3-dimensional histogram in pgfplots

Question

I have a simple 3d histogram

which I want to import into pgfplots, e.g. using matlab2tikz or by hand.

PGFplots does not offer 3d histograms.

Is there an easy way to do this?

Answer 1

You can use \addplot3 graphics to include an image in pgfplots. This allows you to use pgfplots for drawing the axes and to add annotations using the data coordinate system.

If you have saved a plot from Matlab as an image called 3dcolumnchart.png, for example, the following code

\addplot3 graphics[points={%
(-4.4449,4.6547,0) => (110.814,167.827)
(-4.633,-4.5186,0) => (264.187,74.679)
(4.5829,-4.5216,0) => (470.558,145.343)
(-0.45821,-0.43355,1157) => (287.474,379.016)
}] {3dcolumnchart.png};
\node at (axis cs:-1.5,0.5,490) [inner sep=0pt, pin={[pin edge={thick,black},align=left]145:Interesting\\Data Point}] {};

will generate

For this, you need to provide the mapping from the data coordinate system to the figure coordinate system for four points. You can do this by finding the data coordinates for the points using the "Data Cursor" in Matlab, and finding the figure coordinates (in pt) for the same points in an image editor like GIMP. However, this can quickly become a bit tedious.

I've written a Matlab script called pgfplotscsconversion.m that allows you to click on four points in the Matlab figure, and the mapping will be written to the Matlab command prompt.

Here's an example of how I arrived at the above figure.

1. Create the Matlab plot

   hist3(randn(10000,2)) % some random data
   set(get(gca,'child'),'FaceColor','interp','CDataMode','auto'); % colors
   set(gcf,'PaperPositionMode','auto') % make sure the "print" paper format is the same as the screen paper format
   

2. Save the following code as pgfplotscsconversion.m

   function pgfplotscsconversion
   
   % Hook into the Data Cursor "click" event
   h = datacursormode(gcf);
   set(h,'UpdateFcn',@myupdatefcn,'SnapToDataVertex','off');
   datacursormode on
   
   % select four points in plot using mouse
   
   
   % The function that gets called on each Data Cursor click
   function [txt] = myupdatefcn(obj,event_obj)
   
   % Get the screen resolution, in dots per inch
   dpi = get(0,'ScreenPixelsPerInch');
   
   % Get the click position in pixels, relative to the lower left of the
   % screen
   screen_location=get(0,'PointerLocation');
   
   % Get the position of the plot window, relative to the lower left of
   % the screen
   figurePos = get(gcf,'Position');
   
   % Get the data coordinates of the cursor
   pos = get(event_obj,'Position');
   
   % Format the data and figure coordinates. The factor "72.27/dpi" is
   % necessary to convert from pixels to TeX points (72.27 poins per inch)
   display(['(',num2str(pos(1)),',',num2str(pos(2)),',',num2str(pos(3)),') => (',num2str((screen_location(1)-figurePos(1))*72.27/dpi),',',num2str((screen_location(2)-figurePos(2))*72.27/dpi),')'])
   
   % Format the tooltip display
   txt = {['X: ',num2str(pos(1))],['Y: ',num2str(pos(2))],['Z: ',num2str(pos(3))]};
   

   Run pgfplotscsconversion, click on four points in your plot. Preferably select non-colinear points near the edges of the plot. Copy and paste the four lines that were written to the Matlab command window.

3. Export the plot as an image

   axis off
   print -dpng matlabout -r400 % PNG called "matlabout.png" with 400 dpi resolution
   

   If you want to use vector PDF output, you'll have to set the paper size to match the figure size yourself, since the PDF driver doesn't automatically adjust the size:

   currentScreenUnits=get(gcf,'Units')     % Get current screen units
   currentPaperUnits=get(gcf,'PaperUnits') % Get current paper units
   set(gcf,'Units',currentPaperUnits)      % Set screen units to paper units
   plotPosition=get(gcf,'Position')        % Get the figure position and size
   set(gcf,'PaperSize',plotPosition(3:4))  % Set the paper size to the figure size
   set(gcf,'Units',currentScreenUnits)     % Restore the screen units
   
   print -dpdf matlabout      % PDF called "matlabout.pdf"
   

4. Remove the white background of the image, for example using the ImageMagick command

   convert matlabout.png -transparent white 3dcolumnchart.png
   

5. Include the image in your pgfplots axis. If you selected points on the plot corners, your xmin, xmax, ymin and ymax should be set automatically, otherwise you'll have to provide those yourself. Also, you'll need to adjust the width and height of the plot to get the right vertical placement of the plot.

