A simple contour plot of data without interpolation

Question

I have a data set gathered from lab. The measurements are of the form {x, y, z}. I want to plot this data in a way that there is (1) no interpolation between adjacent data points and (2) that is visualised in the form of cubes, i.e. {x, y}, and give the location of the cuboid whilst z gives the height, and then repeat this simply for all data points.

I have tried ListContourPlot and ListDensityPlot with InterpolationOrder -> 0, however I get wierd results. For example, both plots don't show the squares or rectangular patches that I was expecting, instead they seem more triangular.

I have attached an image of a couple of my plots:

.

And this is the code that I have used to generate these plots:

GraphicsGrid[{{ListContourPlot[scanDataCh1, Mesh -> None, 
  InterpolationOrder -> 0, PlotRange -> All, 
  ColorFunction -> "Rainbow", 
  FrameLabel -> {"Hem. Voltage (V)", 
  "Elevation Angle \!\(\*SuperscriptBox[\((\), \(o\)]\))", 
  "ListContourPlot for Channel 1"}, ImageSize -> Large], 
ListDensityPlot[scanDataCh1, Mesh -> None, InterpolationOrder -> 0,
  PlotRange -> All, ColorFunction -> "Rainbow", 
  FrameLabel -> {"Hem. Voltage (V)", 
  "Elevation Angle \!\(\*SuperscriptBox[\((\), \(o\)]\))", 
  "ListDensityPlot for Channel 1"}, ImageSize -> Large]}}]

Thanks!

Answer 1

I create some arbitrary sample data for the sake of an example:

hw2 = 0.02;
dat = RandomReal[{0, 1}, {20, 3}];
Graphics3D[{Cuboid[{#[[1]] - hw2, #[[2]] - hw2, 
      0}, {#[[1]] + hw2, #[[2]] + hw2, #[[3]]}]} & /@ dat]