locally static variables.
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Tue, 9 Oct 2007 05:36:51 -0400 (EDT)

Dear Mathematica Group,

Sorry for the long question on combining Module, 
DynamicModule, LocatorPane, Manipulate to produce a 
GraphicsRow.

I am in the middle of designing small program that uses 
Locator to find the position of a dynamic point and 
Manipulate to control the shape of the locator, and then
compute an expensive result based on the position (from LocatorPlane)
and the size (from Manipulate).

Some calculations are expensive and don't depend on the 
locator position or shape.  Other calculations are 
expensive and do depend on the locator's position and size.

I am wondering how to scope this.  Do I pay a penalty for 
local variables in DynamicModule that won't change?

Here is what I am trying, I've made up an artificial
example below that will (hopefully) show what I am  trying to do.
It is not working; I am not sure why, but guessing that it
has to do with variable scope.

I am hoping for two kinds of help:
1) that someone can comment about computational efficiency and
dynamic variable scope.
2) that someone could point to a demo which does something similar.
3) I believe that I should be using ControlActive to 
separate the time scales from locator movement and graphics 
production. I can't quite see how that should appear here, 
yet.

Does it make sense to have the following
Module[DynamicModule[Manipulate[Locator]]] scoping?
----example-----
demo[f_] :=
  Module[{StaticExpression=ExpensiveFunction[f],
          StaticImage3D,StaticContourPlot,
              PositionInit={1,2}, LocatorSizeInit=1}, (*vars that don't change*)
         StaticImage3D=Plot3D[StaticExpression];
         StaticContourPlot=ContourPlot[StaticExpression]
   GraphicsRow[ (*draw three graphics, 1-fixed, 2-manipulate, 3-result of dynamic variable and manipulate*)
     Flatten[
      {
        StaticImage, (*first-image*)
          DynamicModule[newdata,{position=PositionInit,LocatorShape=Graphics[g[PositionInit,LocatorSizeInit]]},
           {Manipulate[ (*manipulate returns a graphics object?*)
             LocatorShape=Graphics[position,size]; (*dynamic*)
             newdata=ExpensiveCalculation[position,size,StaticExpression];
             LocatorPlane[Dynamic[position],StaticContourPlot,Appearance->LocatorShape],(*draw dynamic locator on static image*)
           {{size,LocatorSizeInit},0,1}],
         ArrayPlot[ExpensivistCalc[position, size, StaticExpression]] (*the final graphics object and most expensive*)
           }
       }
       ] (*dynamic module*)
      ] (*flatten*)
     ] (*graphicsrow*)
  ] (*module*)


W. Craig Carter

• Follow-Ups:
  • Re: DynamicModule, Speed, and locally static variables.
    • From: "W. Craig Carter" <ccarter@mit.edu>