   \documentclass[border=5mm]{standalone}
   \usepackage{pgfplots}
   
   \begin{document}
   \begin{tikzpicture}
   \begin{axis}[3d box,xmin=-5,xmax=5,ymin=-5,ymax=5,width=9cm,height=9.25cm,grid=both, minor z tick num=1]
   \addplot3 graphics[points={%
   (-4.4449,4.6547,0) => (110.814,167.827)
   (-4.633,-4.5186,0) => (264.187,74.679)
   (4.5829,-4.5216,0) => (470.558,145.343)
   (-0.45821,-0.43355,1157) => (287.474,379.016)
   }]
   {3dcolumnchart.png};
   \node at (axis cs:-1.5,0.5,490) [inner sep=0pt, pin={[pin edge={thick,black},align=left]145:Interesting\\Data Point}] {};
   \end{axis}
   \end{tikzpicture}
   \end{document}
   

Answer 2

I managed to achieve a 3-dimensional histogram effect by repeating the coordinates. I just repeat each x,y combination 4 times, once for each of the 4 possible bar tops it could appear in.

For example, the code

\documentclass{minimal}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
    \begin{axis}[
    view = {120}{35},% important to draw x,y in increasing order
    xmin = 0,
    ymin = 0,
    xmax = 3,
    ymax = 3,
    zmin = 0,
    unbounded coords = jump,
    colormap={pos}{color(0cm)=(white); color(6cm)=(blue)}
    ]
    \addplot3[surf,mark=none] coordinates {
        (0,0,0) (0,0,0) (0,1,0) (0,1,0) (0,2,nan) (0,2,nan) (0,3,nan) (0,3,nan)

        (0,0,0) (0,0,2) (0,1,2) (0,1,3) (0,2,3) (0,2,1) (0,3,1) (0,3,0)

        (1,0,0) (1,0,2) (1,1,2) (1,1,3) (1,2,3) (1,2,1) (1,3,1) (1,3,0)

        (1,0,0) (1,0,0) (1,1,0) (1,1,6) (1,2,6) (1,2,0) (1,3,0) (1,3,0)

        (2,0,nan) (2,0,nan) (2,1,0) (2,1,6) (2,2,6) (2,2,0) (2,3,nan) (2,3,nan)

        (2,0,0) (2,0,1) (2,1,1) (2,1,0) (2,2,0) (2,2,0) (2,3,nan) (2,3,nan)

        (3,0,0) (3,0,1) (3,1,1) (3,1,0) (3,2,nan) (3,2,nan) (3,3,nan) (3,3,nan)

        (3,0,0) (3,0,0) (3,1,0) (3,1,0) (3,2,nan) (3,2,nan) (3,3,nan) (3,3,nan)
    };
    \end{axis}
\end{tikzpicture}
\end{document}

produces

The 0 z-coordinate values above are meant to have the same value as zmin and the view has to be set such that the points with lower x and y coordinates are drawn first.

I don't know how to make the colour of the sides of the bars the same as the top, hence the monochrome colormap.

A larger example can be seen here

This is from some data I produced in python. To save it to a file, I had to add a few for loops that make sure all the points at the border are set to have z value equal to zmin. The function below takes the x, y mesh stored in x and y. The respective z values are in z, a list of len(x) - 1 lists of length len(y) - 1. It writes to a file output that can be included with \addplot3 file {}. It assumes that there are no NaN values and sets the z values along the border to zmin.

import csv

def make3dhistogram(x, y, z, zmin, output):
    writer = csv.writer(open(output, 'wb'), delimiter=' ')
    i = 0
    for j in range(len(y)):
        writer.writerow((x[i], y[j], zmin))
        writer.writerow((x[i], y[j], zmin))
    for i in range(len(x)-1):        
        writer.writerow((x[i], y[0], zmin))
        for j in range(len(y)-1):
            writer.writerow((x[i], y[j], z[i][j]))
            writer.writerow((x[i], y[j+1], z[i][j]))            
        writer.writerow((x[i], y[len(y)-1], zmin))
        writer.writerow([])
        writer.writerow((x[i+1], y[0], zmin))
        for j in range(len(y)-1):
            writer.writerow((x[i+1], y[j], z[i][j]))
            writer.writerow((x[i+1], y[j+1], z[i][j]))          
        writer.writerow((x[i+1], y[len(y)-1], zmin))
        writer.writerow([])

    i = len(x)-1
    for j in range(len(y)):
        writer.writerow((x[i], y[j], zmin))
        writer.writerow((x[i], y[j], zmin))

So for example

x = [0,1,2,3]
y = [0,1,2,3]
z = [[2,3,1], [0, 6, 0], [1, 0, 0]]
make3dhistogram(x, y, z, 0.0, 'data')

produces the simple plot above, this time with a grid on the z plane as none of the points are skipped.

