Generate 3d surface plot using black and white heightmap and pgfplots

Question

I am searching for the best way, software or script (latex, python, R, octave), to interactively draw or paint some 3D surface plot for pedagogic usage.

I finally found a way to generate and transform pdf 3D surface plot with svg export using pgfplots latex package. Thus I can redraw/rework initial drawing to render a graphic like this.

But I don't want to use a common mathematic function for input of the 3d drawing, I want to use, if possible, a heightmap to generate the surface.

Is it possible to transform a random black and white heightmap into a 3Dsurface plot with pgfplots ?

Henri Menke · Accepted Answer

I used scipy to transform the heightmap to a data matrix and then wrote the coordinates and the height values to a file.

Exact height profile

#!/usr/bin/python

import numpy as np
from scipy import misc

matrix = misc.imread('536ws.jpg',flatten=True)
x,y = matrix.shape

mesh = ""
for i in range(0,x):
    for j in range(0,y):
        mesh += "%dt%dt%dn" % (i,j,matrix[i,j])
    mesh += "n"

print mesh

I ran the script and piped the output to a file called matrix.dat

python extract.py > matrix.dat

Then I used pgfplots to visualise the matrix

documentclass[tikz]{standalone}
usepackage{pgfplots}
begin{document}
begin{tikzpicture}
  begin{axis}
    addplot3[surf,colormap/blackwhite,mesh/ordering=y varies] table {matrix.dat};
  end{axis}
end{tikzpicture}
end{document}

You need to use lualatex for this as pdflatex will run out of memory.  Processing this file takes ca. 1 minute and 52 seconds on my machine.

In the rendered png the colour map turned out darker than in the pdf.

Averaged height profile

The following script introduces some averaging over all points of the mesh (factor of 5 here).  The rest of the procedure stays the same.

#!/usr/bin/python

import numpy as np
from scipy import misc

matrix = misc.imread('536ws.jpg',flatten=True)
x,y = matrix.shape
matrix = misc.imresize(matrix,(x/5,y/5))
x,y = matrix.shape

mesh = ""
for i in range(0,x):
    for j in range(0,y):
        mesh += "%dt%dt%dn" % (i,j,matrix[i,j])
    mesh += "n"

print mesh

This is now compilable with pdflatex (no more out-of-memory) and takes ca. 3 seconds.

marisol bermudez · Answer

Here an updated Python 3 code:
 #!/usr/bin/python3
 
 import numpy as np
 
 import imageio
 
 matrix = imageio.imread('536ws.jpg', as_gray = True)
 x,y=matrix.shape
 
 mesh = ' ' 
 for i in range(0,x):
     for j in range(0,y):
         mesh += '%d t %d t %d n' % (i,j,matrix[i,j])
         mesh += 'n'
 
 print(mesh)

To get the .dat file:
python3 extract.py > matrix.dat

The latex code is
documentclass[tikz]{standalone}
usepackage{pgfplots}

begin{document}

begin{tikzpicture}
  begin{axis}
    addplot3[surf,colormap/blackwhite,mesh/ordering=y varies] table {matrix.dat};
end{axis}
end{tikzpicture}
end{document}

On the terminal:
lualatex file.tex

Generate 3d surface plot using black and white heightmap and pgfplots

2 Answers

Exact height profile

Averaged height profile

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