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Brentt
Posts:
60
Registered:
9/24/11


Eternal Trouble with Dynamic: fishing for tips on my coding process?
Posted:
Jan 18, 2013 12:50 AM


Hi, everytime I think I have Dynamic down it seemingly inexplicably breaks. I'd much appreciate if I could step through the process that leaves me with code that, with one small change, just stops working. (Maybe some designers might get something out of seeing the coding process of an idiot?)
So I want to draw a set of points on a graphic and then show a dynamically updated interpolating function for those points. This is my interpolating function, having this dynamically update upon drawing a set of points in the graphic is the goal:
parametricInterpolation[param_, pointList_] := > Function[{t}, > Function[{f}, f[t]] /@ > Quiet[(ListInterpolation /@ Transpose[pointList])]][param]; >
The function works if I take a random set of points. So I set it aside to get the dynamic interface working using a more simple function in its place (just so I know if any problems arise, which they have, it has nothing within the above slightly complicated function. )
Ok, so here is where I start. The point set are to be drawn when the mouse is dragged on the graphic. To keep the code as simple as possible I start with a point at the origin:
DynamicModule[ > {r = {{0, 0}}, interpol = {}}, > > interpol = > Dynamic@If[Length[r] >= 3, Circle[Last[r], 1/Length[r]], {}]; > EventHandler[ > Show[ > { > Graphics[{Line[Dynamic[r]]}], > Graphics[{interpol}] > }, > PlotRange > ( { > {1, 1}, > {1, 1} > } ) > ], > {"MouseDragged" :> (r = > DeleteCases[AppendTo[r, MousePosition["Graphics"]], None])}] > ] >
The variable interpol is going to eventually hold my interpolating function. Since it needs at least 3 points to work properly, I have the conditional so it need not evaluate until at least 3 points are drawn. The Circle[Last[r], 1/Length[r]] I'm using as a test function in the interpolating function's place. (it simply draws a circle which shrinks as function of the the number of points).
Code works so far. But the problem is I need the interpolating function to be plotted using ParametricPlot. I need to replace Graphics[{Interpol}] with a ParametricPlot.
Now this seems like it should be a rather simple step. But alas, no such luck. My apparently naive approach is to have interpol hold a graphics object, and then use that as an element in Show's list argument. This way, if it would work for the simpler function which draws the shrinking circle, it would just be a matter of replacing this with a ParametricPlot which plots my interpolation function. But the code breaks before I even get there. Here is the seemingly small step that breaks the code
DynamicModule[ > {r = {{0, 0}}, interpol = {}}, > > interpol = > Dynamic@If[Length[r] >= 3, Graphics[{Circle[Last[r], 1/Length[r]]}], > Graphics[{}]]; > EventHandler[ > Show[ > { > Graphics[{Line[Dynamic[r]]}], > interpol > }, > PlotRange > ( { > {1, 1}, > {1, 1} > } ) > ], > {"MouseDragged" :> (r = > DeleteCases[AppendTo[r, MousePosition["Graphics"]], None])}] > ] >
With the result
Show::gcomb: Could not combine the graphics objects in Show[{\!\(\* GraphicsBox[LineBox[Dynamic[r$4494]]]\),\!\(\* GraphicsBox[{}]\)},PlotRange>{{1,1},{1,1}}]. >>
I'm not sure what to make of the error message. It seems like what I did should work. I'm just passing a graphics object instead of an argument for Graphics and I'm not sure why should that be a problem? Is there something about Graphics that behaves differently that other functions I suppose, but I haven't been able to discern what that is. Any tips would be greatly appreciated (whether it is about this code in particular, or anything about the process. And please forgive me if I seem thick, I'm an undergraduate mathematics major, but not a terribly good one. This isn't for school work, I'm just trying to figure out Mathematica to explore ideas I've learned about. I feel like I have a good sense of how it works except when it comes to this Dynamic functionality.)