Answer 3

matlab2tikz now fully supports 3D histograms. This

load seamount
dat = [-y,x]; % Grid corrected for negative y-values
hist3(dat) % Draw histogram in 2D
n = hist3(dat); % Extract histogram data;
                % default to 10x10 bins
view([-37.5, 30]);

gives

Answer 4

I was not satisfied with the previous answers and therefore created my own solution.

• Jake's solution is present in the documentation but first I couldn't make it work, second it does not generate a image from data, which is what I want from Tikz.

• I worked on Anton's answer. It took me some time to figure out the way coordinates were organized to put it in a automatic code reading data from a file. But even if I managed to do so I couldn't overcome the impossibility to create a personalized coloring. I was then left with the choice between a monochrome plot like Anton shows, and a figure where the top face of a bar has a different color than its sides.

• I don't think that, as Nico said, matlab2tikz now fully supports 3D histograms, or I wouldn't have come here in the first place. I tried matlab2tikz on my picture given by matlab using 'bar3', and the result was bugged.

=> I offer a solution where I got rid of \begin{axis} and the constraints like \edef, \temp and \noexpand, that I had to use to make Anton's way work automatically.

Here is the minimal code :

\documentclass{minimal}
\usepackage{pgfplots}

\begin{document}

\pgfplotstableread{DataTest.dat}{\firsttable}                   
    \pgfplotstablegetrowsof{DataTest.dat}   
    \pgfmathtruncatemacro{\rows}{\pgfplotsretval-1}   

    \pgfplotstablegetelem{0}{[index] 2}\of{\firsttable} 
        \let\maxZ\pgfplotsretval    
    \pgfmathsetmacro{\Zscale}{4/\maxZ}

\begin{tikzpicture}[x={(0.866cm,-0.5cm)},y={(0.866cm,0.5cm)},z={(0cm,4 cm)}]

\colorlet{redhsb}[hsb]{red}     %
\colorlet{bluehsb}[hsb]{blue}   % 

\foreach \p in {1,...,\rows}{
        \pgfplotstablegetelem{\p}{[index] 0}\of{\firsttable} 
        \let\x\pgfplotsretval 
        \pgfplotstablegetelem{\p}{[index] 1}\of{\firsttable} 
        \let\y\pgfplotsretval 
        \pgfplotstablegetelem{\p}{[index] 2}\of{\firsttable} 
        \let\z\pgfplotsretval 

        \pgfmathtruncatemacro{\teinte}{100-((\z/\maxZ)*100)}
        \colorlet{col}[rgb]{bluehsb!\teinte!redhsb}   
         % Visible faces from original view
            \fill[col] (\x+0.5,\y+0.5,\z) -- (\x+0.5,\y-0.5,\z) -- (\x+0.5,\y-0.5,0) -- (\x+0.5,\y+0.5,0) -- (\x+0.5,\y+0.5,\z);
                \draw[black](\x+0.5,\y+0.5,\z) -- (\x+0.5,\y-0.5,\z) -- (\x+0.5,\y-0.5,0) -- (\x+0.5,\y+0.5,0) -- (\x+0.5,\y+0.5,\z);
            \fill[col] (\x+0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,0) -- (\x+0.5,\y-0.5,0) -- (\x+0.5,\y-0.5,\z);
                \draw[black](\x+0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,0) -- (\x+0.5,\y-0.5,0) -- (\x+0.5,\y-0.5,\z);
          % Top face
           \fill[col] (\x-0.5,\y-0.5,\z) -- (\x-0.5,\y+0.5,\z) -- (\x+0.5,\y+0.5,\z) -- (\x+0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,\z) ;
            \draw[black] (\x-0.5,\y-0.5,\z) -- (\x-0.5,\y+0.5,\z) -- (\x+0.5,\y+0.5,\z) -- (\x+0.5,\y-0.5,\z) -- (\x-0.5,\y-0.5,\z);
}

\end{tikzpicture}

\end{document}

Using the file DataTest.dat containing:

X   Y   Z
3   3   1   %max

1   3   1
1   2   0.8
1   1   0.7
2   3   0.75
2   2   0.5
2   1   0.25
3   3   0.3
3   2   0.1
3   1   0

Which gives the following picture :

