BarChart3D with continuous data along one dimension

Question

I'm trying to find an option for BarChart3D (or some other 3D plotting function) which will allow me to visualize a set of data which should be continuous (i.e. interpolated) along one dimension, but discrete along the other. As a concrete example: (generated with BarChart3D[data,ChartLayout -> "Grid",ColorFunction -> "SunsetColors"]

In the above plot, the dimension with only 6 increments is truly discrete, while the dimension with 21 increments is actually continuous, and has just been sampled at discrete points. I'm trying to find a way to have basically the same visual as the bar chart, but with a smooth interpolated curve along the 21-point direction, still with the width/look of the bars. I've tried making some hacky attempts with ListPlot3D, but can never get the colors to work very well. Any advice or help would be appreciated!

Answer 1

Plot3D example:

Plot3D[{
  2 Abs@Sin[x] Boole[0 < y < 2],
  2 Abs@Cos[x] Boole[2 < y < 4],
  4 Abs@Sin[x] Boole[4 < y < 6],
  4 Abs@Cos[x] Boole[6 < y < 8],
  6 Abs@Sin[x] Boole[8 < y < 10]
  },
 {x, 0, 2 Pi},
 {y, 0, 10},
 Filling -> Bottom,
 FillingStyle -> Opacity[1],
 Mesh -> False,
 PlotRange -> {{0, 2 Pi}, {0, 10}, {0, 10}}
 ]

I'm assuming here that you already have the interpolation functions, and that what remains is plotting them.

If you need more control over the look than Plot3D gives you, the best way I can think of is to make the filling yourself with graphics primitives. Here's a proof of concept:

data = Table[{x, 0, Abs@Sin[x]}, {x, 0, 2 Pi, 0.01}];
left = Partition[data, 2, 1];
right = Partition[{0, 2, 0} + # & /@ data, 2, 1];

fillingPolygon[{{x1_, y1_, z1_}, {x2_, y2_, z2_}}] :=
 {
  EdgeForm[],
  ColorData["AvocadoColors", Mean[{z1, z2}]],
  Polygon[{
    {x1, y1, z1},
    {x2, y2, z2},
    {x2, y2, 0},
    {x1, y1, 0}
    }]
  }

Show[
 Graphics3D[{
   fillingPolygon /@ left,
   fillingPolygon /@ right
   }],
 Plot3D[
  Abs@Sin[x],
  {x, 0, 2 Pi},
  {y, 0, 2},
  Mesh -> False,
  ColorFunction -> "AvocadoColors",
  ColorFunctionScaling -> False
  ]
 ]

Answer 2

Update: Combining all steps in a function:

ClearAll[minMax, hybridBarChart]
minMax = Table[f[[1]][{f[[2]][Through@#@x], #2[[1]] < x <= #2[[2]]}, 
       x] &[##], {f, {{NMaxValue, Max}, {NMinValue, Min}}}] &;

hybridBarChart[funcs_, range_, labels_: Automatic, cf_: "Rainbow"][
  opts : OptionsPattern[]] := Module[{minmax = minMax[funcs, range]},
  Show[Table[ParametricPlot3D[{t, i, v funcs[[i]][t]}, {t, range[[1]], 
      range[[2]]}, {v, 0, 1}, 
     ColorFunction -> (ColorData[{cf, minmax}][ funcs[[i]][#4]] &), 
     ColorFunctionScaling -> False, opts, Method -> "Extrusion" -> .5,
      PlotPoints -> 50, Mesh -> None], {i, Length@funcs}], 
   Ticks -> {Automatic, Transpose[{Range[Length@funcs], 
       labels /. Automatic -> Range[Length@funcs]}], Automatic}, 
   FilterRules[{opts}, Options @ Graphics3D], ImageSize -> Large, 
   Lighting -> "Neutral", PlotRange -> All, BoxRatios -> {1, 1, 1/2}]]

Examples :

functions = Function /@ (Range[5] Abs[Sin[#]]);

labels = "data" <> ToString[#] & /@ Range[Length @ functions];

hybridBarChart[functions, {0, 3 Pi}][ImageSize -> Medium, BaseStyle -> Opacity[.5]]

hybridBarChart[functions, {0, 3 Pi}, labels, "SolarColors"][
 Method -> "Extrusion" -> .8, ImageSize -> Medium]

Original answer:

You can also use ParametricPlot3D with the option "Extrusion":

functions = Function /@ (Range[5] Abs[Sin[#]]);

labels = "data" <> ToString[#] & /@ Range[Length @ functions];

max = NMaxValue[{Max[Through@functions@x], 0 < x <= 3 Pi}, x];
min = NMinValue[{Min[Through@functions@x], 0 < x <= 3 Pi}, x];

pp3D[f_, i_] := ParametricPlot3D[{t, i[[1]], v f[t]}, {t, 0, 3 Pi}, {v, 0, 1}, 
  PlotPoints -> 50, Mesh -> None, Method -> "Extrusion" -> .3, 
  ColorFunction -> (ColorData[{"Rainbow", {min, max}}][f[#4]] &), 
  ColorFunctionScaling -> False]

Show[MapIndexed[pp3D, functions],  ImageSize -> Large, 
 Lighting -> "Neutral", PlotRange -> All, BoxRatios -> {1, 1, 1/2}, 
 Ticks -> {Automatic, Transpose[{Range[Length@functions], labels}], Automatic}]

Add the option BaseStyle -> Opacity[.5] in the definition of pp3D to get

Use "Extrusion" -> 1 instead of "Extrusion" -> .3 to get

Change "Rainbow" to "AvocadoColors" to get

Use functions = Function /@ (Range[5] Abs[# Sin[#]]); to get