Python 蟒蛇画平行六面体
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python draw parallelepiped
提问by rogwar
I am trying to draw a parallelepiped. Actually I started from the python script drawing a cube as:
我想画一个平行六面体。实际上，我从绘制立方体的python脚本开始：
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
points = np.array([[-1, -1, -1],
[1, -1, -1 ],
[1, 1, -1],
[-1, 1, -1],
[-1, -1, 1],
[1, -1, 1 ],
[1, 1, 1],
[-1, 1, 1]])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
r = [-1,1]
X, Y = np.meshgrid(r, r)
ax.plot_surface(X,Y,1, alpha=0.5)
ax.plot_surface(X,Y,-1, alpha=0.5)
ax.plot_surface(X,-1,Y, alpha=0.5)
ax.plot_surface(X,1,Y, alpha=0.5)
ax.plot_surface(1,X,Y, alpha=0.5)
ax.plot_surface(-1,X,Y, alpha=0.5)
ax.scatter3D(points[:, 0], points[:, 1], points[:, 2])
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
In order to obtain a parallelepiped, I have multiplied the points matrix by the following matrix:
为了获得平行六面体，我将点矩阵乘以以下矩阵：
P =
[[2.06498904e-01 -6.30755443e-07 1.07477548e-03]
[1.61535574e-06 1.18897198e-01 7.85307721e-06]
[7.08353661e-02 4.48415767e-06 2.05395893e-01]]
as:
作为：
Z = np.zeros((8,3))
for i in range(8):
Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z
My idea is then to represent as follows:
我的想法是表示如下：
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
And this is what I get:
这就是我得到的：
How can I then put surfaces on these different points to form the parallelepiped (in the way of the cube above)?
我怎样才能把表面放在这些不同的点上以形成平行六面体（以上面的立方体的方式）？
回答by pcu
Plot surfaces with 3D PolyCollection (example)
使用 3D PolyCollection 绘制曲面（示例）
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
import matplotlib.pyplot as plt
points = np.array([[-1, -1, -1],
[1, -1, -1 ],
[1, 1, -1],
[-1, 1, -1],
[-1, -1, 1],
[1, -1, 1 ],
[1, 1, 1],
[-1, 1, 1]])
P = [[2.06498904e-01 , -6.30755443e-07 , 1.07477548e-03],
[1.61535574e-06 , 1.18897198e-01 , 7.85307721e-06],
[7.08353661e-02 , 4.48415767e-06 , 2.05395893e-01]]
Z = np.zeros((8,3))
for i in range(8): Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
r = [-1,1]
X, Y = np.meshgrid(r, r)
# plot vertices
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
# list of sides' polygons of figure
verts = [[Z[0],Z[1],Z[2],Z[3]],
[Z[4],Z[5],Z[6],Z[7]],
[Z[0],Z[1],Z[5],Z[4]],
[Z[2],Z[3],Z[7],Z[6]],
[Z[1],Z[2],Z[6],Z[5]],
[Z[4],Z[7],Z[3],Z[0]]]
# plot sides
ax.add_collection3d(Poly3DCollection(verts,
facecolors='cyan', linewidths=1, edgecolors='r', alpha=.25))
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
回答by SimonBiggs
Given that the title of this question is 'python draw 3D cube', this is the article I found when I googled that question.
鉴于此问题的标题是“python draw 3D cube”，这是我在 google 上搜索该问题时找到的文章。
For the purpose of those who do the same as me, who simply want to draw a cube, I have created the following function which takes four points of a cube, a corner first, and then the three adjacent points to that corner.
为了那些和我一样只是想画一个立方体的人的目的，我创建了以下函数，该函数取立方体的四个点，首先是一个角，然后是该角的三个相邻点。
It then plots the cube.
然后绘制立方体。
The function is below:
功能如下：
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
def plot_cube(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
points = []
points += cube_definition_array
vectors = [
cube_definition_array[1] - cube_definition_array[0],
cube_definition_array[2] - cube_definition_array[0],
cube_definition_array[3] - cube_definition_array[0]
]
points += [cube_definition_array[0] + vectors[0] + vectors[1]]
points += [cube_definition_array[0] + vectors[0] + vectors[2]]
points += [cube_definition_array[0] + vectors[1] + vectors[2]]
points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
points = np.array(points)
edges = [
[points[0], points[3], points[5], points[1]],
[points[1], points[5], points[7], points[4]],
[points[4], points[2], points[6], points[7]],
[points[2], points[6], points[3], points[0]],
[points[0], points[2], points[4], points[1]],
[points[3], points[6], points[7], points[5]]
]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
faces.set_facecolor((0,0,1,0.1))
ax.add_collection3d(faces)
# Plot the points themselves to force the scaling of the axes
ax.scatter(points[:,0], points[:,1], points[:,2], s=0)
ax.set_aspect('equal')
cube_definition = [
(0,0,0), (0,1,0), (1,0,0), (0,0,1)
]
plot_cube(cube_definition)
Giving the result:
给出结果：
回答by SimonBiggs
See my other answer (https://stackoverflow.com/a/49766400/3912576) for a simpler solution.