To improve the picture and to have more comments on the code, here is a more detailed solution :

\documentclass{minimal}
\usepackage{pgfplots}

\begin{document}

    \pgfplotstableread{DataTest.dat}{\firsttable}           % Read
      \pgfplotstablegetrowsof{DataTest.dat} 
      \pgfmathtruncatemacro{\rows}{\pgfplotsretval-1}       % Put the number of row minus one in \rows, 
                                                            %     to use : \foreach \p in {0,...,\rows}
% Assign variables max
\pgfplotstablegetelem{0}{[index] 0}\of{\firsttable} 
        \let\maxX\pgfplotsretval 
\pgfplotstablegetelem{0}{[index] 1}\of{\firsttable} 
        \let\maxY\pgfplotsretval 
\pgfplotstablegetelem{0}{[index] 2}\of{\firsttable} 
        \let\maxZ\pgfplotsretval 

\pgfmathsetmacro{\Zscale}{4/\maxZ} % contain the values of z between 0 and 4 cm 
                                       %      (provided that they are positiv)

% Defining by hand the axis
\begin{tikzpicture}[x={(0.866cm,-0.5cm)},y={(0.866cm,0.5cm)},z={(0cm,\Zscale cm)}]

% Defining hsb color to have a color scale
\colorlet{redhsb}[hsb]{red}     %
\colorlet{bluehsb}[hsb]{blue}   % 

% Drawing the system of axes
\draw[->] (0,0,0) -- (1,0,0) node [black,left] {x};
\draw[->] (0,0,0) -- (0,1,0) node [black,left] {y};
\draw[->] (0,0,0) -- (0,0,1/\Zscale) node [black,left] {z};

% Write unit on x and y
\foreach \p in {1,...,\maxX}{
    \draw {(\p,0,0)} node[right] {\p};
    % Draw the grid
    \foreach \q in {1,...,\maxY}{
        \draw[black] (\p-0.5,\q-0.5,0) -- (\p+0.5,\q-0.5,0) -- (\p+0.5,\q+0.5,0) -- (\p-0.5,\q+0.5,0) -- (\p-0.5,\q-0.5,0);
        }
}
\foreach \p in {1,...,\maxY}{
    \draw {(\maxX+1,\p,0)} node[left] {\p};
}

\foreach \p in {1,...,\rows}{
        \pgfplotstablegetelem{\p}{[index] 0}\of{\firsttable}    % The order in which the bars are drawn is determined by
        \let\x\pgfplotsretval                                   %    the order of the lines in the data file.
        \pgfplotstablegetelem{\p}{[index] 1}\of{\firsttable}    % And as the drawings just pile up, the last one just goes
        \let\y\pgfplotsretval                                   %    on top of the previous drawings.
        \pgfplotstablegetelem{\p}{[index] 2}\of{\firsttable}    % The order here works with chosen view angle, if you
        \let\z\pgfplotsretval                                   %    change the angle, you might have to change it.

        \pgfmathsetmacro{\w}{0.8/2} % half the width of the bars

        \pgfmathtruncatemacro{\teinte}{100-((\z/\maxZ)*100)}
        \colorlet{col}[rgb]{bluehsb!\teinte!redhsb}   
        % Unseen faces from orginal view, but if you change the angle ....
            %\fill[col] (\x-\w,\y-\w,\z) -- (\x-\w,\y+\w,\z) -- (\x-\w,\y+\w,0) -- (\x-\w,\y-\w,0) -- (\x-\w,\y-\w,\z);
            %   \draw[black] (\x-\w,\y-\w,\z) -- (\x-\w,\y+\w,\z) -- (\x-\w,\y+\w,0) -- (\x-\w,\y-\w,0) -- (\x-\w,\y-\w,\z);
            %\fill[col] (\x-\w,\y+\w,\z) -- (\x+\w,\y+\w,\z) -- (\x+\w,\y+\w,0) -- (\x-\w,\y+\w,0) -- (\x-\w,\y+\w,\z);
            %   \draw[black](\x-\w,\y+\w,\z) -- (\x+\w,\y+\w,\z) -- (\x+\w,\y+\w,0) -- (\x-\w,\y+\w,0) -- (\x-\w,\y+\w,\z);
         % Visible faces from original view
            \fill[col] (\x+\w,\y+\w,\z) -- (\x+\w,\y-\w,\z) -- (\x+\w,\y-\w,0) -- (\x+\w,\y+\w,0) -- (\x+\w,\y+\w,\z);
                \draw[black](\x+\w,\y+\w,\z) -- (\x+\w,\y-\w,\z) -- (\x+\w,\y-\w,0) -- (\x+\w,\y+\w,0) -- (\x+\w,\y+\w,\z);
            \fill[col!60!gray] (\x+\w,\y-\w,\z) -- (\x-\w,\y-\w,\z) -- (\x-\w,\y-\w,0) -- (\x+\w,\y-\w,0) -- (\x+\w,\y-\w,\z);
                \draw[black](\x+\w,\y-\w,\z) -- (\x-\w,\y-\w,\z) -- (\x-\w,\y-\w,0) -- (\x+\w,\y-\w,0) -- (\x+\w,\y-\w,\z);
          % Top face
           \fill[top color=col!40!gray, bottom color=col!80!gray] (\x-\w,\y-\w,\z) -- (\x-\w,\y+\w,\z) -- (\x+\w,\y+\w,\z) -- (\x+\w,\y-\w,\z) -- (\x-\w,\y-\w,\z) ;
            \draw[black] (\x-\w,\y-\w,\z) -- (\x-\w,\y+\w,\z) -- (\x+\w,\y+\w,\z) -- (\x+\w,\y-\w,\z) -- (\x-\w,\y-\w,\z);
}

