How to visualize the interior of a complicated 3D plot

Question

I have an external data file (can be downloaded here: link 1 or link 2) which contains a dense grid of initial condition in the (x,y,z) space. I read it with Mathematica and plot these initial conditions with different colors according to some specific properties

m = Import["data_3d.out", "Table"];

getColor[m_List, i_Integer] := 
Module[{s = m[[i, 6]]}, 
Which[s == 0, Black, s == 1, Red, s == 2, Darker[Green], s == 3, 
Brown, s == 4, Blue, s == 5, Orange, s == 6, Cyan, s == 7, 
Magenta, s == 8, Yellow, True, White]];

data = Table[{PointSize[0.004], getColor[m, i], 
Point[{m[[i, 1]], m[[i, 2]], m[[i, 3]]}]}, {i, 1, Length[m]}];

P0 = Graphics3D[data, Axes -> True, BoxRatios -> {1, 1, 1}, 
PlotRange -> 6, ImageSize -> 550]

and here is the output

We observe, that several color patterns appear but we can see only the surface of the three-dimensional grid. So, the question:

Is there a way to penetrate inside the 3d surface and visualize how these color patterns are? Any suggestions?

Please, us the original data file for testing. I think, generating simpler but random 3d grids in this case, could be very illusive since all the story is about the color patterns that appear and obviously cannot be replicated randomly.

EDIT

A second working link for retrieving the data file is added.

Answer 1

A tomographic approach:

m = Import["http://www.datafilehost.com/get.php?file=3c69e895", "Data"];

getColor[s_List] := 
  Replace[s, {0 -> Black, 1 -> Red, 2 -> Darker[Green], 3 -> Brown, 
    4 -> Blue, 5 -> Orange, 6 -> Cyan, 7 -> Magenta, 
    8 -> Yellow, _ -> White}, 1];

nfx = Nearest[m[[All, 1]] -> m];

Manipulate[
 Graphics3D[{PointSize[0.004], 
   Point[#[[All, 1 ;; 3]], VertexColors -> getColor[#[[All, 6]]]] &@ nfx[x0]},
  Axes -> True, BoxRatios -> {1, 1, 1}, PlotRange -> 6, ImageSize -> 350],
 {x0, Min[m[[All, 1]]], Max[m[[All, 1]]]}
 ]

Other ways of slicing:

nfy = Nearest[m[[All, 2]] -> m];
nfz = Nearest[m[[All, 3]] -> m];

---

In response to a comment, here is a static approach:

xlist = Range[0, 5, 1]

Graphics3D[{PointSize[0.004], 
  Point[#[[All, 1 ;; 3]], VertexColors -> getColor[#[[All, 6]]]] &@
   Flatten[nfx /@ xlist, 1]}, Axes -> True, BoxRatios -> {1, 1, 1}, 
 PlotRange -> 6, ImageSize -> 350]

(* {0, 1, 2, 3, 4, 5} *)

Answer 2

One easy, although not beautiful way relies on the properties of 3D graphics. When you look how the simulated camera works, then you see that only the volume between near- and farplane is rendered. If you put your near plane in the distance, everything which is too close is cut.

In Mathematica this can be be adjusted using the ViewRange option of Graphics3D. Here is a small example:

data = ExampleData[{"Geometry3D", "Triceratops"}, "VertexData"];
With[{gr = 
   Graphics3D[{{Hue[#3], Sphere[{##}, .2]} & @@@ data}, 
    SphericalRegion -> True]},
 Manipulate[
  Show[gr, ViewPoint -> {0, -1, .5}, 
   ViewRange -> {nearPlane, farPlane}],
  {nearPlane, 4, 10},
  {{farPlane, 15}, 5, 15}
  ]
 ]

Full graphics

Cut graphics

Answer 3

There are couple other ways to visualize 3D images, one of which is new in V10. (Note: The links to the original data are no longer valid.)

The new features, ClipPlanes and IntervalSlider, are useful here. Something like this was demonstrated at WTC 2014.

knee = Raster3D[
   RawArray["Byte", 
    ImageData[ExampleData[{"TestImage3D", "MRknee"}], "Byte"]],
    {{-1, 1, 1}, {1, -1, -1}}, {0, 255}, 
   ColorFunction -> "GrayLevelOpacity"];

Manipulate[
 Graphics3D[knee, 
  ClipPlanes -> {{0, 1, 0, -y[[1]]}, {0, -1, 0, y[[2]]}}, 
  Axes -> True],
 {{y, {-1, 1}}, -1, 1, IntervalSlider}]

ClipRange was introduce in V9 for 3D images.

Image3D[ExampleData[{"TestImage3D", "MRknee"}], ClipRange -> {All, {0, 60}, All}]