I am exploring random stackings of cubes.
I started with 2D and can generate random packings within a rectangle like this:
Now I have the code to generalize the stacking to 3D, but I am struggling to generalize the visualization. An example data set is, filling a 3x3x3 cube with 1x1x1 and 2x2x2 cubes,
#the coordinates of a corner vertex of the 19 1x1x1 cubes
x1 = [1, 0, 2, 0, 0, 0, 2, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 1]
y1 = [1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0]
z1 = [2, 1, 1, 0, 1, 2, 2, 2, 2, 1, 2, 0, 0, 1, 2, 2, 0, 0, 2]
#the coordinates of a corner vertex of the 1 2x2x2 cube
x2 = [1]
y2 = [1]
z2 = [0]
# I believe the random filling is working because
# the total volumes equal: 19 + 2**3 = 3**3
#I would like to start with the lists
X = [x1,x2]
Y = [y1,y2]
Z = [z1,z2]
sizes = [1,2]
#because I want to generalize the visualization to n sizes
So far, all I have the knowledge to do is plot a 3D scatter of the data
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
for ii in range(len(sizes)):
ax.scatter(X[ii],Y[ii],Z[ii])
plt.show()
I would like to make a plot more like this, except with variable sizes.
Any help would be greatly appreciated! I have a lot to learn about matplotlib/pyplot and so on.
I have made a little bit of progress:
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle, PathPatch
from mpl_toolkits.mplot3d import Axes3D
import mpl_toolkits.mplot3d.art3d as art3d
def cube(a,b,c,l):
for zz in [c,c+l]:
for i in ["x","y","z"]:
side = Rectangle((a, b), l,l)
ax.add_patch(side)
art3d.pathpatch_2d_to_3d(side, z=zz, zdir=i)
fig = plt.figure()
ax=fig.gca(projection='3d')
cube(0,0,0,1)
ax.set_xlim3d(-2, 2)
ax.set_ylim3d(-2, 2)
ax.set_zlim3d(-2, 2)
plt.show()
This plots a single cube.
EDIT:
More progress, I am now very close
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle, PathPatch
from mpl_toolkits.mplot3d import Axes3D
import mpl_toolkits.mplot3d.art3d as art3d
cmap = plt.get_cmap('spring') #define the colors of the plot
colors = [cmap(i) for i in np.linspace(0.1, 0.9, n+1)]
def cube(a,b,c,l): #plots a cube of side l at (a,b,c)
for ll in [0,l]:
for i in range(3):
dire= ["x","y","z"]
xdire = [b,a,a]
ydire = [c,c,b]
zdire = [a,b,c]
side = Rectangle((xdire[i], ydire[i]),facecolors[np.where(sizes == l)[0]],edgecolor='black')
ax.add_patch(side)
art3d.pathpatch_2d_to_3d(side, z=zdire[i]+ll, zdir=dire[i])
def plotter3D(X,Y,Z,sizes): #run cube(a,b,c,l) over the whole data set
for iX in range(len(X)):
x = X[iX]
y = Y[iX]
z = Z[iX]
for ix in range(len(x)):
cube(x[ix],y[ix],z[ix],sizes[iX])
fig = plt.figure() #open a figure
ax=fig.gca(projection='3d') #make it 3d
plotter3D(X,Y,Z,sizes) #generate the cubes from the data set
ax.set_xlim3d(0, length) #set the plot ranges
ax.set_ylim3d(0, width)
ax.set_zlim3d(0, height)
plt.show()
This generates the desired output, although it seems to be see-through in some places when viewed from certain angles. You can see this in the small cube-- dead center at coordinates (1.5,2,3) Any idea how to fix this?
Another edit:
The solution outined above has two problems: (1) I can't get equal aspect ratios for the three axes, and (2) The cubes are see-through from certain angles. Here's what the output looks like for a larger system
Related
I have been trying to make a Rubix Cube in python using Matplotlib. I've struggled to get each face of the cube to have its own colour? How do I do this in Matplotlib?