\end{tikzpicture}

\end{document}

Which gives the image :

As you can see I added some features which are detailed in the comments of the code.

I hope it can help someone, thanks for reading.

To complete this, here is the Matlab code I used to generate the data file from the data in the matrix MAC.

fileID = fopen('DataOutMac.dat','w');
  MaxMAC = max(MAC(:));

  %Header
    fprintf(fileID,'X \t\t Y \t\t Z \n');
  %Maximums
    fprintf(fileID,['' num2str(size(MAC,1)) ' \t\t ' num2str(size(MAC,2)) ' \t\t ' num2str(MaxMAC) ' \t\t %% max \n \n']);
  %All the values
    for i=1:size(MAC,1)
      for j=size(MAC,2):-1:1
        if MAC(i,j)>(MaxMAC/10000)  % To remove the smallest bars
            fprintf(fileID,['' num2str(i) ' \t\t ' num2str(j) ' \t\t%12.8f \n'], MAC(i,j));%'%12.8f\n'], MAC(i,j));
        end
      end
    end
fclose(fileID);

Edit to answer the comment:

-First, the reason why I am here in the first place : on the left is matlab's output and on the right matlab2tikz's result.

-Second, here is the result of one of my tries of jake's solution.

Answer 5

WITHOUT EXTERNAL PROGRAMS: Just produce a scatter plot of cubes with the height of the code depending on the data. (I stole the code from here, but the author of the code is fine with me sharing it here ;-)

UPDATE: @sporc found a bug and helped me to improve the code. Thanks! See here for further additions to the code.

If you run this, LaTeX will tell you which prefactor to insert. I could not do this in a simple way because of the expansion issues, essentially because pgfplots is setting the scales only after it is done with the plots. In this example, it would be possible to avoid this by doing an empty plot first. But then the code would blow up and the user would modify things twice, or do some other crazy things, such that I feel adjusting one single number is the lesser evil.

\documentclass[tikz,border=3.14pt]{standalone}
\usetikzlibrary{calc}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.16}
% from https://tex.stackexchange.com/a/102770/121799
\def\pgfplotsinvokeiflessthan#1#2#3#4{%
    \pgfkeysvalueof{/pgfplots/iflessthan/.@cmd}{#1}{#2}{#3}{#4}\pgfeov
}%
\def\pgfplotsmulticmpthree#1#2#3#4#5#6\do#7#8{%
    \pgfplotsset{float <}%
    \pgfplotsinvokeiflessthan{#1}{#4}{%
        % first key <:
        #7%
    }{%
        \pgfplotsinvokeiflessthan{#4}{#1}{%
            % first key >:
            #8%
        }{%
            % first key ==:
            \pgfplotsset{float <}%
            \pgfplotsinvokeiflessthan{#2}{#5}{%
                % second key <
                #7%
            }{%
                \pgfplotsinvokeiflessthan{#5}{#2}{%
                    % second key >
                    #8%
                }{%
                    % second key ==
                    \pgfplotsset{float <}%
                    \pgfplotsinvokeiflessthan{#3}{#6}{%
                        % third key <
                        #7%
                    }{%
                        % third key >=
                        #8%
                    }%
                }%
            }%
        }%
    }%
}%

