using bar3(z) to plot in unusual data visualization

Can someone help me write the script to plot my data as 3 separate bar charts, each along an X, Y, and Z axes, such as:

(this was created w/ help of Photoshop)

Answer 1

[Voss]

red_data   = [ 5  5 20 35 15];
blue_data  = [30 25 20 15  5];
green_data = [30 25 35  5  5];

Nr = numel(red_data);
Nb = numel(blue_data);
Ng = numel(green_data);

data = NaN(Nb+1,Nr+Ng+1);

data(1,1:Nr)     = red_data;
data(2:end,Nr+1) = blue_data;
data(1,Nr+2:end) = green_data;

h = bar3(data);

for ii = [1:Nr Nr+2:Nr+Ng+1]
    h(ii).ZData(6:end,:) = NaN;
end
h(Nr+1).ZData(1:5,:) = NaN;

set(h(1:Nr),'FaceColor','r')
set(h(Nr+1),'FaceColor','b')
set(h(Nr+2:end),'FaceColor','g')

[Stephen]

Perfect! Many thanks!!

[Voss]

You're welcome!

[Stephen]

Update/followup...

Voss, could I trouble you to describe how I could add one more set of data such as:

Much appreciated!

[Voss]

Here is the code (explanation/description to follow momentarily):

red_data    = [ 5  5 20 35 15];
yellow_data = [10 10 35 55 20];
green_data  = [30 25 35  5  5];
blue_data   = [30 25 20 15  5];

Nr = numel(red_data);
Ny = numel(yellow_data);
Ng = numel(green_data);
Nb = numel(blue_data);

data = NaN(Ny+Nb+1,Nr+Ng+1);

data(Ny+1,1:Nr)     = red_data;
data(1:Ny,Nr+1)     = yellow_data;
data(Ny+1,Nr+2:end) = green_data;
data(Ny+2:end,Nr+1) = blue_data;

h = bar3(data);

h(Nr+1).ZData(6*Ny+(1:5),:) = NaN;
for ii = [1:Nr Nr+2:Nr+Ng+1]
    h(ii).ZData([1:6*Ny 6*Ny+7:end],:) = NaN;
end

set(h(1:Nr),'FaceColor','r')
set(h(Nr+2:end),'FaceColor','g')
h(Nr+1).CData = repmat(permute(repelem([1 1 0; 0 0 0; 0 0 1],6*[Ny 1 Nb],1),[1 3 2]),1,4);

[Voss]

red_data    = [ 5  5 20 35 15];
yellow_data = [10 10 35 55 20];
green_data  = [30 25 35  5  5];
blue_data   = [30 25 20 15  5];

First, put the vectors into a matrix of NaNs like this:

Nr = numel(red_data);
Ny = numel(yellow_data);
Ng = numel(green_data);
Nb = numel(blue_data);

data = NaN(Ny+Nb+1,Nr+Ng+1);

data(Ny+1,1:Nr)     = red_data;
data(1:Ny,Nr+1)     = yellow_data;
data(Ny+1,Nr+2:end) = green_data;
data(Ny+2:end,Nr+1) = blue_data;

disp(data)

   NaN   NaN   NaN   NaN   NaN    10   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    10   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    35   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    55   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    20   NaN   NaN   NaN   NaN   NaN
     5     5    20    35    15   NaN    30    25    35     5     5
   NaN   NaN   NaN   NaN   NaN    30   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    25   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    20   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN    15   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN     5   NaN   NaN   NaN   NaN   NaN

When you create a 3d bar graph from that matrix, it looks like this by default:

figure
h = bar3(data);
xlabel('x')
ylabel('y')

So the task is to re-color the objects created by bar3.

bar3 returns a vector of surface objects, one object per x value, and I'll set the properties of those surface objects in order to re-color.

figure
h = bar3(data)

h = 
  1x11 Surface array:

    Surface    Surface    Surface    Surface    Surface    Surface    Surface    Surface    Surface    Surface    Surface

The first thing to do is to eliminate the colored squares from the regions where I don't want any bars. I'll do that by essentially setting their heights to NaN so that they are not rendered. The ZData property of a surface object describes the surface's vertices' locations in the Z-direction, so that's what I'll set to NaN.

For example, the ZData of the middle surface at x = 6 contains the data in the yellow_data and blue_data vectors (as well as a zero-height bar in between the yellow and the blue) but each element is repeated in a 2x2 square and surrounded by zeros which are surrounded by NaNs (so each group of 6 rows in ZData describes a single bar's height):

size(h(Nr+1).ZData) % h(Nr+1) is the middle surface (at x = Nr+1 = 6 in this example)

ans = 1x2

66 4

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disp(h(Nr+1).ZData)

   NaN     0     0   NaN
     0    10    10     0
     0    10    10     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    10    10     0
     0    10    10     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    35    35     0
     0    35    35     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    55    55     0
     0    55    55     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    20    20     0
     0    20    20     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0     0     0     0
     0     0     0     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    30    30     0
     0    30    30     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    25    25     0
     0    25    25     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    20    20     0
     0    20    20     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0    15    15     0
     0    15    15     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN
   NaN     0     0   NaN
     0     5     5     0
     0     5     5     0
   NaN     0     0   NaN
   NaN     0     0   NaN
   NaN   NaN   NaN   NaN

I'll use the fact that each bar takes up 6 rows of ZData to set the appropriate elements of ZData to NaN in order to make the bars I don't want to show up effectively disappear.

This sets the bar between the yellow and blue sections to NaN:

h(Nr+1).ZData(6*Ny+(1:5),:) = NaN;

And this sets the rest of the bars outside the red/green/yellow/blue sections to NaN:

for ii = [1:Nr Nr+2:Nr+Ng+1]
    h(ii).ZData([1:6*Ny 6*Ny+7:end],:) = NaN;
end

So now the plot looks like that.

(Now, repeating that code for a new figure ...)

figure
h = bar3(data);
h(Nr+1).ZData(6*Ny+(1:5),:) = NaN;
for ii = [1:Nr Nr+2:Nr+Ng+1]
    h(ii).ZData([1:6*Ny 6*Ny+7:end],:) = NaN;
end

All that remains is to change the colors of the remaining surfaces.

The first Nr surfaces (for x = 1 to x = Nr) need to be all red, and the last Ng surfaces (for x = Nr+2 to x = Nr+Ng+2) need to be all green. That's easy because each surface is all one color:

set(h(1:Nr),'FaceColor','r')
set(h(Nr+2:end),'FaceColor','g')

But it's tricker for the surface at x = Nr+1 because it needs to contain both yellow and blue bars (this wasn't an issue when there was no yellow section). For surfaces whose faces need to be different colors you can use the CData property instead of FaceColor. CData in this case is going to be a m-by-n-by-3 array of RGB values. It's again 6 rows per bar.

Rather setting that surface's CData all in one line of code, I break it up into two parts for illustration, where first I construct a temporary m-by-3 matrix of RGB colors containing yellow [1 1 0], black [0 0 0] (for the bar in between yellow and blue - doesn't matter what it is since its ZData is NaNs), and blue [0 0 1], each repeated the appropriate number of times:

C = repelem([1 1 0; 0 0 0; 0 0 1],6*[Ny 1 Nb],1)

C = 66x3

1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0

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and then manipulate it to be m-by-4-by-3. I know it has to be 4 since that's how many columns ZData has (because each surface face has four vertices).

h(Nr+1).CData = repmat(permute(C,[1 3 2]),1,4);

[Stephen]

VERY helpful, very clear, very thorough. This is tremendously appreciated, Voss!

[Voss]

You're welcome!