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
axes = [3, 3, 3]
data = np.ones(axes)
alpha = 0.9
colours = np.empty(axes + [4])
colours[0] = [1, 0, 0, alpha] # red
colours[1] = [0, 0, 1, alpha] # blue
colours[2] = [1, 1, 0, alpha] # yellow
figure = plt.figure()
ax = figure.add_subplot(111, projection = '3d')
ax.voxels(data, facecolors = colours, edgecolors = 'grey')
plt.show()
I was looking for a way to build cubes of the same size, then draw a line through this space and output the result in the form of coordinates of cubes that this line intersects and paint these cubes with a different color. The line can be either straight or curved.
I used matplotlib to plot cubes and lines. From these sources:
https://www.geeksforgeeks.org/how-to-draw-3d-cube-using-matplotlib-in-python/
Representing voxels with matplotlib
Example code:
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
axes = [5, 5, 5]
# Create Data
data = np.ones(axes, dtype=np.bool)
# Controll Tranperency
alpha = 0.3
# Control colour
colors = np.empty(axes + [4], dtype=np.float32)
colors[0] = [1, 0, 0, alpha] # red
colors[1] = [0, 1, 0, alpha] # green
colors[2] = [0, 0, 1, alpha] # blue
colors[3] = [1, 1, 0, alpha] # yellow
colors[4] = [1, 1, 1, alpha] # grey
# Plot figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x1 = [1, 4]
y1 = [0, 5]
z1 = [0, 5]
ax.plot3D(x1, y1, z1, 'black', linewidth = 5)
# Voxels is used to customizations of
# the sizes, positions and colors.
ax.voxels(data, facecolors=colors, edgecolors='grey')
result
In short: I need to plot a grid of cubes and draw a line through it. After determine which cubes this line intersects.
Is it possible to do this in Matplotlib or do I need to use another library to solve my question?
God, why do I put myself though this.
Anyways, here is an iterative solution because I do not feel like doing linear algebra. I tried and I failed.
# Here be dragons
def linelamb(x,y,z):
return lambda s: [int(i) for i in [x[0]+s*(x[1]-x[0]), y[0]+s*(y[1]-y[0]), z[0]+s*(z[1]-z[0])]]
line = linelamb(x1,y1,z1)
hitboxes = np.zeros(axes)
x,y,z = 0,0,0
for r in [i for i in np.arange(0,1,0.001)]:
xnew,ynew,znew = line(r)
if not (x == xnew and y == ynew and z == znew):
hitboxes[xnew,ynew,znew] = 1
x,y,z = xnew,ynew,znew
ax.voxels(hitboxes, facecolors=[0,0,0,0.5], edgecolors='black');
I spent some extra time to make this more adaptable but my brain stopped working. You might want to adaptively change the step size of the range but good luck.
I'm doing some linear programming for optimization and I need to present the data, using different colors on the surface based on the value of the optimized function. The optimized function requires all three x, y, z coordinates to be passed in, so basically the surface I need to color iw a concave 3D polyhedron. The walls can be vertical as well. My current approach is something like that:
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d as a3
import scipy as sp
import numpy as np
from matplotlib import colors
verts = [(0, 0, 0), (1, 1, 1), (0, 1, 0), (1, 0, 0)]
faces = [[0, 1, 2], [0, 1, 3]]
ax = a3.Axes3D(plt.figure())
ax.dist = 30
ax.azim = -140
ax.set_xlim([0, 1])
ax.set_ylim([0, 1])
ax.set_zlim([0, 1])
for face in faces:
triangle = verts[face[0]], verts[face[1]], verts[face[2]]
face = a3.art3d.Poly3DCollection([triangle])
face.set_color(colors.rgb2hex(sp.rand(3)))
ax.add_collection3d(face)
plt.show()
But this allows me only to set a single color to a face. My concept is doing it by simply increasing the number of polygons on each wall, but isn't there a simpler way like passing a 3d function to the plot which would map a color to a point based on all three coordinates (I've seen examples for colormaps taking only x and y arguments, but it does not handle vertical walls accordingly.
I have sparse scatter plot to visualize the comparison of predicted vs actual values. The range of the values are 1-4 and there are no decimal points.
I have tried plotly so far with hte following code (but I can also use a matplotlib solution):
my_scatter = go.Scatter(
x = y_actual, y = y_pred, mode = 'markers',
marker = dict(color = 'rgb(240, 189, 89)', opacity=0.5)
)
This prints the graph nicely (see below). I use opacity to see the density at each point. I.e. if two points lie on top of each other, the point will be shown in darker color. However, this is not explanatory enough. Is it possible to add the counts at each point as a label? There are some overlaps at certain intersections. I want to display how many points intersects. Can this be done automatically using matplotlib or plotly?