\begin{document}
\pgfplotstableread[col sep=comma,header=true]{%
x,y,color,myvalue
2,3,1,100
4,3,2,3
2,7,3,0.75
7,7,4,45
8,5,2,3
2,5,1,10
4,-4,2,1
4,1,3,75
5,-1,4,4
5,2,2,3
1,-2,1,10
2,5,2,5
3,-8,3,75
4,5,4,42
7,-2,2,2
}{\datatable}
%
%\pgfplotstablesort[col sep=comma,header=true]\resulttable{\datatable}
\pgfplotstablesort[create on use/sortkey/.style={
        create col/assign/.code={%
            \edef\entry{{\thisrow{x}}{\thisrow{y}}{\thisrow{myvalue}}}%
            \pgfkeyslet{/pgfplots/table/create col/next content}\entry
        }
    },
    sort key=sortkey,
    sort cmp={%
        iflessthan/.code args={#1#2#3#4}{%
            \edef\temp{#1#2}%
            \expandafter\pgfplotsmulticmpthree\temp\do{#3}{#4}%
        },
    },
    sort,
    columns/Mtx/.style={string type},
    columns/Kind/.style={string type},]\resulttable{\datatable}

\begin{tikzpicture}%[x={(0.866cm,-0.5cm)},y={(0.866cm,0.5cm)},z={(0cm,1 cm)}]
\pgfplotsset{set layers}
\begin{axis}[% from section 4.6.4 of the pgfplotsmanual
        view={120}{40},
        width=320pt,
        height=280pt,
        z buffer=none,
        xmin=-1,xmax=9,
        ymin=-10,ymax=8,
        zmin=0,zmax=200,
        enlargelimits=upper,
        ztick={0,100,200},
        zticklabels={0,50,100}, % here one has to "cheat"
        % meaning that one has to put labels which are the actual value 
        % divided by 2. This is because the bars will be centered at these
        % values
        xtick=data,
        extra tick style={grid=major},
        ytick=data,
        grid=minor,
        xlabel={$x$},
        ylabel={$y$},
        zlabel={$z$},
        minor tick num=1,
        point meta=explicit,
        colormap name=viridis,
        scatter/use mapped color={
            draw=mapped color,fill=mapped color!70},
        execute at begin plot={}            
        ]
\path let \p1=($(axis cs:0,0,1)-(axis cs:0,0,0)$) in 
\pgfextra{\pgfmathsetmacro{\conv}{2*\y1}
\typeout{Kindly\space\space consider\space setting\space the\space 
        prefactor\space of\space z\space to\space \conv}};      
\addplot3 [visualization depends on={
0.9952*z \as \myz}, % you'll get told how to adjust the prefactor
scatter/@pre marker code/.append style={/pgfplots/cube/size z=\myz pt},%
scatter,only marks,
mark=cube*,mark size=5,opacity=1]
 table[x expr={\thisrow{x}},y expr={\thisrow{y}},z
 expr={1*\thisrow{myvalue}},
 meta expr={\thisrow{color}}
        ] \resulttable;
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 6

Despite the many solutions and this being an old post, the initial problem/question, i.e. I have a MATLAB 3D histogram and want to put it in a nice tikz environment, is not solved. This is maybe because in the newer MATLAB versions the function histogram2 was introduced, but who knows.

Being myself in this situation, and considering I tend to dislike pgfplots and prefer plain TikZ (easier to make changes later, more low level and understandable) I propose the following MATLAB function that creates a nice TikZ figure from an histogram2 object.

    function histogram2tikz( h, file  )
    %HISTOGRAM2TIKZ
    if nargin < 2
        file = 'figure.tex';
    end

        % Open file for writing / re-writing
        fid = fopen( file, 'w' );

        % Collect relevant variables from histogram
        hvals = h.Values;
        xed = h.XBinEdges;
        yed = h.YBinEdges;
        colorBars = 'blue';
        clear h

        % Begin 3D tikz picture
        fprintf( fid, ...
        '%% Begin 3D tikz picture \n \\tdplotsetmaincoords{20}{100} \n \\begin{tikzpicture}[tdplot_main_coords, yscale = %f] \n', ...
        5/max( hvals(:) ) );

