Plot transparent 3D boxes using gnuplot - gnuplot

Question

I have a data file "data.txt" which contains the coordinates of the borders of several boxes in three dimensions. Each line represents a single box. The file contains over 100 boxes.
x_Min x_Max y_Min y_Max z_Min z_Max
-0.2 0.2 -0.2 0.2 -0.2 0.2
0.2 0.4 -0.2 0.2 -0.2 0.2
....
...
..
Now I want to plot that. In two dimensions it is very easy by using
plot "boxes.txt" u 1:2:3:4 w boxxyerrorbars
With (x-Value):(y-Value):(Half Width):(Half Height).
Than I get this:
But how can I achieve this in three dimensions? I didn't find any solution for this problem.

Answer 1

In case you are still interested in a gnuplot solution...
If it is sufficient to just draw the edges of the boxes you can use the plotting style with vectors. You simply need to select the necessary columns and plot all edges in 3 loops. Here gnuplot's integer division (e.g. 1/2=0) is helpful.
However, if you want to plot surfaces and hide surfaces if they are covered by another box you'd better use with pm3d (check help pm3d). Then, however, you have to re-shape your input data.
Script:
### plot edges of boxes in 3D
reset session
$Data <<EOD
x_Min x_Max y_Min y_Max z_Min z_Max
-0.2 0.2 -0.2 0.2 -0.2 0.2
0.3 0.4 -0.1 0.2 -0.1 0.2
-1.5 -0.5 -1.2 -0.4 -0.9 0.0
0.5 1.0 -1.0 -0.5 -0.5 -0.1
0.0 0.3 -1.4 -1.1 -1.0 -0.7
EOD
set xyplane relative 0
set view equal xyz
set view 60,30,1.7
set xtics 0.5
set ytics 0.5
set ztics 0.5
set key noautotitle
splot for [i=0:3] $Data u 1:i/2+3:i%2+5:($2-$1):(0):(0):0 w vec lc var nohead, \
for [i=0:3] '' u i/2+1:3:i%2+5:(0):($4-$3):(0):0 w vec lc var nohead, \
for [i=0:3] '' u i/2+1:i%2+3:5:(0):(0):($6-$5):0 w vec lc var nohead
### end of script
Result:

Answer 2

I actually found a solution using Python and Matplotlib.
import numpy as np
import matplotlib.pyplot as plt
import random
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
DIM = 3;
# Unit cube
cube = [[[0.0,1.0],[0.0,0.0],[0.0,0.0]],\
[[0.0,0.0],[0.0,1.0],[0.0,0.0]],\
[[0.0,0.0],[0.0,0.0],[0.0,1.0]],\
[[1.0,1.0],[0.0,1.0],[0.0,0.0]],\
[[1.0,0.0],[1.0,1.0],[0.0,0.0]],\
[[1.0,1.0],[0.0,0.0],[0.0,1.0]],\
[[1.0,1.0],[1.0,1.0],[0.0,1.0]],\
[[0.0,0.0],[1.0,1.0],[0.0,1.0]],\
[[0.0,0.0],[0.0,1.0],[1.0,1.0]],\
[[0.0,1.0],[0.0,0.0],[1.0,1.0]],\
[[1.0,1.0],[0.0,1.0],[1.0,1.0]],\
[[0.0,1.0],[1.0,1.0],[1.0,1.0]]]
# Number of Cubes
numb_Cubes = 5
# Array with positions [x, y, z]
pos = [[0 for x in range(DIM)] for y in range(numb_Cubes)]
for k in range(numb_Cubes):
for d in range(DIM):
pos[k][d] = random.uniform(-1,1)
# Size of cubes
size_of_cubes = [0 for y in range(numb_Cubes)]
for k in range(numb_Cubes):
size_of_cubes[k] = random.random()
# Limits
xmin, xmax = -1, 1
ymin, ymax = -1, 1
zmin, zmax = -1, 1
for n in range(numb_Cubes):
for k in range(len(cube)):
x = np.linspace(cube[k][0][0]*size_of_cubes[n]+pos[n][0], cube[k][0][1]*size_of_cubes[n]+pos[n][0], 2)
y = np.linspace(cube[k][1][0]*size_of_cubes[n]+pos[n][1], cube[k][1][1]*size_of_cubes[n]+pos[n][1], 2)
z = np.linspace(cube[k][2][0]*size_of_cubes[n]+pos[n][2], cube[k][2][1]*size_of_cubes[n]+pos[n][2], 2)
ax.plot(x, y, z, 'black', lw=1)
ax.set_xlim([xmin,xmax])
ax.set_ylim([ymin,ymax])
ax.set_zlim([zmin,ymax])
The result I get:
I am still interested in a solution for gnuplot or a faster solution for Python.