Pixelized 2d projection of 3d list

Question

I would like to visualize some 3d data. What I want is similar to

ListPlot3D[{{1, 1, 1, 1}, {1, 2, 1, 2}, {1, 1, 3, 1}, {1, 2, 1, 4}}, 
 Mesh -> All]

however, the result should look like

which is an array plot:

ArrayPlot[RandomReal[1, {10, 20}]]

The crucial difference is, that I would prefer to be able to plot my Data straight away (where z should be colormapped, i.e. 0: black, 1:white).

{{x1, y1, z1}, ... , {xn, yn, zn}}, x_{n+1} - x_{n} != y_{n+1} - y_{n}

It's generated via c++. ideally, i would like to read it out of a HDFS dataspace. Finally, it looks something like this:

{{0.0, 0.0, 0.12343},{0.0,0.1,0.5233},{0.0,0.2,0.86493},{0.0,0.4,0.9854},...},
{0.4, 0.0, 0.45347},{0.4,0.1,0.7231},{0.4,0.2,0.9433},{0.4,0.4,0.7459},...},
{0.8, 0.0, 0.3455},{0.8,0.1,0.3457},{0.8,0.2,0.5422},{0.8,0.4,0.01208},...},
...
{1.2, 0.0, 0.35425},{1.2,0.1,0.68425},{1.2,0.2,0.6546},{1.2,0.4,0.8243},...}}

Of course, I could transform it to

{{a11, a12, ..., a1n}, ... , {am1, am2, ..., amn}}

via

z = data[[All, 3]];
Partition[z, 4];

manually (thanks Okkes), but then, I loose the information of pixel size

(x_{n+1} - x_{n}) x (y_{n+1} - y_{n})

This means, the pixels may be supposed to look non-quadratic.

I have spent some time to find a solution, so any help is much appreciated!

Answer 1

Strongly related QA from where I'm borrowing the technique

Caveat: the ordering of the mesh cells is not the same as the ordering of the initial data points. Using some help from this answer I fix this with an undocumented function Region`Mesh`MeshMemberCellIndex.

Let's generate some test data:

data = RandomReal[1, {36, 3}];
mesh = VoronoiMesh[data[[;; , ;; 2]]];
ind = MeshCellIndex[mesh, 2];
ordereddata = 
 data[[Region`Mesh`MeshMemberCellIndex[mesh][
   data[[;; , ;; 2]]][[;; ,2]] // Ordering]]
style = Style @@@ (Transpose@{ind, GrayLevel /@ ordereddata[[;; , 3]]});
HighlightMesh[mesh, {style}]

This method also works for a rectangular grid:

data = Table[{i, j, RandomReal[]}, {i, 0, 5, .4}, {j, 0, 2, .2}] // Flatten[#, 1] &;

and it is quite easy to clip the large boundaries like so:

With[{xstep = data[[;; , 1]] // Union // Differences // Min,
  ystep = data[[;; , 2]] // Union // Differences // Min},
 xrange = (data[[;; , 1]] // MinMax) + {-.5, .5} xstep;
 yrange = (data[[;; , 2]] // MinMax) + {-.5, .5} ystep;]
mesh = VoronoiMesh[data[[;; , ;; 2]], {xrange, yrange}];

Take care though, the last code snippet has no error checking, so may clip a bit more than desired on an unstructured grid.

Answer 2

Assume your data is in data={{x1, y1, z1}, ... , {xn, yn, zn}} form and you only care about plotting zvalues, then you can do the following. It is up to you how you partition your data.

      SeedRandom@2
data = RandomReal[1, {36, 3}];
z = data[[All, 3]];
Row[{ArrayPlot[Partition[z, 4]], ArrayPlot[Partition[z, 6]], 
  ArrayPlot[Partition[z, 9]]}, Spacer@20]