Python Matplotlib - Plotting cuboids

Question

I'm trying to plot cuboids of different sizes using matplotlib, such that: after rotation the cuboids do not overlap visually in a non-physical way, the cubes have different colors and a box drawn around them.

I've read several blog posts and stackoverflow pages referencing similar problems, but always with a slight difference; none which have worked for me. The easiest way to overcome the overlapping problem was to use voxels (as in https://matplotlib.org/api/_as_gen/mpl_toolkits.mplot3d.axes3d.Axes3D.html?highlight=voxel#mpl_toolkits.mplot3d.axes3d.Axes3D.voxels), but these do not allow me to draw boxes around them. What's the easiest way to do this in matplotlib?

The image below shows what I have on the left, and what I want on the right.

EDIT: I've looked into several approaches that can give the desired effect, of which the main ones are:

• using voxels, but somehow scaling them such that a single voxel represents a single item.
• using surface plots, but then adjusting the drawing order dynamically to avoid non-physical overlapping.

The former seemed easier to execute, but I'm still stumped.

Answer 1

A. Using Poly3DCollection

An option is to create a Poly3DCollection of the faces of the cuboids. As the overlapping issue is not present for artists of the same collection, this might best serve the purpose here.

from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import numpy as np
import matplotlib.pyplot as plt

def cuboid_data2(o, size=(1,1,1)):
    X = [[[0, 1, 0], [0, 0, 0], [1, 0, 0], [1, 1, 0]],
         [[0, 0, 0], [0, 0, 1], [1, 0, 1], [1, 0, 0]],
         [[1, 0, 1], [1, 0, 0], [1, 1, 0], [1, 1, 1]],
         [[0, 0, 1], [0, 0, 0], [0, 1, 0], [0, 1, 1]],
         [[0, 1, 0], [0, 1, 1], [1, 1, 1], [1, 1, 0]],
         [[0, 1, 1], [0, 0, 1], [1, 0, 1], [1, 1, 1]]]
    X = np.array(X).astype(float)
    for i in range(3):
        X[:,:,i] *= size[i]
    X += np.array(o)
    return X

def plotCubeAt2(positions,sizes=None,colors=None, **kwargs):
    if not isinstance(colors,(list,np.ndarray)): colors=["C0"]*len(positions)
    if not isinstance(sizes,(list,np.ndarray)): sizes=[(1,1,1)]*len(positions)
    g = []
    for p,s,c in zip(positions,sizes,colors):
        g.append( cuboid_data2(p, size=s) )
    return Poly3DCollection(np.concatenate(g),  
                            facecolors=np.repeat(colors,6), **kwargs)
    

positions = [(-3,5,-2),(1,7,1)]
sizes = [(4,5,3), (3,3,7)]
colors = ["crimson","limegreen"]

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')

pc = plotCubeAt2(positions,sizes,colors=colors, edgecolor="k")
ax.add_collection3d(pc)    

ax.set_xlim([-4,6])
ax.set_ylim([4,13])
ax.set_zlim([-3,9])

plt.show()

B. Using plot_surface

Adapting the solution from this question, which uses plot_surface, and allow for different sizes as desired here seems to work just fine for most cases:

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

def cuboid_data(o, size=(1,1,1)):
    # code taken from
    # https://stackoverflow.com/a/35978146/4124317
    # suppose axis direction: x: to left; y: to inside; z: to upper
    # get the length, width, and height
    l, w, h = size
    x = [[o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  
         [o[0], o[0] + l, o[0] + l, o[0], o[0]]]  
    y = [[o[1], o[1], o[1] + w, o[1] + w, o[1]],  
         [o[1], o[1], o[1] + w, o[1] + w, o[1]],  
         [o[1], o[1], o[1], o[1], o[1]],          
         [o[1] + w, o[1] + w, o[1] + w, o[1] + w, o[1] + w]]   
    z = [[o[2], o[2], o[2], o[2], o[2]],                       
         [o[2] + h, o[2] + h, o[2] + h, o[2] + h, o[2] + h],   
         [o[2], o[2], o[2] + h, o[2] + h, o[2]],               
         [o[2], o[2], o[2] + h, o[2] + h, o[2]]]               
    return np.array(x), np.array(y), np.array(z)

def plotCubeAt(pos=(0,0,0), size=(1,1,1), ax=None,**kwargs):
    # Plotting a cube element at position pos
    if ax !=None:
        X, Y, Z = cuboid_data( pos, size )
        ax.plot_surface(X, Y, Z, rstride=1, cstride=1, **kwargs)

positions = [(-3,5,-2),(1,7,1)]
sizes = [(4,5,3), (3,3,7)]
colors = ["crimson","limegreen"]


fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')

for p,s,c in zip(positions,sizes,colors):
    plotCubeAt(pos=p, size=s, ax=ax, color=c)

plt.show()

Answer 2

The following code will not only work for cuboid but for any polygon

Type your coordinates for x, y and z respectively

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

#input values
x=[1,10,50,100,150]
y=[1,300,350,250,50]
z=[0,1]
def edgecoord(pointx,pointy,pointz):
    edgex=[pointx[0],pointx[1],pointx[1],pointx[0]]
    edgey=[pointy[0],pointy[1],pointy[1],pointy[0]]
    edgez=[pointz[0],pointz[0],pointz[1],pointz[1]]
    return list(zip(edgex,edgey,edgez))

def coordConvert(x,y,lheight,uheight):
    if len(x) != len(y) and len(x)>2:
        return
    vertices=[]
    #Top layer
    vertices.append(list(zip(x,y,list(np.full(len(x),uheight)))))
    # Side layers
    for it in np.arange(len(x)):
        it1=it+1
        if it1>=len(x):
            it1=0
        vertices.append(edgecoord([x[it],x[it1]],[y[it],y[it1]],[lheight,uheight]))
    #Bottom layer
    vertices.append(list(zip(x,y,list(np.full(len(x),lheight)))))
    print(np.array(vertices))
    return vertices

vec=coordConvert(x,y,z[0],z[1])

plt.figure()
plt.subplot(111,projection='3d')
plt.gca().add_collection3d(Poly3DCollection(vec, alpha=.75,edgecolor='k', facecolor='teal'))
plt.xlim([0,200])
plt.ylim([0,400])
plt.show()

Polygon Prism