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plotting - 3D heatmap density plot


I have a set of data that looks like {{x1, y1, z1}, {x2, y2, z2}, ...} so it describes points in 3D space. I want to make a heatmap out of this data. So that points with a high density are shown as a cloud and marked with different colors dependend of the density.


In fact, I want the result of this script just for 3D:


data = RandomReal[1, {100, 2}];
SmoothDensityHistogram[data, 0.02, "PDF", ColorFunction -> "Rainbow", Mesh -> 0]


enter image description here



Answer



If you want to plot a distribution that is three dimensional then first you need to form it! SmoothDensityHistogram plots a smooth kernel histogram of the values $\{x_i,y_i\}$ but as we have three dimensional data here we need the function called SmoothKernelDistribution!


data = RandomReal[1, {1000, 3}];
dist = SmoothKernelDistribution[data];

Now you have got the probability distribution with three variables. So we can simply plot the PDF as a 3d contour plot using ContourPlot3D. Keep in mind that this function is reputed to be little slow.


ContourPlot3D[Evaluate@PDF[dist, {x, y, z}], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
PlotRange -> All, Mesh -> None, MaxRecursion -> 0, PlotPoints -> 160,
ContourStyle -> Opacity[0.45], Mesh -> None, 

ColorFunction -> Function[{x, y, z, f}, ColorData["Rainbow"][z]], 
AxesLabel -> {x, y, z}]

enter image description here


To cut through the contours I used the option!


RegionFunction -> Function[{x, y, z}, x < z || z > y]

In order to check that the data points density is responsible for the shape of the contours we can use Graphics3D


pic = Graphics3D[{ColorData["DarkRainbow"][#[[3]]],
PointSize -> Large, Point[#]} & /@ data, Boxed -> False];

Show[con, pic]

enter image description here


BR


EDIT


To follow up on the 2D example and get warm colours for higher densities


 data = RandomReal[1, {500, 3}];
 dist = SmoothKernelDistribution[data];
 ContourPlot3D[Evaluate@PDF[dist, {x, y, z}], {x, -2, 2}, {y, -2, 2}, 
 {z, -2, 2},PlotRange -> All, Mesh -> None, MaxRecursion -> 0, PlotPoints -> 150, 

  ContourStyle -> Opacity[0.45], Contours -> 5, Mesh -> None,
  ColorFunction -> Function[{x, y, z, f}, ColorData["Rainbow"][f/Max[data]]], 
  AxesLabel -> {x, y, z},
  RegionFunction -> Function[{x, y, z}, x < z || z > y]]

Mathematica graphics


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