How can I imitate the style of a certain 3D bar chart?

Question

I would like to get a 3D visualization of a given matrix.

Here is a figure which may come from Mathematica. I want to plot something like it. When I use ListPlot3D or BarChart3D to plot my matrix, it does not have the style of one shown below, which is what I'm look for. How can I do a nice 3D visualization of my matrix?

data = ( {
    {1, 2, 3},
    {5, 4, 8},
    {2, 5, 7}
   } );

data = ArrayPad[data, {0, 1}];
xTicks = {{1.5, "A"}, {2.5, "B"}, {3.5, "C"}};
yTicks = {{1.5, "X"}, {2.5, "Y"}, {3.5, "Z"}};
zTicks = {{0, "0"}, 0, {4, "4"}, {8, "8"}};

pic = ListPlot3D[data, 
  Mesh -> None, 
  InterpolationOrder -> 0, 
  ColorFunction -> "Rainbow",
  Filling -> Bottom,
  FillingStyle -> {Opacity[0.9]},
  PlotRange -> {Min[data] - 0.5, Max[data] + 0.2},
  BoxRatios -> {1, 1, 0.5},
  Ticks -> {xTicks, yTicks, zTicks},
  DataRange -> All,
  Boxed -> False,
  FaceGrids -> {Bottom, Back, Left},
  ImageSize -> 400]

this is the code that I plot a matrix using ListPlot3D. The cuboids in it are not separate from each other, and the edges of the cuboid are fuzzy.

Answer 1

If I have time later tonight I'll give you a graphic matching demo as I did for other users here and here.

As usual I recommend building a specific graphic from Graphics (or Graphics3D) primitives so I suggest you spend some time reading about those, e.g. Cuboid.

As a quick fix you can use BarChart3D as follows:

data = SparseArray[Tuples[{1, 4}, 2] -> 0.3, {4, 4}, 0.01];

chart = BarChart3D[data, ChartLayout -> "Grid"]

There are many Options you can use to customize this. Please spend some time reading about those as well. Once you get comfortable with graphics primitives and the internal format of these objects you can perform manipulations on the output to further customize them.

---

Okay, here is a fairly close approximation:

data = SparseArray[Tuples[{1, 4}, 2] -> 0.3, {4, 4}, 0.01];
data[[2 ;; 3, 2 ;; 3]] += 0.1;
data3D = Join @@ MapIndexed[Append[#2, #] &, data, {2}];

labels = {"VV", "VH", "HV", "HH"};

bar[n_][{x_, y_, z_}] := Cuboid[{x - n, y - n, 0}, {x + n, y + n, z}]
Graphics3D[
 bar[0.25] /@ data3D,
 Axes -> True,
 LabelStyle -> {FontFamily -> "Helvetica", 19},
 Ticks -> {MapIndexed[{5 - #2[[1]], #} &, labels],
           MapIndexed[{#2[[1]], #} &, labels], 
           Automatic},
 FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}},
 BoxRatios -> {1, 1, 1},
 BoxStyle -> AbsoluteThickness[2.5],
 PlotRangePadding -> 0.25,
 ViewPoint -> 1.5 {1.77, -2.29, 1.74},
 ImageSize -> 330
]

The original:

Answer 2

 data = ({{1, 2, 3}, {5, 4, 8}, {2, 5, 7}});
 data = ArrayPad[data, {0, 1}];
 xTicks = {{1, "A"}, {2, "B"}, {3, "C"}};
 yTicks = {{1, "X"}, {2, "Y"}, {3, "Z"}};
 zTicks = {{0, "0"}, 0, {4, "4"}, {8, "8"}};
 pltstyl = {ColorFunction -> "Rainbow", 
  PlotRange -> {Min[data] - .2, Max[data] + 0.2}, 
   BoxRatios -> {1, 1, 0.5}, Ticks -> {xTicks, yTicks, zTicks}, 
   Boxed -> False, FaceGrids -> {Bottom, Back, Left},  ImageSize -> 400};

Using BubbleChart3D with a custom ChartElementFunction:

