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I have a list of 3D points.

data = 
  {{57.3333, 198.833, 1}, {2.40909, 180.045, 1}, {32.1842, 170.342, 1}, 
   {195.25, 147.5, 1}, {85.7941, 143.735, 1}, {59.8333, 117.5, 1}, 
   {5.83333, 100.167, 1}, {151.5, 95., 1}, {31.3, 88.1, 1}, 
   {87.2222, 67.2222, 1}, {61., 39., 1}, ...}

image

  • How can I color the points to indicate volumes of high point density?
  • How can I draw lines through those clusters of points that look like linear structures, i.e., paths?
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  • $\begingroup$ the line detection is a real challenge, google "3d hough transform line detection". I dont think there is a straightforward built in method in mathematica. $\endgroup$ – george2079 Nov 6 '17 at 23:16
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    $\begingroup$ I don't know what the current state of the art is, but in the early 1990s I worked on this problem, trying to find good heuristics to solve it. I made some progress, but it turned out to be very difficult and I can't say I solved it. Maybe today machine learning could be a useful approach. One thing I learned is the problem is very sensitive to the data, so anyone who wanted to work on your problem would need your full data, not just a few points. $\endgroup$ – m_goldberg Nov 6 '17 at 23:34
  • $\begingroup$ Thanks, ill google it. Any idea for the points density? Or some way to visualise the poits distribution? :) $\endgroup$ – Adri HC Nov 6 '17 at 23:49
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    $\begingroup$ Many cluster techniques tend to end up with clusters that look like ellipsoids but as you want clusters that are linear features you consider the following article: Clustering by fast search and find of density peaks. Alex Rodriguez and Alessandro Laio. Science 344, 1492 (2014). $\endgroup$ – JimB Nov 7 '17 at 0:59
  • $\begingroup$ As far as visualizing the density goes, have you seen ListDensityPlot3D? $\endgroup$ – aardvark2012 Nov 7 '17 at 3:42

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