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I am trying to show and calculate the area of two overlapping, shifted hexagons using the following code:

Needs["Polytopes`"]; DynamicModule[{tv, r, pt, sup},
LocatorPane[Dynamic[pt],
tv = Dynamic@TranslationTransform[pt][Vertices[Hexagon]];
r = Dynamic@RegionIntersection[{MeshRegion[Vertices[Hexagon], 
    Polygon[{1, 2, 3, 4, 5, 6}]], MeshRegion[tv, Polygon[{1, 2, 3, 4, 5, 6}]]}];
sup = Dynamic@Chop[N@RegionMeasure[r, 2], 10^-5];
If[Length[r] == 0, 
   Dynamic@Show[{RegionPlot[r], 
      Graphics[{{EdgeForm[Thick], White, Opacity[0], 
         Polygon[Vertices[Hexagon]]}, {EdgeForm[Thick], White, 
         Opacity[0], Polygon[tv]}}]}, Frame -> True, 
     PlotLabel -> "Area = " <> ToString[sup], 
     PlotRange -> {{-1, 3}, {-3, 3}}, AspectRatio -> 5.5/4], 
   Dynamic@Show[
     Graphics[{{EdgeForm[Thick], White, Opacity[0], 
        Polygon[Vertices[Hexagon]]}, {EdgeForm[Thick], White, 
        Opacity[0], Polygon[tv]}}], Frame -> True, 
     PlotLabel -> "Area = 0", PlotRange -> {{-1, 3}, {-3, 3}}, 
     AspectRatio -> 5.5/4]
   ]
  ]
 ]

My problem is that I cannot figure out why the intersection region is not plotted.

I obtain something like this:

enter image description here

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  • $\begingroup$ Dynamic@TranslationTransform[pt][Vertices[Hexagon]]; does nothing. Dynamic updates pixels on the screen so whenever you have Dynamic@Something; nothing is being updated. $\endgroup$ – Mike Honeychurch Nov 13 '14 at 21:32
3
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Too many Dynamics and in the wrong place:

DynamicModule[{tv, r, pt = {1., 0.}, sup},
 LocatorPane[Dynamic[pt],
  Dynamic[
   tv = TranslationTransform[pt][Vertices[Hexagon]];
   r = RegionIntersection[{MeshRegion[Vertices[Hexagon], 
       Polygon[{1, 2, 3, 4, 5, 6}]], 
      MeshRegion[tv, Polygon[{1, 2, 3, 4, 5, 6}]]}];
   sup = Chop[N@RegionMeasure[r, 2], 10^-5];
   If[Length[r] == 0, 
    Show[{RegionPlot[r], 
      Graphics[{{EdgeForm[Thick], White, Opacity[0], 
         Polygon[Vertices[Hexagon]]}, {EdgeForm[Thick], White, 
         Opacity[0], Polygon[tv]}}]}, Frame -> True, 
     PlotLabel -> "Area = " <> ToString[sup], 
     PlotRange -> {{-1, 3}, {-3, 3}}, AspectRatio -> 5.5/4], 
    Show[Graphics[{{EdgeForm[Thick], White, Opacity[0], 
        Polygon[Vertices[Hexagon]]}, {EdgeForm[Thick], White, 
        Opacity[0], Polygon[tv]}}], Frame -> True, 
     PlotLabel -> "Area = 0", PlotRange -> {{-1, 3}, {-3, 3}}, 
     AspectRatio -> 5.5/4]]]]]

Mathematica graphics

Notes: (1) In your code, you have a couple of assignments like

tv = Dynamic@TranslationTransform[pt][Vertices[Hexagon]];

This means that tv would never be equal to TranslationTransform.... Dynamic[code] does not return the value of code. It holds code unevaluated to be interpreted by the Front End. When and if the Front End sees output to be displayed that contains Dynamic[code], it shows the current value of code and updates it according to the rules of dynamic updating (which are complex). This sort of assignment is rare, since one usually wants to use result, not just display it -- in your case, the translated hexagon tv is used to compute r.

(2) I removed the Dynamic around Show. The use of Dynamic inside a code block is to mark code that can be updated and displayed independently of some other variables. But the whole code displayed by the LocatorPane is a function of pt; it all needs to be evaluated whenever pt moves.

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  • $\begingroup$ Nice explanation regarding the use of "Dynamic" $\endgroup$ – José Antonio Díaz Navas Nov 14 '14 at 10:23

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