        % Plot axis and grid
            % Axis
            maxx = max( xed ); maxy = max( yed ); maxval = max( hvals(:) );
            minx = min( xed ); miny = min( yed );
            fprintf( fid, ...
            '%% Plot axis and grid \n\t%% Axis \n  \\draw[->] (%f,%f,0) -- (%f,%f,0) node[anchor=west]{$y$} ;\n', ...
            minx, miny, minx, maxy );
            fprintf( fid, ...
            '\\draw[->] (%f,%f,0) -- (%f,%f,0) node[anchor=north]{$x$};\n', ...
            minx, miny, maxx, miny );
            fprintf( fid, ...
            '\\draw[->] (%f,%f,0) -- (%f,%f,%f);\n', ...
            minx, miny, minx, miny, maxval );
            % Grid
            fprintf( fid, '\t%%Grid and ticks\n');
            for ii = 1:length( xed )
                fprintf( fid, ...
                '\\draw[gray,thin] (%f,%f,0) -- (%f,%f,0);\n', ...
                xed(ii), miny, xed(ii), maxy );
            end
            for ii = 1:length( yed )
                fprintf( fid, ...
                '\\draw[gray,thin] (%f,%f,0) -- (%f,%f,0);\n', ...
                minx, yed(ii), maxx, yed(ii) );
            end

        % Plot bars
        for ii = 1:length( xed )-1
            for jj = 1:length( yed )-1
                bar( xed(ii:ii+1), yed(jj:jj+1), hvals(ii,jj), fid, colorBars );
            end
        end

        % Finish tikzfigure and close file
        fprintf( fid, ...
        '%% Finish tikz picture \n \\end{tikzpicture}' );
        fclose( fid );

    end

    function bar( xbin, ybin, h, fid, cB )
        fprintf( fid, '%%Bar with edges x: %.2f,%.2f; edges y: %.2f,%.2f ; height: %.2f\n', ...
                 xbin(1), xbin(2), ybin(1), ybin(2), h );
        if h>0
            % Draw bottom square
            fprintf( fid, ...
                '\\draw[thin] (%f,%f,0) -- (%f,%f,0) -- (%f,%f,0) -- (%f,%f,0) -- cycle;\n', ...
                xbin(1), ybin(1), ...
                xbin(1), ybin(2), ...
                xbin(2), ybin(2), ...
                xbin(2), ybin(1) );
            % Draw back faces
            fprintf( fid, ...
                '\\draw[thin,fill=%s!70!black] (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- cycle;\n', ...
                cB, ...
                xbin(1), ybin(1), 0, ...
                xbin(2), ybin(1), 0, ...
                xbin(2), ybin(1), h, ...
                xbin(1), ybin(1), h ); 
            fprintf( fid, ...
                '\\draw[thin,fill=%s!70!black] (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- cycle;\n', ...
                cB, ...
                xbin(1), ybin(1), 0, ...
                xbin(1), ybin(2), 0, ...
                xbin(1), ybin(2), h, ...
                xbin(1), ybin(1), h ); 
            % Draw front faces
            fprintf( fid, ...
                '\\draw[thin,fill=%s!70!black] (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- cycle;\n', ...
                cB, ...
                xbin(1), ybin(2), 0, ...
                xbin(2), ybin(2), 0, ...
                xbin(2), ybin(2), h, ...
                xbin(1), ybin(2), h ); 
            fprintf( fid, ...
                '\\draw[thin,fill=%s!70!black] (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- cycle;\n', ...
                cB, ...
                xbin(2), ybin(1), 0, ...
                xbin(2), ybin(2), 0, ...
                xbin(2), ybin(2), h, ...
                xbin(2), ybin(1), h ); 
            % Draw top square
            fprintf( fid, ...
                '\\path[fill=%s] (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- (%f,%f,%f) -- cycle;\n', ...
                cB, ...
                xbin(1), ybin(1), h, ...
                xbin(1), ybin(2), h, ...
                xbin(2), ybin(2), h, ...
                xbin(2), ybin(1), h );  
        end
    end

A minimal working example would be running in MATLAB

% Generate Multivariate normal data
d = mvnrnd( [0,0], eye(2), 200 );
% Get Histogram
h = histogram2( d(:,1), d(:,2) );
% Generate TikZ figure
histogram2tikz(h)

and having in the same folder the minimal LaTeX document

\documentclass{article}
% Graphics in tikz format
\usepackage{tikz}
% 3D tikz, simple library
\usepackage{tikz-3dplot}
%% Document begins
\begin{document}
    \input{figure}
\end{document}

which produces

The great thing about this is that then you can get into the generated file and change colors for every bar, as well as anything other you might want, in a pretty straightforward manner if you know your basic TikZ. For example, replacing all fill=blue!70!black by fill=blue!70!black,fill opacity=0.6 and change the yscale for it to look nicer, you get

Answer 7

Regardless of the fact that this is a confusing perspective, you can create a 3D bar diagram with pgfplots like this:

The idea is to use mark=cube* and manipulate the cube/size z in such a way that the desired 3D bars are created. Similar to the answer from @user121799, with the difference that reading out and using the unit length in the z-direction should be automated.