This answer uses matplotlib.
To answer the initial question first: You need to find out how often the data produces a point at a given coordinate to be able to annotate the points. If all values are integers this can easily be done using a 2d histogram. Out of the hstogram one would then select only those bins where the count value is nonzero and annotate the respective values in a loop:
x = [3, 0, 1, 2, 2, 0, 1, 3, 3, 3, 4, 1, 4, 3, 0]
y = [1, 0, 4, 3, 2, 1, 4, 0, 3, 0, 4, 2, 3, 3, 1]
import matplotlib.pyplot as plt
import numpy as np
x = np.array(x)
y = np.array(y)
hist, xbins,ybins = np.histogram2d(y,x, bins=range(6))
X,Y = np.meshgrid(xbins[:-1], ybins[:-1])
X = X[hist != 0]; Y = Y[hist != 0]
Z = hist[hist != 0]
fig, ax = plt.subplots()
ax.scatter(x,y, s=49, alpha=0.4)
for i in range(len(Z)):
ax.annotate(str(int(Z[i])), xy=(X[i],Y[i]), xytext=(4,0),
textcoords="offset points" )
plt.show()
You may then decide not to plot all points but the result from the histogramming which offers the chance to change the color and size of the scatter points,
ax.scatter(X,Y, s=(Z*20)**1.4, c = Z/Z.max(), cmap="winter_r", alpha=0.4)
Since all values are integers, you may also opt for an image plot,
fig, ax = plt.subplots()
ax.imshow(hist, cmap="PuRd")
for i in range(len(Z)):
ax.annotate(str(int(Z[i])), xy=(X[i],Y[i]), xytext=(0,0), color="w",
ha="center", va="center", textcoords="offset points" )
Without the necesity to calculate the number of occurances, another option is to use a hexbin plot. This gives slightly inaccurate positions of the dots, du to the hexagonal binning, but I still wanted to mention this option.
import matplotlib.pyplot as plt
import matplotlib.colors
import numpy as np
x = np.array(x)
y = np.array(y)
fig, ax = plt.subplots()
cmap = plt.cm.PuRd
cmaplist = [cmap(i) for i in range(cmap.N)]
cmaplist[0] = (1.0,1.0,1.0,1.0)
cmap = matplotlib.colors.LinearSegmentedColormap.from_list('mcm',cmaplist, cmap.N)
ax.hexbin(x,y, gridsize=20, cmap=cmap, linewidth=0 )
plt.show()
I'd like to prepare some statistics for my boss. The flat style of matplotlib bar chart would make them look cheap for those used to Excel charts, although for clarity, using styles like this probably should be avoided.
I'm not that far away, but I don't get how to give the right thickness of the bars:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
row = [0, 0, 0, 22, 0, 0, 4, 16, 2, 0, 4, 4, 12, 26]
length = len(row)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = np.arange(length)
y = np.zeros(14)
z = np.array(row)
width = 0.8
ax.bar3d(x, y, [0]*length, 0.5, 0.001, z)
ax.set_xticks(x + width/2)
ax.set_xticklabels(titles[2:], rotation=90)
ax.set_yticks(y)
ax.set_zlabel('count')
plt.show()
Result:
The thickness of the bars are set by the dx, dy arguments in ax.bar3d for which you have the values 0.5, 0.001. The issue, as I'm sure you noticed is that changing dy will change the length of the bar (in your case the untitled axis), but matplotlib helpfully rescales the y axis so the data fills it. This makes it look strange (I am assuming this is the problem, sorry if it isn't).
To remedy this you could set the y limits using ax.set_ylim(0, 0.002) (basically your y values go from 0->0.001). If you change either dy or the value of y given to bar3d which is currently 0, then you will need to update the limits accordingly.
Example:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
row = [0, 0, 0, 22, 0, 0, 4, 16, 2, 0, 4, 4, 12, 26]
length = len(row)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.bar3d(range(length), [0]*length, [0]*length, 0.5, 0.001, row)
ax.set_ylim(-0.005, 0.005)
plt.show()