(* transform data to a form acceptabele to BubbleChart3D:*)
bcdata =Join@@MapIndexed[Composition[Append[#, 1] &, Flatten, Reverse, List], data, {2}]; 
(* custom ChartElementFunction to produce cuboids with appropriate heights *)
ceFunc[{{xmin_, xmax_}, {ymin_, ymax_}, {zmin_, zmax_}}, v_, meta_] :=
  {Cuboid[{xmin, ymin, 0.}, {xmax, ymax, (zmax + zmin)/2}]};
BubbleChart3D[bcdata, ColorFunction -> (ColorData["Rainbow"][#3] &), 
 ChartStyle -> Opacity[.9],
 ChartElementFunction -> ceFunc, BubbleSizes -> {0.15, .15}, 
 Evaluate@pltstyl]

Post-processing BubbleChart3D to reshape the cuboids

BubbleChart3D[bcdata, ColorFunction -> (ColorData["Rainbow"][#3] &), 
 ChartStyle -> Opacity[.9], ChartElementFunction -> "Cube", BubbleSizes -> {0.15, .15}, 
 Evaluate@pltstyl] /. 
CuboidBox[{a_, b_, c_}, {e_, f_, g_},rest___]:>CuboidBox[{a, b, 0}, {e, f,(c + g)/2}, rest]

Using DiscretePlot3D with Interpolation:

(* interpolation of 3D data: *)
intF = Interpolation[Join @@ MapIndexed[Composition[Reverse, List], data, {2}]];
DiscretePlot3D[intF[i, j], {i, 1, 4}, {j, 1, 4}, 
ExtentSize -> Scaled[.75], Evaluate@pltstyl]

Answer 3

I tried to follow in the steps of the great Mr.Wizard, using cuboids, or rather polygons:

cuboid[origin_, box_List, colors_List] := 
 Module[
  {vertexList = {
     {{1, 1, 1}, {0, 1, 1}, {0, 0, 1}, {1, 0, 1}}, (* up *)
     {{1, 1, 1}, {1, 0, 1}, {1, 0, 0}, {1, 1, 0}}, (* right *)
     {{0, 1, 1}, {0, 1, 0}, {0, 0, 0}, {0, 0, 1}}, (* left *)
     {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}, {1, 0, 1}}, (* front *) 
     {{1, 1, 1}, {1, 1, 0}, {0, 1, 0}, {0, 1, 1}}, (* back *)
     {{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}}} (* down *) 
   },
   (* scale *)
   vertexList = Map[Times[box, #] &, vertexList, {2}];
   (* move *)
   vertexList = Map[Plus[origin, #] &, vertexList, {2}];
   Riffle[colors, Polygon /@  vertexList]] 

Then, with some suitable data:

fullData = {{1, 1, 1}, {1, 2, 2}, {1, 3, 3}, {2, 1, 4}, 
    {2, 2, 5}, {2, 3, 6}, {3, 1, 7}, {3, 2, 8}, {3, 3, 9}};
xTicks = {{1.5, "A"}, {2.5, "B"}, {3.5, "C"}};
yTicks = {{1.5, "X"}, {2.5, "Y"}, {3.5, "Z"}};
zTicks = {{0, "0"}, 0, {4, "4"}, {8, "8"}};

Graphics3D[
 {
  cuboid[{#[[1]], #[[2]], 0}, {.5, .5, #[[3]]}, 
    {Cyan, Orange, LightGray, Purple, Gray, Gray}] & /@ fullData
  }, 
 Boxed -> True, 
 Axes -> True, 
 AxesLabel -> {x, y, z}, 
 Lighting -> {{"Ambient", White}},
 FaceGridsStyle -> Directive[Opacity[0.4], Gray],
 PlotRange -> {-2, 10},
 BoxRatios -> {1, 1, 0.7},
 Ticks -> {xTicks, yTicks, zTicks},
 FaceGrids -> {Bottom, Back, Left}

Each face has its own color.

With this sort of graphic, it's quite hard to read the heights accurately. But that's another story.