If one put e.g. cube/size z=4mm, so the cube dimensions grow from its room position by 2mm and by -2mm in the z-direction. So they have to be positioned at
x=X, y=Y, z expr={0.5*\thisrow{Z}}.

The correct height of the cubes can be made with

visualization depends on={\thisrow{Z} \as \zvalue}, 
scatter/@pre marker code/.append style={
/utils/exec=\pgfmathsetmacro{\barheight}{\zunitlength*\zvalue},
/pgfplots/cube/size z=\barheight },

where the zunitlength is found with

\path let \p1=($(axis cs:0,0,1)-(axis cs:0,0,0)$) in 
\pgfextra{   \pgfmathsetglobalmacro{\zunitlength}{\y1}   }    };

Note: It turns out that it makes sense to set zmax=\zMax, where this maximum z-value \zMax can be determined in the form

\pgfplotstablegetrowsof{\datatable}
\pgfmathtruncatemacro{\RowsNo}{\pgfplotsretval-1}  
%Number of Rows: \RowsNo
\pgfmathsetmacro\zMax{0}
\foreach \n in {0,...,\RowsNo}{
\pgfplotstablegetelem{\n}{Z}\of{\datatable}
\pgfmathparse{\pgfplotsretval > \zMax ? \pgfplotsretval : \zMax}
\xdef\zMax{\pgfmathresult}
}
%Maximum z-Axis: \zMax

\documentclass[border=5pt, tikz]{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.17}
\usetikzlibrary{calc}

\def\pgfmathsetglobalmacro#1#2{\pgfmathparse{#2}%
\global\let#1\pgfmathresult}

\pgfplotsset{
colormap = {mycolormap}{
color(0)  = (blue!50!black); 
color(1) = (purple);
color(2) = (green!55!black);
color(3) = (brown);
color(4) = (blue!66)
color(5) = (violet)
},
colormap name=mycolormap,
%colormap name=viridis
}

\begin{document}
\pgfplotstableread[col sep=comma,header=true]{
X,   Y,    Z
2,    0,   4
1,    0,   5
0,    1,   10
3,    1,   1
1,    1,   3
2,    1,   0
1,    2,   0
2,    2,   5
2,    3,   6
1,    4,   7
1,    5,   11
}{\datatable}

% z-Maximum determination ==================
\pgfplotstablegetrowsof{\datatable}
\pgfmathtruncatemacro{\RowsNo}{\pgfplotsretval-1}  
%Number of rows: \RowsNo

\pgfmathsetmacro\zMax{0}
\foreach \n in {0,...,\RowsNo}{
\pgfplotstablegetelem{\n}{Z}\of{\datatable}
\pgfmathparse{\pgfplotsretval > \zMax ? \pgfplotsretval : \zMax}
\xdef\zMax{\pgfmathresult}
}
%Maximum z-Axis: \zMax
% ============================

\begin{tikzpicture}[]
\begin{axis}[
%height=2cm,  width=7cm, 
% view={120}{40}, x dir=reverse,
xmin=0, 
ymin=0,
zmin=0, zmax=\zMax, 
enlarge z limits={rel=0.25,upper},
xtick={1,...,10},
ytick={1,...,10},
%ytick={0,25,...,100},
grid=both,
xlabel={$x$},  ylabel={$y$},   zlabel={$z$},
minor z tick num=1,
point meta=explicit,
scatter/use mapped color={draw=mapped color!50!black, 
fill=mapped color!70},
]
% unitlenghth z-Axis determination 
\path let \p1=($(axis cs:0,0,1)-(axis cs:0,0,0)$) in 
\pgfextra{   \pgfmathsetglobalmacro{\zunitlength}{\y1}   } node[xshift=2cm, yshift=2cm]{%\zunitlength % show value
}; 
\addplot3[
scatter, only marks,
mark=cube*, mark size=5,  %opacity=0.8,
nodes near coords*=, % will er...
%%% barheight determination 
visualization depends on={\thisrow{Z} \as \zvalue}, 
scatter/@pre marker code/.append style={
/utils/exec=\pgfmathsetmacro{\barheight}{\zunitlength*\zvalue},
/pgfplots/cube/size z=\barheight        
},
] table[x=X, y=Y,     
z expr={0.5*\thisrow{Z}}, 
meta expr={\thisrow{Y}}
]{\datatable}; 
\end{axis}
\end{tikzpicture}
\end{document}