有关更简单的解决方案，请参阅我的其他答案（https://stackoverflow.com/a/49766400/3912576）。
Here is a more complicated set of functions which make matplotlib scale better and always forces the input to be a cube.
这是一组更复杂的函数，它们使 matplotlib 更好地缩放并始终强制输入为立方体。
The first parameter passed to cubify_cube_definition is the starting point, the second parameter is the second point, cube length is defined from this point, the third is a rotation point, it will be moved to match the length of the first and second.
传递给 cubify_cube_definition 的第一个参数是起点，第二个参数是第二个点，立方体长度从这个点开始定义，第三个是旋转点，它将被移动以匹配第一个和第二个的长度。
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
def cubify_cube_definition(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
start = cube_definition_array[0]
length_decider_vector = cube_definition_array[1] - cube_definition_array[0]
length = np.linalg.norm(length_decider_vector)
rotation_decider_vector = (cube_definition_array[2] - cube_definition_array[0])
rotation_decider_vector = rotation_decider_vector / np.linalg.norm(rotation_decider_vector) * length
orthogonal_vector = np.cross(length_decider_vector, rotation_decider_vector)
orthogonal_vector = orthogonal_vector / np.linalg.norm(orthogonal_vector) * length
orthogonal_length_decider_vector = np.cross(rotation_decider_vector, orthogonal_vector)
orthogonal_length_decider_vector = (
orthogonal_length_decider_vector / np.linalg.norm(orthogonal_length_decider_vector) * length)
final_points = [
tuple(start),
tuple(start + orthogonal_length_decider_vector),
tuple(start + rotation_decider_vector),
tuple(start + orthogonal_vector)
]
return final_points
def cube_vertices(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
points = []
points += cube_definition_array
vectors = [
cube_definition_array[1] - cube_definition_array[0],
cube_definition_array[2] - cube_definition_array[0],
cube_definition_array[3] - cube_definition_array[0]
]
points += [cube_definition_array[0] + vectors[0] + vectors[1]]
points += [cube_definition_array[0] + vectors[0] + vectors[2]]
points += [cube_definition_array[0] + vectors[1] + vectors[2]]
points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
points = np.array(points)
return points
def get_bounding_box(points):
x_min = np.min(points[:,0])
x_max = np.max(points[:,0])
y_min = np.min(points[:,1])
y_max = np.max(points[:,1])
z_min = np.min(points[:,2])
z_max = np.max(points[:,2])
max_range = np.array(
[x_max-x_min, y_max-y_min, z_max-z_min]).max() / 2.0
mid_x = (x_max+x_min) * 0.5
mid_y = (y_max+y_min) * 0.5
mid_z = (z_max+z_min) * 0.5
return [
[mid_x - max_range, mid_x + max_range],
[mid_y - max_range, mid_y + max_range],
[mid_z - max_range, mid_z + max_range]
]
def plot_cube(cube_definition):
points = cube_vertices(cube_definition)
edges = [
[points[0], points[3], points[5], points[1]],
[points[1], points[5], points[7], points[4]],
[points[4], points[2], points[6], points[7]],
[points[2], points[6], points[3], points[0]],
[points[0], points[2], points[4], points[1]],
[points[3], points[6], points[7], points[5]]
]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
faces.set_facecolor((0,0,1,0.1))
ax.add_collection3d(faces)
bounding_box = get_bounding_box(points)
ax.set_xlim(bounding_box[0])
ax.set_ylim(bounding_box[1])
ax.set_zlim(bounding_box[2])
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_aspect('equal')
cube_definition = cubify_cube_definition([(0,0,0), (0,3,0), (1,1,0.3)])
plot_cube(cube_definition)
Which produces the following result:
这产生以下结果：
回答by Preetham Dasari
Done using matplotlib and coordinate geometry
使用 matplotlib 和坐标几何完成
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def cube_coordinates(edge_len,step_size):
X = np.arange(0,edge_len+step_size,step_size)
Y = np.arange(0,edge_len+step_size,step_size)
Z = np.arange(0,edge_len+step_size,step_size)
temp=list()
for i in range(len(X)):
temp.append((X[i],0,0))
temp.append((0,Y[i],0))
temp.append((0,0,Z[i]))
temp.append((X[i],edge_len,0))
temp.append((edge_len,Y[i],0))
temp.append((0,edge_len,Z[i]))
temp.append((X[i],edge_len,edge_len))
temp.append((edge_len,Y[i],edge_len))
temp.append((edge_len,edge_len,Z[i]))
temp.append((edge_len,0,Z[i]))
temp.append((X[i],0,edge_len))
temp.append((0,Y[i],edge_len))
return temp
edge_len = 10
A=cube_coordinates(edge_len,0.01)
A=list(set(A))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
A=zip(*A)
X,Y,Z=list(A[0]),list(A[1]),list(A[2])
ax.scatter(X,Y,Z,c='g')
plt.show()
