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I have a list of elements where the first 3 numbers in each curly bracket are x,y,z coordinates and the last number is an intensity:

data = {{2, 2, 2, 30}, {0, 0, 0, 10}, {1, 0, 0, 10}, {2, 0, 0, 
   10}, {3, 0, 0, 10}, {4, 0, 0, 10}, {0, 0, 4, 10}, {1, 0, 4, 
   10}, {2, 0, 4, 10}, {3, 0, 4, 10}, {4, 0, 4, 10}, {0, 4, 0, 
   10}, {1, 4, 0, 10}, {2, 4, 0, 10}, {3, 4, 0, 10}, {4, 4, 0, 
   10}, {0, 4, 4, 10}, {1, 4, 4, 10}, {2, 4, 4, 10}, {3, 4, 4, 
   10}, {4, 4, 4, 10}, {0, 1, 0, 10}, {0, 2, 0, 10}, {0, 3, 0, 
   10}, {0, 1, 4, 10}, {0, 2, 4, 10}, {0, 3, 4, 10}, {0, 0, 1, 
   10}, {0, 0, 2, 10}, {0, 0, 3, 10}, {0, 4, 1, 10}, {0, 4, 2, 
   10}, {0, 4, 3, 10}, {4, 1, 0, 10}, {4, 2, 0, 10}, {4, 3, 0, 
   10}, {4, 1, 4, 10}, {4, 2, 4, 10}, {4, 3, 4, 10}, {4, 0, 1, 
   10}, {4, 0, 2, 10}, {4, 0, 3, 10}, {4, 4, 1, 10}, {4, 4, 2, 
   10}, {4, 4, 3, 10}, {1, 1, 1, 20}, {2, 1, 1, 20}, {3, 1, 1, 
   20}, {1, 1, 3, 20}, {2, 1, 3, 20}, {3, 1, 3, 20}, {1, 3, 1, 
   20}, {2, 3, 1, 20}, {3, 3, 1, 20}, {1, 3, 3, 20}, {2, 3, 3, 
   20}, {3, 3, 3, 20}, {1, 2, 3, 20}, {3, 2, 3, 20}, {1, 2, 1, 
   20}, {3, 2, 1, 20}}

The data represents points comprised within a cube, where the point with the max intensity is in the middle and the intensity then decreases as the points are further away from the middle. The points in space look as shown:

pts = data[[1 ;;, {1, 2, 3}]];
ListPointPlot3D[pts, PlotStyle -> PointSize -> Medium]

enter image description here

I am trying to find the best way to visualise such data. So far I tried the following:

ListPlot3D[data, PlotRange -> All, Mesh -> None, 
 PlotLegends -> Automatic, ColorFunction -> "Rainbow", 
 PlotLabel -> Style["Intensity", FontSize -> 14]]

enter image description here

 ListContourPlot3D[data, PlotRange -> All, PlotLegends -> Automatic, 
     Contours -> 1, MaxPlotPoints -> 100, ColorFunction -> "Rainbow", 
     PlotLabel -> Style["Intensity", FontSize -> 14]]

enter image description here

Can anyone suggest a way of visualising such data showing the variation of intensity throughout the cube? Perhaps like a transparent thermal plot or a surface connecting all the points of common intensities together...

I am using Mathematica 10.0.1.0

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4 Answers 4

Reset to default
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Example: 

ListDensityPlot3D @ data

Note: In the above data is the data you've posted in your original post.

Output:

example

Reference:

ListDensityPlot3D

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  • $\begingroup$ Thank you @E.Doroskevic, I was unaware of this function and it was released in version 10.2. Is there a way to do this with previous versions of Mathematica (10.0)? $\endgroup$
    – GEF
    Jun 15, 2016 at 9:50
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    $\begingroup$ @GEF Hi, I will try something out later on in the day. For now, I would suggest to use one of the alternative solutions proposed above! $\endgroup$
    – e.doroskevic
    Jun 15, 2016 at 10:32
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You can color the data points according to their intensity.

i1 = Min[data[[All, 4]]]; i2 = Max[data[[All, 4]]];
r = 0.1;
Grid[{{Graphics3D[{ColorData["Rainbow"][(#[[4]] - i1)/(i2 - i1)], 
   Sphere[#[[1 ;; 3]], r]} & /@ data, ImageSize -> 300, Axes -> True],
BarLegend[{"Rainbow", {i1, i2}}]}}]

enter image description here

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atoms = {"H", "O", "N"};
gr1 = Graphics3D[{ColorData["Atoms", atoms[[#[[4]]/10]]], 
 Sphere[#[[1 ;; 3]], #[[4]]/30]} & /@ data, Lighting -> "Neutral"]

enter image description here

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You could try BubbleChart3D that uses the 4th element in the list as the size of the sphere:

enter image description here

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