How to hide zero values in bar3 plot in MATLAB

I've got a 2-D histogram (the plot is 3D - several histograms graphed side by side) that I've generated with the bar3 plot command. However, all the zero values show up as flat squares in the x-y plane. Is there a way I can prevent MATLAB from displaying the values? I already tried replacing all zeros with NaNs, but it didn't change anything about the plot. Here's the code I've been experimenting with:

x1=normrnd(50,15,100,1); %generate random data to test code
x2=normrnd(40,13,100,1);
x3=normrnd(65,12,100,1);

low=min([x1;x2;x3]);
high=max([x1;x2;x3]);
y=linspace(low,high,(high-low)/4); %establish consistent bins for histogram
z1=hist(x1,y);
z2=hist(x2,y);
z3=hist(x3,y);
z=[z1;z2;z3]';
bar3(z)

As you can see, there are quite a few zero values on the plot. Closing the figure and re-plotting after replacing zeros with NaNs seems to change nothing:

close
z(z==0)=NaN;
bar3(z)

One solution is to modify the graphics objects created by bar3. First, you have to get the handles returned from bar3:

h = bar3(z);

In your case, h will be a 3-element vector of handles, one for each set of colored bars. The following code should then make the bins with counts of zero invisible:

for i = 1:numel(h)
  index = logical(kron(z(:, i) == 0, ones(6, 1)));
  zData = get(h(i), 'ZData');
  zData(index, :) = nan;
  set(h(i), 'ZData', zData);
end

And here's an illustration (with obligatory free-hand circles):

How it works...

If your vector of bin counts is N-by-1, then bar3 will plot 6*N rectangular patches (i.e. the 6 faces of a cuboid for each bin). The 'ZData' property for each set of patch objects in h will therefore be (6*N)-by-4, since there are 4 corners for each rectangular face. Each cluster of 6 rows of the 'ZData' property is therefore a set of z-coordinates for the 6 faces of one bin.

The above code first creates a logical vector with ones everywhere the bin count equals 0, then replicates each element of this vector 6 times using the kron function. This becomes an index for the rows of the 'ZData' property, and this index is used to set the z-coordinates to nan for the patches of empty bins. This will cause the patches to not be rendered.

EDIT:

Here's a slightly modified version of the code that makes it more general by fetching the bar height from the 'ZData' property of the plotted bars, so all that's needed for it to work are the handles returned from bar3. I've also wrapped the code in a function (sans error and input checking):

function remove_empty_bars(hBars)
  for iSeries = 1:numel(hBars)
    zData = get(hBars(iSeries), 'ZData');  % Get the z data
    index = logical(kron(zData(2:6:end, 2) == 0, ones(6, 1)));  % Find empty bars
    zData(index, :) = nan;                 % Set the z data for empty bars to nan
    set(hBars(iSeries), 'ZData', zData);   % Update the graphics objects
  end
end

Here is an example that shows how to hide bars with zero-values. We start with a normal BAR3 plot:

x = 1:7;
Y = jet(numel(x));
h = bar3(x,Y,'detached');
xlabel x; ylabel y; zlabel z; box on;

Note that the variable h contains an array of surface handles (3 in this case, one for each "group" of bars. The groups correspond to the columns of the Y matrix, each represented by a different color).

And now the code to hide zero values:

for i=1:numel(h)
    %# get the ZData matrix of the current group
    Z = get(h(i), 'ZData');

    %# row-indices of Z matrix. Columns correspond to each rectangular bar
    rowsInd = reshape(1:size(Z,1), 6,[]);

    %# find bars with zero height
    barsIdx = all([Z(2:6:end,2:3) Z(3:6:end,2:3)]==0, 2);

    %# replace their values with NaN for those bars
    Z(rowsInd(:,barsIdx),:) = NaN;

    %# update the ZData
    set(h(i), 'ZData',Z)
end

Explanation:

For each group of bars, a surface graphic object is created (with handle stored in h(i)). It's Z-coordinates matrix ZData is represented as a 6*N-by-4 matrix (same thing for XData, YData, and CData matrices), where N is the number of rectangular bars in each group or 7 in the example above.

This way each rectangle is represented with 6x4 matrices (one for each of X/Y/Z coordinates). For example the coordinates of one such rectangle would look like:

>> xx = get(h(3),'XData'); yy = get(h(3),'YData'); zz = get(h(3),'ZData');

>> xx(1:6,:)
ans =
          NaN          2.6          3.4          NaN
          2.6          2.6          3.4          3.4
          2.6          2.6          3.4          3.4
          NaN          2.6          3.4          NaN
          NaN          2.6          3.4          NaN
          NaN          NaN          NaN          NaN

>> yy(1:6,:)
ans =
          NaN          0.6          0.6          NaN
          0.6          0.6          0.6          0.6
          1.4          1.4          1.4          1.4
          NaN          1.4          1.4          NaN
          NaN          0.6          0.6          NaN
          NaN          NaN          NaN          NaN

>> zz(1:6,:)
ans =
          NaN            0            0          NaN
            0            1            1            0
            0            1            1            0
          NaN            0            0          NaN
          NaN            0            0          NaN
          NaN          NaN          NaN          NaN

The second column of each traces the points along the left face, the third column traces the points along the right face, and when the two are connected would draw 4 faces of the rectangle:

>> surface(xx(1:6,2:3), yy(1:6,2:3), zz(1:6,2:3), cc(1:6,2:3))
>> view(3)

The first and last columns would draw the two remaining faces by closing the sides of the rectangle.

All such matrices are concatenated as one tall matrix, and the rectangles are all drawn using a single surface object. This is achieved by using NaN values to separate the different parts, both inside the points of the same rectangle, and in-between the difference rectangles.

So what the above code does is to look for rectangles where the Z-height is zero, and replace all its values with NaN values which effectively tells MATLAB not to draw the surfaces formed by those points.